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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# HA 04 und 04 Schmidt "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "## 0 Initialization and Helper Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pathlib # for handling file system\n",
+ "import random\n",
+ "import time \n",
+ "import copy # for copy objects \n",
+ "import itertools # use products for iterations\n",
+ "\n",
+ "from matplotlib import pyplot as plt\n",
+ "from matplotlib import animation as animation\n",
+ "from matplotlib.colors import ListedColormap\n",
+ "\n",
+ "from IPython.display import HTML\n",
+ "\n",
+ "from collections import deque # properties of a linked list to left and right\n",
+ "from queue import Queue, PriorityQueue\n",
+ "import numpy as np\n",
+ "import pandas as pd"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def plot_puzzle_config(ax, config):\n",
+ " \"\"\"Visualise a given configuration of the 8-puzzle.\"\"\"\n",
+ " cmap = ListedColormap([\"lightgray\", \"lightblue\"])\n",
+ " ax.matshow(config == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " for row in range(3):\n",
+ " for col in range(3):\n",
+ " value = config[row, col]\n",
+ " ax.text(col, row, str(value), \n",
+ " va=\"center\", ha=\"center\", \n",
+ " font={'weight': 'bold' if value == 0 else 'normal'})"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def animate_moves(solution_path, output_path = None, delay = 2000, video_inplace = True, filename = \"8puzzle_steps.mp4\"):\n",
+ " \"\"\"Given a initial configuration of the 8 puzzle animate all movesments that lead to the target configuration.\"\"\"\n",
+ "\n",
+ " def add_text(ax, config):\n",
+ " for row in range(3):\n",
+ " for col in range(3):\n",
+ " value: np.unit8 = config[row, col]\n",
+ " ax.text(col, row, str(value), \n",
+ " va=\"center\", ha=\"center\", \n",
+ " font={'weight': 'bold' if value == 0 else 'normal'})\n",
+ "\n",
+ " def animate(img, ax, config):\n",
+ " ax.clear()\n",
+ " img = ax.matshow(root.state == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " img.set_array(config == 0)\n",
+ " add_text(ax, config)\n",
+ " return (ax,)\n",
+ "\n",
+ " fig, ax = plt.subplots()\n",
+ "\n",
+ " cmap = ListedColormap([\"lightgray\", \"lightblue\"])\n",
+ " root = solution_path[0]\n",
+ " img_mat = ax.matshow(root.state == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " add_text(ax, root.state)\n",
+ "\n",
+ " anim = animation.FuncAnimation(\n",
+ " fig, lambda p: animate(img_mat, ax, p.state), solution_path, interval=delay\n",
+ " )\n",
+ " plt.close(fig)\n",
+ " \n",
+ " if not video_inplace and output_path is not None:\n",
+ " output_path.mkdir(parents=True, exist_ok=True)\n",
+ " anim.save(output_path / filename ) \n",
+ " return anim"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class Node:\n",
+ " \"\"\"Base class that implements commonly-used methods for the tree search algorithms\"\"\"\n",
+ " \n",
+ " def __init__(self, state):\n",
+ " \"\"\"Initialiser of the base class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State array representing a certain digit arrangement of the 8 puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Sets attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.state = state\n",
+ " self.empty_pos = self._get_empty_pos()\n",
+ " self.hash_value = hash(repr(self))\n",
+ "\n",
+ "\n",
+ " def _get_empty_pos(self):\n",
+ " \"\"\"Locate the position of the empty spot in the puzzle\"\"\"\n",
+ " row, col = np.where(self.state == 0)\n",
+ " return row[0], col[0]\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"Node({self.state})\"\n",
+ " \n",
+ " def __hash__(self):\n",
+ " return self.hash_value\n",
+ "\n",
+ " def __eq__(self, rhs): \n",
+ " return self.hash_value == rhs.hash_value\n",
+ "\n",
+ " def __ne__(self, rhs):\n",
+ " return not (self == rhs)\n",
+ " \n",
+ " def _next_positions(self):\n",
+ " \"\"\"Given a tuple of the current position of the 0 yield tuples of possible next positions.\n",
+ " \n",
+ " Parameters:\n",
+ " No parameters.\n",
+ " \n",
+ " Returns:\n",
+ " Generator[Tuple[int, int], None, None]. (See: https://docs.python.org/3/library/typing.html#typing.Generator)\n",
+ " When calling `next` on this generator a tuple with ints is returned which represents the \n",
+ " next position of the 0 in the array.\n",
+ " \"\"\"\n",
+ " # Values for the indices should be in the range 0 <= x < 2\n",
+ " idx0, idx1 = self.empty_pos\n",
+ " assert idx0 in range(3), \"idx0 must be in range(3)\"\n",
+ " assert idx1 in range(3), \"idx1 must be in range(3)\"\n",
+ "\n",
+ " # Can we move up?\n",
+ " if idx0 > 0:\n",
+ " yield (idx0 - 1, idx1)\n",
+ " # Can we move left?\n",
+ " if idx1 > 0:\n",
+ " yield (idx0, idx1 - 1)\n",
+ " # Can we move down?\n",
+ " if idx0 < 2:\n",
+ " yield (idx0 + 1, idx1)\n",
+ " # Can we move right?\n",
+ " if idx1 < 2:\n",
+ " yield (idx0, idx1 + 1)\n",
+ "\n",
+ " def _make_new_state(self, empty_pos_new):\n",
+ " \"\"\"Move the empty spot in the puzzle and thus make a new state but leave the state as is\n",
+ " \n",
+ " Parameters:\n",
+ " empty_pos_new: tuple\n",
+ " Pair of integer values that represent the next position of the empty spot of the puzzle.\n",
+ " buffer: np.ndarray\n",
+ " State array that will hold the new state of the puzzle after having moved the empty spot.\n",
+ " Output:\n",
+ " buffer, which is the new state.\n",
+ " \"\"\"\n",
+ " buffer = self.state.copy() # very important to leave the state unchanged\n",
+ " buffer[empty_pos_new] = self.state[self.empty_pos]\n",
+ " buffer[self.empty_pos] = self.state[empty_pos_new]\n",
+ "\n",
+ " return buffer \n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeRandom(Node):\n",
+ " \n",
+ " def randomise_state(self, num_moves):\n",
+ " \"\"\"Randomly change the current state of the puzzle\n",
+ " \n",
+ " Parameters:\n",
+ " num_moves: int\n",
+ " Number of times to randomly change the state of the puzzle.\n",
+ " \n",
+ " Output: Node\n",
+ " The (modified) version of the class instance. If `num_moves == 0` the instance of the class is returned unchanged. \n",
+ " \"\"\"\n",
+ " if num_moves > 0:\n",
+ " for _ in range(num_moves):\n",
+ " pos_new_random = random.choice(tuple(self._next_positions()))\n",
+ " self.state[:, :] = self._make_new_state(pos_new_random)\n",
+ " self.empty_pos = pos_new_random\n",
+ " \n",
+ " self.hash_value = hash(repr(self)) \n",
+ " return self\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeBFS(Node):\n",
+ " \"\"\"Node for the BFS tree search algorithm\"\"\"\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return f\"NodeBFS({self.state})\"\n",
+ "\n",
+ " \n",
+ " def next_nodes(self):\n",
+ " \"\"\"Generate other state nodes that from the current node.\n",
+ " \n",
+ " Parameters:\n",
+ " No parameters.\n",
+ " \n",
+ " Output:\n",
+ " Generator[NodeBFS, None, None]. \n",
+ " Yields a node representing a state of the the puzzle that can be generated through\n",
+ " a single move of the empty spot in the current state.\n",
+ " \"\"\"\n",
+ " for pos_new in self._next_positions():\n",
+ " yield type(self)(self._make_new_state(pos_new))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def reconstruct_path(to_node, parent):\n",
+ " \"\"\"Reconstruct all nodes on the path root_node --> to_node.\n",
+ "\n",
+ " Parameters:\n",
+ " to_node: Node\n",
+ " Node at the end of the path.\n",
+ " parent: dict\n",
+ " Child - parent relationship between nodes in the search tree.\n",
+ " \n",
+ " Output:\n",
+ " path: deque\n",
+ " List with all the nodes along the path root_node --> to_node.\n",
+ " \"\"\"\n",
+ " path = deque()\n",
+ " current = to_node\n",
+ " while current is not None:\n",
+ " path.appendleft(current)\n",
+ " current = parent[current]\n",
+ " return path\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def find_target_bfs(initial, final):\n",
+ " \"\"\"Find a solutions of the 8-puzzle when given an initial configuration by using the BFS algorithm.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: NodeBFS\n",
+ " Initial state of the 8-puzzle.\n",
+ " final: NodeBFS\n",
+ " Final state of the 8-puzzle.\n",
+ "\n",
+ " Output:\n",
+ " n: number of visited nodes\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " q = Queue() # FIFO queue\n",
+ " q.put(initial)\n",
+ " parent = {initial: None} # dictionary \n",
+ " \n",
+ " n = 1 # Counter for number of nodes that have been put into the queue.\n",
+ "\n",
+ " if initial == final:\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ " \n",
+ " \n",
+ " while not q.empty():\n",
+ " node = q.get()\n",
+ " for child in node.next_nodes():\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " q.put(child)\n",
+ " parent[child] = node \n",
+ " if child == final:\n",
+ " return n, reconstruct_path(child, parent)\n",
+ "\n",
+ " \n",
+ " return -1, []"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def state_difference(state, final_state):\n",
+ " \"\"\"Compute the difference of two states of the 8 puzzle.\n",
+ "\n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State of the 8 puzzle for which to compute the distance to the final state.\n",
+ " final_state: np.ndarray\n",
+ " Solved state of the 8 puzzle.\n",
+ " \n",
+ " Output:\n",
+ " int: The difference of the two states. The difference is computed by the number digits in state\n",
+ " that are *not* in the same position in final_state.\n",
+ " \"\"\"\n",
+ " return np.sum((state != 0) & (state != final_state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeGreedy(Node): \n",
+ " def __init__(self, state, estimated_cost):\n",
+ " \"\"\"Initialiser of the class\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is\n",
+ " forwarded to the base class.\n",
+ " estimated_cost: int\n",
+ " An estimate of the cost of getting from the current state to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.estimated_cost = estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeGreedy({self.state}, {self.estimated_cost})\"\n",
+ "\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller estimated cost to reach the final state as the other node else False.\n",
+ " \n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.estimated_cost < rhs.estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, cost_estimator: callable):\n",
+ " \"\"\"Generate other state nodes from the current node.\n",
+ " \n",
+ " Parameters:\n",
+ " final: NodeGreedy\n",
+ " A node representing the solved state of the puzzle.\n",
+ " estimator: callable\n",
+ " Cost function to estimated the cost from getting the generated state to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " Generator[NodeGreedy, None, None]. \n",
+ " Yields a node representing a state of the puzzle that can be generated through \n",
+ " a single move of the empty spot in the current state.\n",
+ " \"\"\"\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), cost_estimator(buffer, \n",
+ " final.state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def informed_search(initial, final, cost_estimator: callable):\n",
+ " \"\"\"Find path from initial to final node.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: Node[Greedy, Astar]\n",
+ " Node representing the initial state of the 8 puzzle.\n",
+ " final: Node[Greedy, Astar]\n",
+ " Node representing the solved state of the 8 puzzle.\n",
+ " cost_estimator: callable\n",
+ " Function to estimate the cost to get from some node to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " pq = PriorityQueue()\n",
+ " pq.put(initial)\n",
+ " parent = {initial: None} # dictionary\n",
+ " \n",
+ " n = 1 # Counter for the number of nodes that have been put into the queue.\n",
+ "\n",
+ " if np.array_equal(initial.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ "\n",
+ " \n",
+ " while not pq.empty():\n",
+ " current = pq.get()\n",
+ " for child in current.next_nodes(final, cost_estimator):\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " pq.put(child)\n",
+ " parent[child] = current\n",
+ " if np.array_equal(child.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(child, parent)\n",
+ " \n",
+ " return -1, []"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeAstar(Node):\n",
+ " def __init__(self, state, accumulated_cost, estimated_cost):\n",
+ " \"\"\"Initialiser of the class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray \n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is \n",
+ " forwarded to the base class.\n",
+ " accumulated_cost: int\n",
+ " Number of steps executed so far.\n",
+ " estimated_cost: int>\n",
+ " Estimated cost for getting from the current state to the solved state of the puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.accumulated_cost, self.estimated_cost = accumulated_cost, \\\n",
+ " estimated_cost\n",
+ " self.total_estimated_cost = accumulated_cost + estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeAstar({self.state}, {self.accumulated_cost}, \\\n",
+ " {self.estimated_cost})\"\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller *total estimated cost* to reach the final state as the other node else False.\n",
+ " >\n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.total_estimated_cost < rhs.total_estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, estimator):\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), self.accumulated_cost + 1, \n",
+ " estimator(buffer, final.state))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Meine Bearbeitung"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Summe der euklidischen/manhatten Abstände ist keine zulässige Heuristik. Auch hier muss die 0 ausgeschlossen werden."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import math as m\n",
+ "\n",
+ "def manhatten_distance(state, final_state):\n",
+ " \"\"\"Compute the manhattan distance between two arrays of identical shape\"\"\"\n",
+ " distance = 0\n",
+ " for i, row in enumerate(state):\n",
+ " for j, value in enumerate(row):\n",
+ " if value != 0:\n",
+ " x, y = np.where(final_state == value)\n",
+ " distance += abs(x[0]-i) + abs(y[0]-j)\n",
+ " #print(f\"Distance for value {value} is {abs(x[0]-i) + abs(y[0]-j)}\")\n",
+ " return distance\n",
+ "\n",
+ "def euclidian_distance(state, final_state):\n",
+ " \"\"\"Compute the euclidian distance between two arrays of identical shape\"\"\"\n",
+ " distance = 0\n",
+ " for i, row in enumerate(state):\n",
+ " for j, value in enumerate(row):\n",
+ " if value != 0:\n",
+ " x, y = np.where(final_state == value)\n",
+ " distance += m.sqrt(pow((x[0]-i), 2) + pow((y[0]-j),2))\n",
+ " #print(f\"Distance for value {value} is {m.sqrt(pow((x[0]-i), 2) + pow((y[0]-j),2))}\")\n",
+ " return distance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ARRAY_INITIAL = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ " \n",
+ "ARRAY_FINAl = np.array(((1, 3, 6),\n",
+ " (8, 0, 2),\n",
+ " (7, 4, 5)), dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Anzahl falscher Positionen: 7 \n",
+ " Manhattan Abstand: 14 \n",
+ " Euklidischer Abstand: 11.30056307974577\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(f\"Anzahl falscher Positionen: {state_difference(ARRAY_INITIAL, ARRAY_FINAl)} \\n \\\n",
+ " Manhattan Abstand: {manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl)} \\n \\\n",
+ " Euklidischer Abstand: {euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl)}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "###### Greedy Suche mit Anzahl falscher Positionen\n",
+ " Besuchte Knoten: 490 \n",
+ " Länge des Pfades: 27\n",
+ "###### Greedy Suche mit Manhattan-Abstand\n",
+ " Besuchte Knoten: 83 \n",
+ " Länge des Pfades: 33\n",
+ "###### Greedy Suche mit Euklidischem-Abstand\n",
+ " Besuchte Knoten: 333 \n",
+ " Länge des Pfades: 41\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "###### Astar Suche mit Anzahl falscher Positionen\n",
+ " Besuchte Knoten: 1048 \n",
+ " Länge des Pfades: 17\n",
+ "###### Astar Suche mit Manhattan-Abstand\n",
+ " Besuchte Knoten: 107 \n",
+ " Länge des Pfades: 17\n",
+ "###### Astar Suche mit Euklidischem-Abstand\n",
+ " Besuchte Knoten: 143 \n",
+ " Länge des Pfades: 17\n"
+ ]
+ }
+ ],
+ "source": [
+ "manhattan_greedy_start = NodeGreedy(ARRAY_INITIAL, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "euclidian_greedy_start = NodeGreedy(ARRAY_INITIAL, euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "eucilidan_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "difference_greedy_start = NodeGreedy(ARRAY_INITIAL, state_difference(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "difference_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "difference_greedy_n, difference_greedy_path = informed_search(difference_greedy_start, difference_greedy_final, state_difference)\n",
+ "print(f\"###### Greedy Suche mit Anzahl falscher Positionen\\n \\\n",
+ "Besuchte Knoten: {difference_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(difference_greedy_path)}\")\n",
+ "manhatten_greedy_n, manhattan_greedy_path = informed_search(manhattan_greedy_start, manhattan_greedy_final, manhatten_distance)\n",
+ "print(f\"###### Greedy Suche mit Manhattan-Abstand\\n \\\n",
+ "Besuchte Knoten: {manhatten_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(manhattan_greedy_path)}\")\n",
+ "euclidian_greedy_n, euclidian_greedy_path = informed_search(euclidian_greedy_start, eucilidan_greedy_final, euclidian_distance)\n",
+ "print(f\"###### Greedy Suche mit Euklidischem-Abstand\\n \\\n",
+ "Besuchte Knoten: {euclidian_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(euclidian_greedy_path)}\")\n",
+ "\n",
+ "manhattan_Astar_start = NodeAstar(ARRAY_INITIAL, 0, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "euclidian_Astar_start = NodeAstar(ARRAY_INITIAL, 0, euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "eucilidan_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "difference_Astar_start = NodeAstar(ARRAY_INITIAL, 0, state_difference(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "difference_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "difference_Astar_n, difference_Astar_path = informed_search(difference_Astar_start, difference_Astar_final, state_difference)\n",
+ "print(f\"###### Astar Suche mit Anzahl falscher Positionen\\n \\\n",
+ "Besuchte Knoten: {difference_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(difference_Astar_path)}\")\n",
+ "manhatten_Astar_n, manhattan_Astar_path = informed_search(manhattan_Astar_start, manhattan_Astar_final, manhatten_distance)\n",
+ "print(f\"###### Astar Suche mit Manhattan-Abstand\\n \\\n",
+ "Besuchte Knoten: {manhatten_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(manhattan_Astar_path)}\")\n",
+ "euclidian_Astar_n, euclidian_Astar_path = informed_search(euclidian_Astar_start, eucilidan_Astar_final, euclidian_distance)\n",
+ "print(f\"###### Astar Suche mit Euklidischem-Abstand\\n \\\n",
+ "Besuchte Knoten: {euclidian_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(euclidian_Astar_path)}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Tiefe: 2 - Anzahl Anfangszustände: 12\n",
+ "Tiefe: 4 - Anzahl Anfangszustände: 32\n",
+ "Tiefe: 6 - Anzahl Anfangszustände: 98\n",
+ "Tiefe: 8 - Anzahl Anfangszustände: 201\n",
+ "Tiefe: 10 - Anzahl Anfangszustände: 344\n",
+ "Tiefe: 12 - Anzahl Anfangszustände: 386\n",
+ "Tiefe: 14 - Anzahl Anfangszustände: 384\n",
+ "Tiefe: 16 - Anzahl Anfangszustände: 273\n",
+ "Tiefe: 18 - Anzahl Anfangszustände: 166\n",
+ "Tiefe: 20 - Anzahl Anfangszustände: 73\n"
+ ]
+ }
+ ],
+ "source": [
+ "import time\n",
+ "time.perf_counter_ns()\n",
+ "import yaml\n",
+ "with open(\"initial_states.yaml\", \"r\") as f:\n",
+ " intial_states = yaml.safe_load(f)\n",
+ "for d, states in intial_states.items():\n",
+ " print(f\"Tiefe: {d:3d} - Anzahl Anfangszustände: {len(states):4d}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def time_algorithm(intial_states, node_type_names, heuristics, heuristic_names):\n",
+ " algorithm = []\n",
+ " used_heuristic = []\n",
+ " depth = []\n",
+ " runtime = []\n",
+ " visited_node = []\n",
+ " path_length = []\n",
+ " for node_type_name in node_type_names:\n",
+ " print(f\"Beginning measurement of {node_type_name}...\")\n",
+ " if node_type_name == \"BFS\":\n",
+ " heuristic_helper = [(None, \"Keine\")]\n",
+ " else:\n",
+ " heuristic_helper = zip(heuristics, heuristic_names)\n",
+ " for heuristic, heuristic_name in heuristic_helper:\n",
+ " print(f\"For heuristic: {heuristic_name} ...\")\n",
+ " for current_depth, problems in intial_states.items():\n",
+ " print(f\"In depth: {current_depth} ...\")\n",
+ " for problem in problems:\n",
+ " start_array = np.asarray(problem[0], dtype=int)\n",
+ " final_array = np.asarray(problem[1], dtype=int)\n",
+ " if node_type_name == \"BFS\":\n",
+ " start = NodeBFS(start_array)\n",
+ " final = NodeBFS(final_array)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = find_target_bfs(start, final)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " if node_type_name == \"Greedy\":\n",
+ " start = NodeGreedy(start_array, heuristic(start_array, final_array))\n",
+ " final = NodeGreedy(final_array, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(start, final, heuristic)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " if node_type_name == \"A*\":\n",
+ " start = NodeAstar(start_array, 0, heuristic(start_array, final_array))\n",
+ " final = NodeAstar(final_array, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(start, final, heuristic)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " algorithm.append(node_type_name)\n",
+ " used_heuristic.append(heuristic_name)\n",
+ " depth.append(current_depth)\n",
+ " runtime.append(final_time - start_time)\n",
+ " visited_node.append(n)\n",
+ " path_length.append(len(path))\n",
+ " print(f\"Finished depth: {current_depth}.\")\n",
+ " print(f\"Finished heuristic: {heuristic_name}.\")\n",
+ " print(f\"Finished {node_type_name}.\")\n",
+ " return algorithm, used_heuristic, depth, visited_node, path_length, runtime\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Beginning measurement of BFS...\n",
+ "For heuristic: Keine ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Keine.\n",
+ "Finished BFS.\n",
+ "Beginning measurement of Greedy...\n",
+ "For heuristic: Difference ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Difference.\n",
+ "For heuristic: Euklidisch ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Euklidisch.\n",
+ "For heuristic: Manhattan ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Manhattan.\n",
+ "Finished Greedy.\n",
+ "Beginning measurement of A*...\n",
+ "For heuristic: Difference ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Difference.\n",
+ "For heuristic: Euklidisch ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Euklidisch.\n",
+ "For heuristic: Manhattan ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Manhattan.\n",
+ "Finished A*.\n"
+ ]
+ }
+ ],
+ "source": [
+ "node_type_names = [\"BFS\", \"Greedy\", \"A*\"]\n",
+ "heuristics = [state_difference, manhatten_distance, euclidian_distance]\n",
+ "heuristic_names = [\"Difference\", \"Euklidisch\", \"Manhattan\"]\n",
+ "\n",
+ "algorithm, used_heuristic, depth, visited_node, path_length, runtime = time_algorithm(intial_states, node_type_names, heuristics, heuristic_names)\n",
+ "\n",
+ "\n",
+ "\n",
+ "results = pd.DataFrame({\n",
+ " \"Algorithmus\": algorithm,\n",
+ " \"Heuristik\": used_heuristic,\n",
+ " \"Tiefe\": depth,\n",
+ " \"Besuchte Knoten\": visited_node,\n",
+ " \"Pfadlaenge\": path_length,\n",
+ " \"Zeit\": runtime,\n",
+ "})\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "mask1 = results[\"Heuristik\"] == \"Euklidisch\"\n",
+ "mask2 = results[\"Heuristik\"] == \"Manhattan\"\n",
+ "\n",
+ "results.loc[mask1, \"Heuristik\"] = \"Manhattan\"\n",
+ "results.loc[mask2, \"Heuristik\"] = \"Euklidisch\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "<class 'pandas.core.frame.DataFrame'>\n",
+ "RangeIndex: 13783 entries, 0 to 13782\n",
+ "Data columns (total 6 columns):\n",
+ " # Column Non-Null Count Dtype \n",
+ "--- ------ -------------- ----- \n",
+ " 0 Algorithmus 13783 non-null object\n",
+ " 1 Heuristik 13783 non-null object\n",
+ " 2 Tiefe 13783 non-null int64 \n",
+ " 3 Besuchte Knoten 13783 non-null int64 \n",
+ " 4 Pfadlaenge 13783 non-null int64 \n",
+ " 5 Zeit 13783 non-null int64 \n",
+ "dtypes: int64(4), object(2)\n",
+ "memory usage: 646.2+ KB\n"
+ ]
+ }
+ ],
+ "source": [
+ "results = pd.read_csv(\"results.csv\").iloc[:, 1:]\n",
+ "results.info()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<Axes: xlabel='Tiefe', ylabel='Pfadlänge'>"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "(\n",
+ " results\n",
+ " .pipe(lambda adf: adf[adf[\"Algorithmus\"] != \"A*\"])\n",
+ " .pivot_table(\n",
+ " values = 'Pfadlaenge',\n",
+ " columns = ['Algorithmus', 'Heuristik'],\n",
+ " index = 'Tiefe',\n",
+ " aggfunc = 'mean'\n",
+ " )\n",
+ " .plot(logy=False, ylabel=\"Pfadlänge\", xticks=(2,4,6,8,10,12,14,16,18,20))\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 130,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array(['BFS', 'Greedy', 'A*'], dtype=object)"
+ ]
+ },
+ "execution_count": 130,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "results[\"Algorithmus\"].unique()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 135,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import scipy\n",
+ "import scipy.optimize\n",
+ "\n",
+ "def func_tiefe(x, b, c):\n",
+ " return (b ** x) * c\n",
+ "\n",
+ "def func_knoten(x, b, c):\n",
+ " return (b * x) + c\n",
+ "\n",
+ "def mittleres_Skalengesetz(algorithmus, heuristik, x_column):\n",
+ " x = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [x_column]\n",
+ " )\n",
+ " y = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Zeit\"]\n",
+ " )\n",
+ "\n",
+ " if x_column == \"Tiefe\":\n",
+ " func = func_tiefe\n",
+ " func_x = np.arange(0,22,0.5)\n",
+ " if x_column == \"Besuchte Knoten\":\n",
+ " func = func_knoten\n",
+ " func_x = np.arange(0,max(x)+100,100)\n",
+ " \n",
+ " (b, c), _ = scipy.optimize.curve_fit(func, x, y)\n",
+ "\n",
+ " print(f\"B: {b}\")\n",
+ " print(f\"C: {c}\")\n",
+ "\n",
+ " func_y = func(func_x, b, c)\n",
+ "\n",
+ "\n",
+ " fig, ax = plt.subplots()\n",
+ " ax.set_title(f\"Mittleres Skalengesetz für {algorithmus} mit {heuristik} Heuristik\")\n",
+ " ax.set_ylabel(\"Zeit in Nanosekunden\")\n",
+ " ax.set_xlabel(x_column)\n",
+ " ax.scatter(x,y)\n",
+ " ax.plot(func_x, func_y, color='orange')\n",
+ " return fig"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 148,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "B: 1.4180160045233512\n",
+ "C: 126997.29495831158\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "execution_count": 148,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "mittleres_Skalengesetz(\"A*\", \"Manhattan\", \"Tiefe\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 157,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def func_tiefe_und_knoten(xdata, b, c):\n",
+ " tiefe = xdata[0]\n",
+ " knoten = xdata[1]\n",
+ " return (b ** tiefe) * knoten * c\n",
+ "\n",
+ "def mittleres_Skalengesetz_2(algorithmus, heuristik):\n",
+ " tiefen = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Tiefe\"]\n",
+ " )\n",
+ " knoten = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Besuchte Knoten\"]\n",
+ " )\n",
+ " y = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Zeit\"]\n",
+ " )\n",
+ " \n",
+ " xdata = np.array([tiefen, knoten])\n",
+ " print(xdata.shape)\n",
+ "\n",
+ " (b, c), _ = scipy.optimize.curve_fit(func_tiefe_und_knoten, xdata, y)\n",
+ "\n",
+ " print(f\"Zusammenhang für {algorithmus} mit {heuristik} Heuristik:\")\n",
+ " print(f\"B: {b}\")\n",
+ " print(f\"C: {c}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 163,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(2, 1969)\n",
+ "Zusammenhang für A* mit Manhattan Heuristik:\n",
+ "B: 1.0123224209580304\n",
+ "C: 92500.85226522778\n"
+ ]
+ }
+ ],
+ "source": [
+ "mittleres_Skalengesetz_2(\"A*\", \"Manhattan\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Tiefe: 2 - Anzahl Anfangszustände: 12\n",
+ "Tiefe: 4 - Anzahl Anfangszustände: 32\n",
+ "Tiefe: 6 - Anzahl Anfangszustände: 98\n",
+ "Tiefe: 8 - Anzahl Anfangszustände: 201\n",
+ "Tiefe: 10 - Anzahl Anfangszustände: 344\n",
+ "Tiefe: 12 - Anzahl Anfangszustände: 386\n",
+ "Tiefe: 14 - Anzahl Anfangszustände: 384\n",
+ "Tiefe: 16 - Anzahl Anfangszustände: 273\n",
+ "Tiefe: 18 - Anzahl Anfangszustände: 166\n",
+ "Tiefe: 20 - Anzahl Anfangszustände: 73\n"
+ ]
+ }
+ ],
+ "source": [
+ "import yaml\n",
+ "with open(\"initial_states.yaml\", \"r\") as f:\n",
+ " intial_states = yaml.safe_load(f)\n",
+ "for d, states in intial_states.items():\n",
+ " print(f\"Tiefe: {d:3d} - Anzahl Anfangszustände: {len(states):4d}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeAstar_2(Node):\n",
+ " def __init__(self, state, accumulated_cost, estimated_cost):\n",
+ " \"\"\"Initialiser of the class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray \n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is \n",
+ " forwarded to the base class.\n",
+ " accumulated_cost: int\n",
+ " Number of steps executed so far.\n",
+ " estimated_cost: int>\n",
+ " Estimated cost for getting from the current state to the solved state of the puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.accumulated_cost, self.estimated_cost = accumulated_cost, \\\n",
+ " estimated_cost\n",
+ " self.total_estimated_cost = accumulated_cost + estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeAstar({self.state}, {self.accumulated_cost}, \\\n",
+ " {self.estimated_cost})\"\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller *total estimated cost* to reach the final state as the other node else False.\n",
+ " >\n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.total_estimated_cost < rhs.total_estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, estimator, w):\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), self.accumulated_cost + (8 * w), \n",
+ " (9 - (w ** 2)) * estimator(buffer, final.state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def informed_search_2(initial, final, cost_estimator: callable, w):\n",
+ " \"\"\"Find path from initial to final node.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: Node[Greedy, Astar]\n",
+ " Node representing the initial state of the 8 puzzle.\n",
+ " final: Node[Greedy, Astar]\n",
+ " Node representing the solved state of the 8 puzzle.\n",
+ " cost_estimator: callable\n",
+ " Function to estimate the cost to get from some node to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " pq = PriorityQueue()\n",
+ " pq.put(initial)\n",
+ " parent = {initial: None} # dictionary\n",
+ " \n",
+ " n = 1 # Counter for the number of nodes that have been put into the queue.\n",
+ "\n",
+ " if np.array_equal(initial.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ "\n",
+ " \n",
+ " while not pq.empty():\n",
+ " current = pq.get()\n",
+ " for child in current.next_nodes(final, cost_estimator, w):\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " pq.put(child)\n",
+ " parent[child] = current\n",
+ " if np.array_equal(child.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(child, parent)\n",
+ " \n",
+ " raise \"problem not solveable\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 166,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ARRAY_INITIAL = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ " \n",
+ "ARRAY_FINAl = np.array(((1, 3, 6),\n",
+ " (8, 0, 2),\n",
+ " (7, 4, 5)), dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 174,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "107"
+ ]
+ },
+ "execution_count": 174,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "manhattan_Astar_2_start = NodeAstar_2(ARRAY_INITIAL, 0, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_Astar_2_final = NodeAstar_2(ARRAY_FINAl, -1, 0)\n",
+ "\n",
+ "n, path = informed_search_2(manhattan_Astar_2_start, manhattan_Astar_2_final, manhatten_distance, w = 1)\n",
+ "n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Starting to solve with w: 0.0\n",
+ "Starting to solve with w: 0.1\n",
+ "Starting to solve with w: 0.2\n",
+ "Starting to solve with w: 0.30000000000000004\n",
+ "Starting to solve with w: 0.4\n",
+ "Starting to solve with w: 0.5\n",
+ "Starting to solve with w: 0.6000000000000001\n",
+ "Starting to solve with w: 0.7000000000000001\n",
+ "Starting to solve with w: 0.8\n",
+ "Starting to solve with w: 0.9\n",
+ "Starting to solve with w: 1.0\n",
+ "Starting to solve with w: 1.1\n",
+ "Starting to solve with w: 1.2000000000000002\n",
+ "Starting to solve with w: 1.3\n",
+ "Starting to solve with w: 1.4000000000000001\n",
+ "Starting to solve with w: 1.5\n",
+ "Starting to solve with w: 1.6\n",
+ "Starting to solve with w: 1.7000000000000002\n",
+ "Starting to solve with w: 1.8\n",
+ "Starting to solve with w: 1.9000000000000001\n",
+ "Starting to solve with w: 2.0\n",
+ "Starting to solve with w: 2.1\n",
+ "Starting to solve with w: 2.2\n",
+ "Starting to solve with w: 2.3000000000000003\n",
+ "Starting to solve with w: 2.4000000000000004\n",
+ "Starting to solve with w: 2.5\n",
+ "Starting to solve with w: 2.6\n",
+ "Starting to solve with w: 2.7\n",
+ "Starting to solve with w: 2.8000000000000003\n",
+ "Starting to solve with w: 2.9000000000000004\n",
+ "Starting to solve with w: 3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "runtime = []\n",
+ "visited_nodes = []\n",
+ "path_length = []\n",
+ "w_value = []\n",
+ "for w in np.arange(0, 3.01, 0.1):\n",
+ " print(f\"Starting to solve with w: {w}\")\n",
+ " for i, problem in enumerate(intial_states[12]):\n",
+ " ARRAY_INITIAL = np.asarray(problem[0], dtype=int)\n",
+ " ARRAY_FINAL = np.asarray(problem[1], dtype=int)\n",
+ " manhattan_Astar_2_start = NodeAstar_2(ARRAY_INITIAL, 0, (9 - (w ** 2)) *manhatten_distance(ARRAY_INITIAL, ARRAY_FINAL))\n",
+ " manhattan_Astar_2_final = NodeAstar_2(ARRAY_FINAL, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search_2(manhattan_Astar_2_start, manhattan_Astar_2_final, manhatten_distance, w = w)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime.append(final_time-start_time)\n",
+ " visited_nodes.append(n)\n",
+ " path_length.append(len(path)-1)\n",
+ " w_value.append(w)\n",
+ "\n",
+ "results_4 = pd.DataFrame({\n",
+ " \"W\":w_value,\n",
+ " \"Zeit\": runtime,\n",
+ " \"Pfadlaenge\": path_length,\n",
+ " \"Besuchte Knoten\": visited_nodes\n",
+ "})\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "results_4.to_csv(\"results_4.csv\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x1d053d57310>]"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = results_4[\"W\"].unique()\n",
+ "y1 = (\n",
+ " results_4\n",
+ " .groupby([\"W\"])\n",
+ " .agg(\"mean\")\n",
+ " [\"Besuchte Knoten\"]\n",
+ ")\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "ax.scatter(x, y1)\n",
+ "ax.set_xlabel(\"W\")\n",
+ "ax.set_ylabel(\"Besuchte Knoten\")\n",
+ "ax.plot(x, y1, color=\"orange\")\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style scoped>\n",
+ " .dataframe tbody tr th:only-of-type {\n",
+ " vertical-align: middle;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Zeit</th>\n",
+ " <th>Pfadlaenge</th>\n",
+ " <th>Besuchte Knoten</th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>W</th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0.0</th>\n",
+ " <td>5.454133e+07</td>\n",
+ " <td>26.590674</td>\n",
+ " <td>175.404145</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.1</th>\n",
+ " <td>2.759089e+08</td>\n",
+ " <td>16.958549</td>\n",
+ " <td>960.067358</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.2</th>\n",
+ " <td>1.095760e+08</td>\n",
+ " <td>14.414508</td>\n",
+ " <td>396.108808</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.3</th>\n",
+ " <td>5.963669e+07</td>\n",
+ " <td>13.145078</td>\n",
+ " <td>225.645078</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.4</th>\n",
+ " <td>3.127483e+07</td>\n",
+ " <td>12.336788</td>\n",
+ " <td>128.031088</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.5</th>\n",
+ " <td>2.345782e+07</td>\n",
+ " <td>12.217617</td>\n",
+ " <td>99.404145</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.6</th>\n",
+ " <td>1.861436e+07</td>\n",
+ " <td>12.051813</td>\n",
+ " <td>80.841969</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.7</th>\n",
+ " <td>1.657493e+07</td>\n",
+ " <td>12.036269</td>\n",
+ " <td>72.950777</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.8</th>\n",
+ " <td>1.490684e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>66.808290</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.9</th>\n",
+ " <td>1.523352e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>66.808290</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.0</th>\n",
+ " <td>1.911567e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>82.173575</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.1</th>\n",
+ " <td>1.955509e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>84.215026</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.2</th>\n",
+ " <td>2.446751e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>93.795337</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.3</th>\n",
+ " <td>3.581351e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>139.738342</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.4</th>\n",
+ " <td>4.551088e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>173.209845</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.5</th>\n",
+ " <td>5.609567e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>211.722798</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.6</th>\n",
+ " <td>6.585994e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>242.126943</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.7</th>\n",
+ " <td>9.558220e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>341.976684</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.8</th>\n",
+ " <td>9.739779e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>411.865285</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.9</th>\n",
+ " <td>5.600187e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>453.119171</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.0</th>\n",
+ " <td>7.719742e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>619.689119</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.1</th>\n",
+ " <td>8.059190e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>640.450777</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.2</th>\n",
+ " <td>1.036646e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>809.481865</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.3</th>\n",
+ " <td>1.103883e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>855.191710</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.4</th>\n",
+ " <td>1.356776e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1044.380829</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.5</th>\n",
+ " <td>1.720562e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1319.230570</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.6</th>\n",
+ " <td>2.225932e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1504.556995</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.7</th>\n",
+ " <td>2.514645e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1679.178756</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.8</th>\n",
+ " <td>2.930559e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1901.264249</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.9</th>\n",
+ " <td>2.920653e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1901.590674</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3.0</th>\n",
+ " <td>3.956456e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>2707.658031</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Zeit Pfadlaenge Besuchte Knoten\n",
+ "W \n",
+ "0.0 5.454133e+07 26.590674 175.404145\n",
+ "0.1 2.759089e+08 16.958549 960.067358\n",
+ "0.2 1.095760e+08 14.414508 396.108808\n",
+ "0.3 5.963669e+07 13.145078 225.645078\n",
+ "0.4 3.127483e+07 12.336788 128.031088\n",
+ "0.5 2.345782e+07 12.217617 99.404145\n",
+ "0.6 1.861436e+07 12.051813 80.841969\n",
+ "0.7 1.657493e+07 12.036269 72.950777\n",
+ "0.8 1.490684e+07 12.000000 66.808290\n",
+ "0.9 1.523352e+07 12.000000 66.808290\n",
+ "1.0 1.911567e+07 12.000000 82.173575\n",
+ "1.1 1.955509e+07 12.000000 84.215026\n",
+ "1.2 2.446751e+07 12.000000 93.795337\n",
+ "1.3 3.581351e+07 12.000000 139.738342\n",
+ "1.4 4.551088e+07 12.000000 173.209845\n",
+ "1.5 5.609567e+07 12.000000 211.722798\n",
+ "1.6 6.585994e+07 12.000000 242.126943\n",
+ "1.7 9.558220e+07 12.000000 341.976684\n",
+ "1.8 9.739779e+07 12.000000 411.865285\n",
+ "1.9 5.600187e+07 12.000000 453.119171\n",
+ "2.0 7.719742e+07 12.000000 619.689119\n",
+ "2.1 8.059190e+07 12.000000 640.450777\n",
+ "2.2 1.036646e+08 12.000000 809.481865\n",
+ "2.3 1.103883e+08 12.000000 855.191710\n",
+ "2.4 1.356776e+08 12.000000 1044.380829\n",
+ "2.5 1.720562e+08 12.000000 1319.230570\n",
+ "2.6 2.225932e+08 12.000000 1504.556995\n",
+ "2.7 2.514645e+08 12.000000 1679.178756\n",
+ "2.8 2.930559e+08 12.000000 1901.264249\n",
+ "2.9 2.920653e+08 12.000000 1901.590674\n",
+ "3.0 3.956456e+08 12.000000 2707.658031"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "( \n",
+ " results_4\n",
+ " .groupby([\"W\"])\n",
+ " .agg(\"mean\")\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[5, 1, 0],\n",
+ " [4, 8, 3],\n",
+ " [7, 6, 2]])"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "ARRAY = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ "\n",
+ "ARRAY_SOLVED = np.array(((1, 2, 3),\n",
+ " (4, 5, 6),\n",
+ " (7, 8, 0)), dtype=int)\n",
+ "\n",
+ "solvable_bfs = []\n",
+ "runtime_bfs = []\n",
+ "visited_nodes_bfs = []\n",
+ "solvable_greedy = []\n",
+ "runtime_greedy = []\n",
+ "visited_nodes_greedy = []\n",
+ "solvable_astar = []\n",
+ "runtime_astar = []\n",
+ "visited_nodes_astar = []\n",
+ "for i in range(1000):\n",
+ " np.random.shuffle(ARRAY)\n",
+ " bfs_start = NodeBFS(ARRAY)\n",
+ " bfs_final = NodeBFS(ARRAY_SOLVED)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = find_target_bfs(bfs_start, bfs_final)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_bfs.append(final_time-start_time)\n",
+ " visited_nodes_bfs.append(n)\n",
+ " solvable_bfs.append(n == -1)\n",
+ " if n == -1:\n",
+ " greedy_start = NodeGreedy(ARRAY, manhatten_distance(ARRAY, ARRAY_SOLVED))\n",
+ " greedy_final = NodeGreedy(ARRAY_SOLVED, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(greedy_start, greedy_final, manhatten_distance)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_greedy.append(final_time-start_time)\n",
+ " visited_nodes_greedy.append(n)\n",
+ " solvable_greedy.append(n == -1)\n",
+ "\n",
+ " astar_start = NodeAstar(ARRAY, 0, manhatten_distance(ARRAY, ARRAY_SOLVED))\n",
+ " astar_final = NodeAstar(ARRAY_SOLVED, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(astar_start, astar_final, manhatten_distance)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_astar.append(final_time-start_time)\n",
+ " visited_nodes_astar.append(n)\n",
+ " solvable_astar.append(n == -1)\n",
+ " runtime_greedy.append(None)\n",
+ " visited_nodes_greedy.append(None)\n",
+ " solvable_greedy.append(None)\n",
+ " runtime_astar.append(None)\n",
+ " visited_nodes_astar.append(None)\n",
+ " solvable_astar.append(None)\n",
+ "\n",
+ "results_5 = pd.DataFrame({\n",
+ " \"Lösbarkeit BFS\": solvable_bfs,\n",
+ " \"Besuchte Knoten BFS\": visited_nodes_bfs,\n",
+ " \"Laufzeit BFS\": runtime_bfs,\n",
+ "\n",
+ " \"Lösbarkeit Greedy\": solvable_greedy,\n",
+ " \"Besuchte Knoten Greedy\": visited_nodes_greedy,\n",
+ " \"Laufzeit Greedy\": runtime_greedy,\n",
+ "\n",
+ " \"Lösbarkeit A*\": solvable_astar,\n",
+ " \"Besuchte Knoten A*\": visited_nodes_astar,\n",
+ " \"Laufzeit A*\": runtime_astar,\n",
+ "})\n",
+ "\n",
+ "\n",
+ "results_5.to_csv(\"results_5.csv\")\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Tom/HA_03_04_Schmidt.ipynb b/Tom/HA_03_04_Schmidt.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..4a8e87dceb91d2d6ebc425e0df37f04f758f80ab
--- /dev/null
+++ b/Tom/HA_03_04_Schmidt.ipynb
@@ -0,0 +1,1918 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# HA 04 und 04 Schmidt "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "## 0 Initialization and Helper Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pathlib # for handling file system\n",
+ "import random\n",
+ "import time \n",
+ "import copy # for copy objects \n",
+ "import itertools # use products for iterations\n",
+ "\n",
+ "from matplotlib import pyplot as plt\n",
+ "from matplotlib import animation as animation\n",
+ "from matplotlib.colors import ListedColormap\n",
+ "\n",
+ "from IPython.display import HTML\n",
+ "\n",
+ "from collections import deque # properties of a linked list to left and right\n",
+ "from queue import Queue, PriorityQueue\n",
+ "import numpy as np\n",
+ "import pandas as pd"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def plot_puzzle_config(ax, config):\n",
+ " \"\"\"Visualise a given configuration of the 8-puzzle.\"\"\"\n",
+ " cmap = ListedColormap([\"lightgray\", \"lightblue\"])\n",
+ " ax.matshow(config == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " for row in range(3):\n",
+ " for col in range(3):\n",
+ " value = config[row, col]\n",
+ " ax.text(col, row, str(value), \n",
+ " va=\"center\", ha=\"center\", \n",
+ " font={'weight': 'bold' if value == 0 else 'normal'})"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def animate_moves(solution_path, output_path = None, delay = 2000, video_inplace = True, filename = \"8puzzle_steps.mp4\"):\n",
+ " \"\"\"Given a initial configuration of the 8 puzzle animate all movesments that lead to the target configuration.\"\"\"\n",
+ "\n",
+ " def add_text(ax, config):\n",
+ " for row in range(3):\n",
+ " for col in range(3):\n",
+ " value: np.unit8 = config[row, col]\n",
+ " ax.text(col, row, str(value), \n",
+ " va=\"center\", ha=\"center\", \n",
+ " font={'weight': 'bold' if value == 0 else 'normal'})\n",
+ "\n",
+ " def animate(img, ax, config):\n",
+ " ax.clear()\n",
+ " img = ax.matshow(root.state == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " img.set_array(config == 0)\n",
+ " add_text(ax, config)\n",
+ " return (ax,)\n",
+ "\n",
+ " fig, ax = plt.subplots()\n",
+ "\n",
+ " cmap = ListedColormap([\"lightgray\", \"lightblue\"])\n",
+ " root = solution_path[0]\n",
+ " img_mat = ax.matshow(root.state == 0, cmap=cmap)\n",
+ " ax.set_xticks([x - 0.5 for x in ax.get_xticks()][1:], minor='true')\n",
+ " ax.set_yticks([y - 0.5 for y in ax.get_yticks()][1:], minor='true')\n",
+ " ax.grid(which='minor')\n",
+ " add_text(ax, root.state)\n",
+ "\n",
+ " anim = animation.FuncAnimation(\n",
+ " fig, lambda p: animate(img_mat, ax, p.state), solution_path, interval=delay\n",
+ " )\n",
+ " plt.close(fig)\n",
+ " \n",
+ " if not video_inplace and output_path is not None:\n",
+ " output_path.mkdir(parents=True, exist_ok=True)\n",
+ " anim.save(output_path / filename ) \n",
+ " return anim"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class Node:\n",
+ " \"\"\"Base class that implements commonly-used methods for the tree search algorithms\"\"\"\n",
+ " \n",
+ " def __init__(self, state):\n",
+ " \"\"\"Initialiser of the base class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State array representing a certain digit arrangement of the 8 puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Sets attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.state = state\n",
+ " self.empty_pos = self._get_empty_pos()\n",
+ " self.hash_value = hash(repr(self))\n",
+ "\n",
+ "\n",
+ " def _get_empty_pos(self):\n",
+ " \"\"\"Locate the position of the empty spot in the puzzle\"\"\"\n",
+ " row, col = np.where(self.state == 0)\n",
+ " return row[0], col[0]\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"Node({self.state})\"\n",
+ " \n",
+ " def __hash__(self):\n",
+ " return self.hash_value\n",
+ "\n",
+ " def __eq__(self, rhs): \n",
+ " return self.hash_value == rhs.hash_value\n",
+ "\n",
+ " def __ne__(self, rhs):\n",
+ " return not (self == rhs)\n",
+ " \n",
+ " def _next_positions(self):\n",
+ " \"\"\"Given a tuple of the current position of the 0 yield tuples of possible next positions.\n",
+ " \n",
+ " Parameters:\n",
+ " No parameters.\n",
+ " \n",
+ " Returns:\n",
+ " Generator[Tuple[int, int], None, None]. (See: https://docs.python.org/3/library/typing.html#typing.Generator)\n",
+ " When calling `next` on this generator a tuple with ints is returned which represents the \n",
+ " next position of the 0 in the array.\n",
+ " \"\"\"\n",
+ " # Values for the indices should be in the range 0 <= x < 2\n",
+ " idx0, idx1 = self.empty_pos\n",
+ " assert idx0 in range(3), \"idx0 must be in range(3)\"\n",
+ " assert idx1 in range(3), \"idx1 must be in range(3)\"\n",
+ "\n",
+ " # Can we move up?\n",
+ " if idx0 > 0:\n",
+ " yield (idx0 - 1, idx1)\n",
+ " # Can we move left?\n",
+ " if idx1 > 0:\n",
+ " yield (idx0, idx1 - 1)\n",
+ " # Can we move down?\n",
+ " if idx0 < 2:\n",
+ " yield (idx0 + 1, idx1)\n",
+ " # Can we move right?\n",
+ " if idx1 < 2:\n",
+ " yield (idx0, idx1 + 1)\n",
+ "\n",
+ " def _make_new_state(self, empty_pos_new):\n",
+ " \"\"\"Move the empty spot in the puzzle and thus make a new state but leave the state as is\n",
+ " \n",
+ " Parameters:\n",
+ " empty_pos_new: tuple\n",
+ " Pair of integer values that represent the next position of the empty spot of the puzzle.\n",
+ " buffer: np.ndarray\n",
+ " State array that will hold the new state of the puzzle after having moved the empty spot.\n",
+ " Output:\n",
+ " buffer, which is the new state.\n",
+ " \"\"\"\n",
+ " buffer = self.state.copy() # very important to leave the state unchanged\n",
+ " buffer[empty_pos_new] = self.state[self.empty_pos]\n",
+ " buffer[self.empty_pos] = self.state[empty_pos_new]\n",
+ "\n",
+ " return buffer \n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeRandom(Node):\n",
+ " \n",
+ " def randomise_state(self, num_moves):\n",
+ " \"\"\"Randomly change the current state of the puzzle\n",
+ " \n",
+ " Parameters:\n",
+ " num_moves: int\n",
+ " Number of times to randomly change the state of the puzzle.\n",
+ " \n",
+ " Output: Node\n",
+ " The (modified) version of the class instance. If `num_moves == 0` the instance of the class is returned unchanged. \n",
+ " \"\"\"\n",
+ " if num_moves > 0:\n",
+ " for _ in range(num_moves):\n",
+ " pos_new_random = random.choice(tuple(self._next_positions()))\n",
+ " self.state[:, :] = self._make_new_state(pos_new_random)\n",
+ " self.empty_pos = pos_new_random\n",
+ " \n",
+ " self.hash_value = hash(repr(self)) \n",
+ " return self\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeBFS(Node):\n",
+ " \"\"\"Node for the BFS tree search algorithm\"\"\"\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return f\"NodeBFS({self.state})\"\n",
+ "\n",
+ " \n",
+ " def next_nodes(self):\n",
+ " \"\"\"Generate other state nodes that from the current node.\n",
+ " \n",
+ " Parameters:\n",
+ " No parameters.\n",
+ " \n",
+ " Output:\n",
+ " Generator[NodeBFS, None, None]. \n",
+ " Yields a node representing a state of the the puzzle that can be generated through\n",
+ " a single move of the empty spot in the current state.\n",
+ " \"\"\"\n",
+ " for pos_new in self._next_positions():\n",
+ " yield type(self)(self._make_new_state(pos_new))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def reconstruct_path(to_node, parent):\n",
+ " \"\"\"Reconstruct all nodes on the path root_node --> to_node.\n",
+ "\n",
+ " Parameters:\n",
+ " to_node: Node\n",
+ " Node at the end of the path.\n",
+ " parent: dict\n",
+ " Child - parent relationship between nodes in the search tree.\n",
+ " \n",
+ " Output:\n",
+ " path: deque\n",
+ " List with all the nodes along the path root_node --> to_node.\n",
+ " \"\"\"\n",
+ " path = deque()\n",
+ " current = to_node\n",
+ " while current is not None:\n",
+ " path.appendleft(current)\n",
+ " current = parent[current]\n",
+ " return path\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def find_target_bfs(initial, final):\n",
+ " \"\"\"Find a solutions of the 8-puzzle when given an initial configuration by using the BFS algorithm.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: NodeBFS\n",
+ " Initial state of the 8-puzzle.\n",
+ " final: NodeBFS\n",
+ " Final state of the 8-puzzle.\n",
+ "\n",
+ " Output:\n",
+ " n: number of visited nodes\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " q = Queue() # FIFO queue\n",
+ " q.put(initial)\n",
+ " parent = {initial: None} # dictionary \n",
+ " \n",
+ " n = 1 # Counter for number of nodes that have been put into the queue.\n",
+ "\n",
+ " if initial == final:\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ " \n",
+ " \n",
+ " while not q.empty():\n",
+ " node = q.get()\n",
+ " for child in node.next_nodes():\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " q.put(child)\n",
+ " parent[child] = node \n",
+ " if child == final:\n",
+ " return n, reconstruct_path(child, parent)\n",
+ "\n",
+ " \n",
+ " return -1, []"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def state_difference(state, final_state):\n",
+ " \"\"\"Compute the difference of two states of the 8 puzzle.\n",
+ "\n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State of the 8 puzzle for which to compute the distance to the final state.\n",
+ " final_state: np.ndarray\n",
+ " Solved state of the 8 puzzle.\n",
+ " \n",
+ " Output:\n",
+ " int: The difference of the two states. The difference is computed by the number digits in state\n",
+ " that are *not* in the same position in final_state.\n",
+ " \"\"\"\n",
+ " return np.sum((state != 0) & (state != final_state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeGreedy(Node): \n",
+ " def __init__(self, state, estimated_cost):\n",
+ " \"\"\"Initialiser of the class\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray\n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is\n",
+ " forwarded to the base class.\n",
+ " estimated_cost: int\n",
+ " An estimate of the cost of getting from the current state to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.estimated_cost = estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeGreedy({self.state}, {self.estimated_cost})\"\n",
+ "\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller estimated cost to reach the final state as the other node else False.\n",
+ " \n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.estimated_cost < rhs.estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, cost_estimator: callable):\n",
+ " \"\"\"Generate other state nodes from the current node.\n",
+ " \n",
+ " Parameters:\n",
+ " final: NodeGreedy\n",
+ " A node representing the solved state of the puzzle.\n",
+ " estimator: callable\n",
+ " Cost function to estimated the cost from getting the generated state to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " Generator[NodeGreedy, None, None]. \n",
+ " Yields a node representing a state of the puzzle that can be generated through \n",
+ " a single move of the empty spot in the current state.\n",
+ " \"\"\"\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), cost_estimator(buffer, \n",
+ " final.state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def informed_search(initial, final, cost_estimator: callable):\n",
+ " \"\"\"Find path from initial to final node.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: Node[Greedy, Astar]\n",
+ " Node representing the initial state of the 8 puzzle.\n",
+ " final: Node[Greedy, Astar]\n",
+ " Node representing the solved state of the 8 puzzle.\n",
+ " cost_estimator: callable\n",
+ " Function to estimate the cost to get from some node to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " pq = PriorityQueue()\n",
+ " pq.put(initial)\n",
+ " parent = {initial: None} # dictionary\n",
+ " \n",
+ " n = 1 # Counter for the number of nodes that have been put into the queue.\n",
+ "\n",
+ " if np.array_equal(initial.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ "\n",
+ " \n",
+ " while not pq.empty():\n",
+ " current = pq.get()\n",
+ " for child in current.next_nodes(final, cost_estimator):\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " pq.put(child)\n",
+ " parent[child] = current\n",
+ " if np.array_equal(child.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(child, parent)\n",
+ " \n",
+ " return -1, []"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeAstar(Node):\n",
+ " def __init__(self, state, accumulated_cost, estimated_cost):\n",
+ " \"\"\"Initialiser of the class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray \n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is \n",
+ " forwarded to the base class.\n",
+ " accumulated_cost: int\n",
+ " Number of steps executed so far.\n",
+ " estimated_cost: int>\n",
+ " Estimated cost for getting from the current state to the solved state of the puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.accumulated_cost, self.estimated_cost = accumulated_cost, \\\n",
+ " estimated_cost\n",
+ " self.total_estimated_cost = accumulated_cost + estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeAstar({self.state}, {self.accumulated_cost}, \\\n",
+ " {self.estimated_cost})\"\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller *total estimated cost* to reach the final state as the other node else False.\n",
+ " >\n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.total_estimated_cost < rhs.total_estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, estimator):\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), self.accumulated_cost + 1, \n",
+ " estimator(buffer, final.state))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Meine Bearbeitung"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Summe der euklidischen/manhatten Abstände ist keine zulässige Heuristik. Auch hier muss die 0 ausgeschlossen werden."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import math as m\n",
+ "\n",
+ "def manhatten_distance(state, final_state):\n",
+ " \"\"\"Compute the manhattan distance between two arrays of identical shape\"\"\"\n",
+ " distance = 0\n",
+ " for i, row in enumerate(state):\n",
+ " for j, value in enumerate(row):\n",
+ " if value != 0:\n",
+ " x, y = np.where(final_state == value)\n",
+ " distance += abs(x[0]-i) + abs(y[0]-j)\n",
+ " #print(f\"Distance for value {value} is {abs(x[0]-i) + abs(y[0]-j)}\")\n",
+ " return distance\n",
+ "\n",
+ "def euclidian_distance(state, final_state):\n",
+ " \"\"\"Compute the euclidian distance between two arrays of identical shape\"\"\"\n",
+ " distance = 0\n",
+ " for i, row in enumerate(state):\n",
+ " for j, value in enumerate(row):\n",
+ " if value != 0:\n",
+ " x, y = np.where(final_state == value)\n",
+ " distance += m.sqrt(pow((x[0]-i), 2) + pow((y[0]-j),2))\n",
+ " #print(f\"Distance for value {value} is {m.sqrt(pow((x[0]-i), 2) + pow((y[0]-j),2))}\")\n",
+ " return distance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ARRAY_INITIAL = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ " \n",
+ "ARRAY_FINAl = np.array(((1, 3, 6),\n",
+ " (8, 0, 2),\n",
+ " (7, 4, 5)), dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Anzahl falscher Positionen: 7 \n",
+ " Manhattan Abstand: 14 \n",
+ " Euklidischer Abstand: 11.30056307974577\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(f\"Anzahl falscher Positionen: {state_difference(ARRAY_INITIAL, ARRAY_FINAl)} \\n \\\n",
+ " Manhattan Abstand: {manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl)} \\n \\\n",
+ " Euklidischer Abstand: {euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl)}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "###### Greedy Suche mit Anzahl falscher Positionen\n",
+ " Besuchte Knoten: 490 \n",
+ " Länge des Pfades: 27\n",
+ "###### Greedy Suche mit Manhattan-Abstand\n",
+ " Besuchte Knoten: 83 \n",
+ " Länge des Pfades: 33\n",
+ "###### Greedy Suche mit Euklidischem-Abstand\n",
+ " Besuchte Knoten: 333 \n",
+ " Länge des Pfades: 41\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "###### Astar Suche mit Anzahl falscher Positionen\n",
+ " Besuchte Knoten: 1048 \n",
+ " Länge des Pfades: 17\n",
+ "###### Astar Suche mit Manhattan-Abstand\n",
+ " Besuchte Knoten: 107 \n",
+ " Länge des Pfades: 17\n",
+ "###### Astar Suche mit Euklidischem-Abstand\n",
+ " Besuchte Knoten: 143 \n",
+ " Länge des Pfades: 17\n"
+ ]
+ }
+ ],
+ "source": [
+ "manhattan_greedy_start = NodeGreedy(ARRAY_INITIAL, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "euclidian_greedy_start = NodeGreedy(ARRAY_INITIAL, euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "eucilidan_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "difference_greedy_start = NodeGreedy(ARRAY_INITIAL, state_difference(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "difference_greedy_final = NodeGreedy(ARRAY_FINAl, 0)\n",
+ "difference_greedy_n, difference_greedy_path = informed_search(difference_greedy_start, difference_greedy_final, state_difference)\n",
+ "print(f\"###### Greedy Suche mit Anzahl falscher Positionen\\n \\\n",
+ "Besuchte Knoten: {difference_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(difference_greedy_path)}\")\n",
+ "manhatten_greedy_n, manhattan_greedy_path = informed_search(manhattan_greedy_start, manhattan_greedy_final, manhatten_distance)\n",
+ "print(f\"###### Greedy Suche mit Manhattan-Abstand\\n \\\n",
+ "Besuchte Knoten: {manhatten_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(manhattan_greedy_path)}\")\n",
+ "euclidian_greedy_n, euclidian_greedy_path = informed_search(euclidian_greedy_start, eucilidan_greedy_final, euclidian_distance)\n",
+ "print(f\"###### Greedy Suche mit Euklidischem-Abstand\\n \\\n",
+ "Besuchte Knoten: {euclidian_greedy_n} \\n \\\n",
+ "Länge des Pfades: {len(euclidian_greedy_path)}\")\n",
+ "\n",
+ "manhattan_Astar_start = NodeAstar(ARRAY_INITIAL, 0, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "euclidian_Astar_start = NodeAstar(ARRAY_INITIAL, 0, euclidian_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "eucilidan_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "difference_Astar_start = NodeAstar(ARRAY_INITIAL, 0, state_difference(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "difference_Astar_final = NodeAstar(ARRAY_FINAl, -1, 0)\n",
+ "difference_Astar_n, difference_Astar_path = informed_search(difference_Astar_start, difference_Astar_final, state_difference)\n",
+ "print(f\"###### Astar Suche mit Anzahl falscher Positionen\\n \\\n",
+ "Besuchte Knoten: {difference_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(difference_Astar_path)}\")\n",
+ "manhatten_Astar_n, manhattan_Astar_path = informed_search(manhattan_Astar_start, manhattan_Astar_final, manhatten_distance)\n",
+ "print(f\"###### Astar Suche mit Manhattan-Abstand\\n \\\n",
+ "Besuchte Knoten: {manhatten_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(manhattan_Astar_path)}\")\n",
+ "euclidian_Astar_n, euclidian_Astar_path = informed_search(euclidian_Astar_start, eucilidan_Astar_final, euclidian_distance)\n",
+ "print(f\"###### Astar Suche mit Euklidischem-Abstand\\n \\\n",
+ "Besuchte Knoten: {euclidian_Astar_n} \\n \\\n",
+ "Länge des Pfades: {len(euclidian_Astar_path)}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Tiefe: 2 - Anzahl Anfangszustände: 12\n",
+ "Tiefe: 4 - Anzahl Anfangszustände: 32\n",
+ "Tiefe: 6 - Anzahl Anfangszustände: 98\n",
+ "Tiefe: 8 - Anzahl Anfangszustände: 201\n",
+ "Tiefe: 10 - Anzahl Anfangszustände: 344\n",
+ "Tiefe: 12 - Anzahl Anfangszustände: 386\n",
+ "Tiefe: 14 - Anzahl Anfangszustände: 384\n",
+ "Tiefe: 16 - Anzahl Anfangszustände: 273\n",
+ "Tiefe: 18 - Anzahl Anfangszustände: 166\n",
+ "Tiefe: 20 - Anzahl Anfangszustände: 73\n"
+ ]
+ }
+ ],
+ "source": [
+ "import time\n",
+ "time.perf_counter_ns()\n",
+ "import yaml\n",
+ "with open(\"initial_states.yaml\", \"r\") as f:\n",
+ " intial_states = yaml.safe_load(f)\n",
+ "for d, states in intial_states.items():\n",
+ " print(f\"Tiefe: {d:3d} - Anzahl Anfangszustände: {len(states):4d}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def time_algorithm(intial_states, node_type_names, heuristics, heuristic_names):\n",
+ " algorithm = []\n",
+ " used_heuristic = []\n",
+ " depth = []\n",
+ " runtime = []\n",
+ " visited_node = []\n",
+ " path_length = []\n",
+ " for node_type_name in node_type_names:\n",
+ " print(f\"Beginning measurement of {node_type_name}...\")\n",
+ " if node_type_name == \"BFS\":\n",
+ " heuristic_helper = [(None, \"Keine\")]\n",
+ " else:\n",
+ " heuristic_helper = zip(heuristics, heuristic_names)\n",
+ " for heuristic, heuristic_name in heuristic_helper:\n",
+ " print(f\"For heuristic: {heuristic_name} ...\")\n",
+ " for current_depth, problems in intial_states.items():\n",
+ " print(f\"In depth: {current_depth} ...\")\n",
+ " for problem in problems:\n",
+ " start_array = np.asarray(problem[0], dtype=int)\n",
+ " final_array = np.asarray(problem[1], dtype=int)\n",
+ " if node_type_name == \"BFS\":\n",
+ " start = NodeBFS(start_array)\n",
+ " final = NodeBFS(final_array)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = find_target_bfs(start, final)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " if node_type_name == \"Greedy\":\n",
+ " start = NodeGreedy(start_array, heuristic(start_array, final_array))\n",
+ " final = NodeGreedy(final_array, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(start, final, heuristic)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " if node_type_name == \"A*\":\n",
+ " start = NodeAstar(start_array, 0, heuristic(start_array, final_array))\n",
+ " final = NodeAstar(final_array, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(start, final, heuristic)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " algorithm.append(node_type_name)\n",
+ " used_heuristic.append(heuristic_name)\n",
+ " depth.append(current_depth)\n",
+ " runtime.append(final_time - start_time)\n",
+ " visited_node.append(n)\n",
+ " path_length.append(len(path))\n",
+ " print(f\"Finished depth: {current_depth}.\")\n",
+ " print(f\"Finished heuristic: {heuristic_name}.\")\n",
+ " print(f\"Finished {node_type_name}.\")\n",
+ " return algorithm, used_heuristic, depth, visited_node, path_length, runtime\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Beginning measurement of BFS...\n",
+ "For heuristic: Keine ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Keine.\n",
+ "Finished BFS.\n",
+ "Beginning measurement of Greedy...\n",
+ "For heuristic: Difference ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Difference.\n",
+ "For heuristic: Euklidisch ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Euklidisch.\n",
+ "For heuristic: Manhattan ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Manhattan.\n",
+ "Finished Greedy.\n",
+ "Beginning measurement of A*...\n",
+ "For heuristic: Difference ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Difference.\n",
+ "For heuristic: Euklidisch ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Euklidisch.\n",
+ "For heuristic: Manhattan ...\n",
+ "In depth: 2 ...\n",
+ "Finished depth: 2.\n",
+ "In depth: 4 ...\n",
+ "Finished depth: 4.\n",
+ "In depth: 6 ...\n",
+ "Finished depth: 6.\n",
+ "In depth: 8 ...\n",
+ "Finished depth: 8.\n",
+ "In depth: 10 ...\n",
+ "Finished depth: 10.\n",
+ "In depth: 12 ...\n",
+ "Finished depth: 12.\n",
+ "In depth: 14 ...\n",
+ "Finished depth: 14.\n",
+ "In depth: 16 ...\n",
+ "Finished depth: 16.\n",
+ "In depth: 18 ...\n",
+ "Finished depth: 18.\n",
+ "In depth: 20 ...\n",
+ "Finished depth: 20.\n",
+ "Finished heuristic: Manhattan.\n",
+ "Finished A*.\n"
+ ]
+ }
+ ],
+ "source": [
+ "node_type_names = [\"BFS\", \"Greedy\", \"A*\"]\n",
+ "heuristics = [state_difference, manhatten_distance, euclidian_distance]\n",
+ "heuristic_names = [\"Difference\", \"Euklidisch\", \"Manhattan\"]\n",
+ "\n",
+ "algorithm, used_heuristic, depth, visited_node, path_length, runtime = time_algorithm(intial_states, node_type_names, heuristics, heuristic_names)\n",
+ "\n",
+ "\n",
+ "\n",
+ "results = pd.DataFrame({\n",
+ " \"Algorithmus\": algorithm,\n",
+ " \"Heuristik\": used_heuristic,\n",
+ " \"Tiefe\": depth,\n",
+ " \"Besuchte Knoten\": visited_node,\n",
+ " \"Pfadlaenge\": path_length,\n",
+ " \"Zeit\": runtime,\n",
+ "})\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "mask1 = results[\"Heuristik\"] == \"Euklidisch\"\n",
+ "mask2 = results[\"Heuristik\"] == \"Manhattan\"\n",
+ "\n",
+ "results.loc[mask1, \"Heuristik\"] = \"Manhattan\"\n",
+ "results.loc[mask2, \"Heuristik\"] = \"Euklidisch\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "<class 'pandas.core.frame.DataFrame'>\n",
+ "RangeIndex: 13783 entries, 0 to 13782\n",
+ "Data columns (total 6 columns):\n",
+ " # Column Non-Null Count Dtype \n",
+ "--- ------ -------------- ----- \n",
+ " 0 Algorithmus 13783 non-null object\n",
+ " 1 Heuristik 13783 non-null object\n",
+ " 2 Tiefe 13783 non-null int64 \n",
+ " 3 Besuchte Knoten 13783 non-null int64 \n",
+ " 4 Pfadlaenge 13783 non-null int64 \n",
+ " 5 Zeit 13783 non-null int64 \n",
+ "dtypes: int64(4), object(2)\n",
+ "memory usage: 646.2+ KB\n"
+ ]
+ }
+ ],
+ "source": [
+ "results = pd.read_csv(\"results.csv\").iloc[:, 1:]\n",
+ "results.info()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<Axes: xlabel='Tiefe', ylabel='Pfadlänge'>"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "(\n",
+ " results\n",
+ " .pipe(lambda adf: adf[adf[\"Algorithmus\"] != \"A*\"])\n",
+ " .pivot_table(\n",
+ " values = 'Pfadlaenge',\n",
+ " columns = ['Algorithmus', 'Heuristik'],\n",
+ " index = 'Tiefe',\n",
+ " aggfunc = 'mean'\n",
+ " )\n",
+ " .plot(logy=False, ylabel=\"Pfadlänge\", xticks=(2,4,6,8,10,12,14,16,18,20))\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 130,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array(['BFS', 'Greedy', 'A*'], dtype=object)"
+ ]
+ },
+ "execution_count": 130,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "results[\"Algorithmus\"].unique()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 135,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import scipy\n",
+ "import scipy.optimize\n",
+ "\n",
+ "def func_tiefe(x, b, c):\n",
+ " return (b ** x) * c\n",
+ "\n",
+ "def func_knoten(x, b, c):\n",
+ " return (b * x) + c\n",
+ "\n",
+ "def mittleres_Skalengesetz(algorithmus, heuristik, x_column):\n",
+ " x = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [x_column]\n",
+ " )\n",
+ " y = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Zeit\"]\n",
+ " )\n",
+ "\n",
+ " if x_column == \"Tiefe\":\n",
+ " func = func_tiefe\n",
+ " func_x = np.arange(0,22,0.5)\n",
+ " if x_column == \"Besuchte Knoten\":\n",
+ " func = func_knoten\n",
+ " func_x = np.arange(0,max(x)+100,100)\n",
+ " \n",
+ " (b, c), _ = scipy.optimize.curve_fit(func, x, y)\n",
+ "\n",
+ " print(f\"B: {b}\")\n",
+ " print(f\"C: {c}\")\n",
+ "\n",
+ " func_y = func(func_x, b, c)\n",
+ "\n",
+ "\n",
+ " fig, ax = plt.subplots()\n",
+ " ax.set_title(f\"Mittleres Skalengesetz für {algorithmus} mit {heuristik} Heuristik\")\n",
+ " ax.set_ylabel(\"Zeit in Nanosekunden\")\n",
+ " ax.set_xlabel(x_column)\n",
+ " ax.scatter(x,y)\n",
+ " ax.plot(func_x, func_y, color='orange')\n",
+ " return fig"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 148,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "B: 1.4180160045233512\n",
+ "C: 126997.29495831158\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "execution_count": 148,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "mittleres_Skalengesetz(\"A*\", \"Manhattan\", \"Tiefe\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 157,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def func_tiefe_und_knoten(xdata, b, c):\n",
+ " tiefe = xdata[0]\n",
+ " knoten = xdata[1]\n",
+ " return (b ** tiefe) * knoten * c\n",
+ "\n",
+ "def mittleres_Skalengesetz_2(algorithmus, heuristik):\n",
+ " tiefen = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Tiefe\"]\n",
+ " )\n",
+ " knoten = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Besuchte Knoten\"]\n",
+ " )\n",
+ " y = (\n",
+ " results\n",
+ " .loc[results[\"Algorithmus\"] == algorithmus]\n",
+ " .loc[results[\"Heuristik\"] == heuristik]\n",
+ " [\"Zeit\"]\n",
+ " )\n",
+ " \n",
+ " xdata = np.array([tiefen, knoten])\n",
+ " print(xdata.shape)\n",
+ "\n",
+ " (b, c), _ = scipy.optimize.curve_fit(func_tiefe_und_knoten, xdata, y)\n",
+ "\n",
+ " print(f\"Zusammenhang für {algorithmus} mit {heuristik} Heuristik:\")\n",
+ " print(f\"B: {b}\")\n",
+ " print(f\"C: {c}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 163,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(2, 1969)\n",
+ "Zusammenhang für A* mit Manhattan Heuristik:\n",
+ "B: 1.0123224209580304\n",
+ "C: 92500.85226522778\n"
+ ]
+ }
+ ],
+ "source": [
+ "mittleres_Skalengesetz_2(\"A*\", \"Manhattan\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Tiefe: 2 - Anzahl Anfangszustände: 12\n",
+ "Tiefe: 4 - Anzahl Anfangszustände: 32\n",
+ "Tiefe: 6 - Anzahl Anfangszustände: 98\n",
+ "Tiefe: 8 - Anzahl Anfangszustände: 201\n",
+ "Tiefe: 10 - Anzahl Anfangszustände: 344\n",
+ "Tiefe: 12 - Anzahl Anfangszustände: 386\n",
+ "Tiefe: 14 - Anzahl Anfangszustände: 384\n",
+ "Tiefe: 16 - Anzahl Anfangszustände: 273\n",
+ "Tiefe: 18 - Anzahl Anfangszustände: 166\n",
+ "Tiefe: 20 - Anzahl Anfangszustände: 73\n"
+ ]
+ }
+ ],
+ "source": [
+ "import yaml\n",
+ "with open(\"initial_states.yaml\", \"r\") as f:\n",
+ " intial_states = yaml.safe_load(f)\n",
+ "for d, states in intial_states.items():\n",
+ " print(f\"Tiefe: {d:3d} - Anzahl Anfangszustände: {len(states):4d}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class NodeAstar_2(Node):\n",
+ " def __init__(self, state, accumulated_cost, estimated_cost):\n",
+ " \"\"\"Initialiser of the class.\n",
+ " \n",
+ " Parameters:\n",
+ " state: np.ndarray \n",
+ " State array representing a certain digit arrangement of the 8 puzzle. The state is \n",
+ " forwarded to the base class.\n",
+ " accumulated_cost: int\n",
+ " Number of steps executed so far.\n",
+ " estimated_cost: int>\n",
+ " Estimated cost for getting from the current state to the solved state of the puzzle.\n",
+ " \n",
+ " Output:\n",
+ " No output. Initialises the attribute variables of the class.\n",
+ " \"\"\"\n",
+ " self.accumulated_cost, self.estimated_cost = accumulated_cost, \\\n",
+ " estimated_cost\n",
+ " self.total_estimated_cost = accumulated_cost + estimated_cost\n",
+ " super().__init__(state)\n",
+ "\n",
+ " def __repr__(self):\n",
+ " return f\"NodeAstar({self.state}, {self.accumulated_cost}, \\\n",
+ " {self.estimated_cost})\"\n",
+ " \n",
+ " def __lt__(self, rhs):\n",
+ " \"\"\"Test if a node instance is 'smaller' than another instance.\n",
+ " \n",
+ " Parameters:\n",
+ " rhs: NodeAstar\n",
+ " Other node instance.\n",
+ " \n",
+ " Output: bool\n",
+ " True in case the node has a smaller *total estimated cost* to reach the final state as the other node else False.\n",
+ " >\n",
+ " The < binary operator is needed to be able to use instances of this class with PriorityQueue. \n",
+ " \"\"\"\n",
+ " return self.total_estimated_cost < rhs.total_estimated_cost\n",
+ "\n",
+ " def next_nodes(self, final, estimator, w):\n",
+ " for pos_new in self._next_positions():\n",
+ " buffer = self._make_new_state(pos_new)\n",
+ " yield type(self)(buffer.copy(), self.accumulated_cost + (8 * w), \n",
+ " (9 - (w ** 2)) * estimator(buffer, final.state))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def informed_search_2(initial, final, cost_estimator: callable, w):\n",
+ " \"\"\"Find path from initial to final node.\n",
+ " \n",
+ " Parameters:\n",
+ " initial: Node[Greedy, Astar]\n",
+ " Node representing the initial state of the 8 puzzle.\n",
+ " final: Node[Greedy, Astar]\n",
+ " Node representing the solved state of the 8 puzzle.\n",
+ " cost_estimator: callable\n",
+ " Function to estimate the cost to get from some node to the solved state.\n",
+ " \n",
+ " Output:\n",
+ " deque: All nodes that lie on the path from the root node to the final node.\n",
+ " \"\"\"\n",
+ " pq = PriorityQueue()\n",
+ " pq.put(initial)\n",
+ " parent = {initial: None} # dictionary\n",
+ " \n",
+ " n = 1 # Counter for the number of nodes that have been put into the queue.\n",
+ "\n",
+ " if np.array_equal(initial.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(initial, parent)\n",
+ "\n",
+ " \n",
+ " while not pq.empty():\n",
+ " current = pq.get()\n",
+ " for child in current.next_nodes(final, cost_estimator, w):\n",
+ " if child not in parent:\n",
+ " n += 1\n",
+ " pq.put(child)\n",
+ " parent[child] = current\n",
+ " if np.array_equal(child.state, final.state): # == is not possible because == includes cost functions also\n",
+ " return n, reconstruct_path(child, parent)\n",
+ " \n",
+ " raise \"problem not solveable\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 166,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ARRAY_INITIAL = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ " \n",
+ "ARRAY_FINAl = np.array(((1, 3, 6),\n",
+ " (8, 0, 2),\n",
+ " (7, 4, 5)), dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 174,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "107"
+ ]
+ },
+ "execution_count": 174,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "manhattan_Astar_2_start = NodeAstar_2(ARRAY_INITIAL, 0, manhatten_distance(ARRAY_INITIAL, ARRAY_FINAl))\n",
+ "manhattan_Astar_2_final = NodeAstar_2(ARRAY_FINAl, -1, 0)\n",
+ "\n",
+ "n, path = informed_search_2(manhattan_Astar_2_start, manhattan_Astar_2_final, manhatten_distance, w = 1)\n",
+ "n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Starting to solve with w: 0.0\n",
+ "Starting to solve with w: 0.1\n",
+ "Starting to solve with w: 0.2\n",
+ "Starting to solve with w: 0.30000000000000004\n",
+ "Starting to solve with w: 0.4\n",
+ "Starting to solve with w: 0.5\n",
+ "Starting to solve with w: 0.6000000000000001\n",
+ "Starting to solve with w: 0.7000000000000001\n",
+ "Starting to solve with w: 0.8\n",
+ "Starting to solve with w: 0.9\n",
+ "Starting to solve with w: 1.0\n",
+ "Starting to solve with w: 1.1\n",
+ "Starting to solve with w: 1.2000000000000002\n",
+ "Starting to solve with w: 1.3\n",
+ "Starting to solve with w: 1.4000000000000001\n",
+ "Starting to solve with w: 1.5\n",
+ "Starting to solve with w: 1.6\n",
+ "Starting to solve with w: 1.7000000000000002\n",
+ "Starting to solve with w: 1.8\n",
+ "Starting to solve with w: 1.9000000000000001\n",
+ "Starting to solve with w: 2.0\n",
+ "Starting to solve with w: 2.1\n",
+ "Starting to solve with w: 2.2\n",
+ "Starting to solve with w: 2.3000000000000003\n",
+ "Starting to solve with w: 2.4000000000000004\n",
+ "Starting to solve with w: 2.5\n",
+ "Starting to solve with w: 2.6\n",
+ "Starting to solve with w: 2.7\n",
+ "Starting to solve with w: 2.8000000000000003\n",
+ "Starting to solve with w: 2.9000000000000004\n",
+ "Starting to solve with w: 3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "runtime = []\n",
+ "visited_nodes = []\n",
+ "path_length = []\n",
+ "w_value = []\n",
+ "for w in np.arange(0, 3.01, 0.1):\n",
+ " print(f\"Starting to solve with w: {w}\")\n",
+ " for i, problem in enumerate(intial_states[12]):\n",
+ " ARRAY_INITIAL = np.asarray(problem[0], dtype=int)\n",
+ " ARRAY_FINAL = np.asarray(problem[1], dtype=int)\n",
+ " manhattan_Astar_2_start = NodeAstar_2(ARRAY_INITIAL, 0, (9 - (w ** 2)) *manhatten_distance(ARRAY_INITIAL, ARRAY_FINAL))\n",
+ " manhattan_Astar_2_final = NodeAstar_2(ARRAY_FINAL, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search_2(manhattan_Astar_2_start, manhattan_Astar_2_final, manhatten_distance, w = w)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime.append(final_time-start_time)\n",
+ " visited_nodes.append(n)\n",
+ " path_length.append(len(path)-1)\n",
+ " w_value.append(w)\n",
+ "\n",
+ "results_4 = pd.DataFrame({\n",
+ " \"W\":w_value,\n",
+ " \"Zeit\": runtime,\n",
+ " \"Pfadlaenge\": path_length,\n",
+ " \"Besuchte Knoten\": visited_nodes\n",
+ "})\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "results_4.to_csv(\"results_4.csv\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x1d053d57310>]"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = results_4[\"W\"].unique()\n",
+ "y1 = (\n",
+ " results_4\n",
+ " .groupby([\"W\"])\n",
+ " .agg(\"mean\")\n",
+ " [\"Besuchte Knoten\"]\n",
+ ")\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "ax.scatter(x, y1)\n",
+ "ax.set_xlabel(\"W\")\n",
+ "ax.set_ylabel(\"Besuchte Knoten\")\n",
+ "ax.plot(x, y1, color=\"orange\")\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style scoped>\n",
+ " .dataframe tbody tr th:only-of-type {\n",
+ " vertical-align: middle;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Zeit</th>\n",
+ " <th>Pfadlaenge</th>\n",
+ " <th>Besuchte Knoten</th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>W</th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0.0</th>\n",
+ " <td>5.454133e+07</td>\n",
+ " <td>26.590674</td>\n",
+ " <td>175.404145</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.1</th>\n",
+ " <td>2.759089e+08</td>\n",
+ " <td>16.958549</td>\n",
+ " <td>960.067358</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.2</th>\n",
+ " <td>1.095760e+08</td>\n",
+ " <td>14.414508</td>\n",
+ " <td>396.108808</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.3</th>\n",
+ " <td>5.963669e+07</td>\n",
+ " <td>13.145078</td>\n",
+ " <td>225.645078</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.4</th>\n",
+ " <td>3.127483e+07</td>\n",
+ " <td>12.336788</td>\n",
+ " <td>128.031088</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.5</th>\n",
+ " <td>2.345782e+07</td>\n",
+ " <td>12.217617</td>\n",
+ " <td>99.404145</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.6</th>\n",
+ " <td>1.861436e+07</td>\n",
+ " <td>12.051813</td>\n",
+ " <td>80.841969</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.7</th>\n",
+ " <td>1.657493e+07</td>\n",
+ " <td>12.036269</td>\n",
+ " <td>72.950777</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.8</th>\n",
+ " <td>1.490684e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>66.808290</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>0.9</th>\n",
+ " <td>1.523352e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>66.808290</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.0</th>\n",
+ " <td>1.911567e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>82.173575</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.1</th>\n",
+ " <td>1.955509e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>84.215026</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.2</th>\n",
+ " <td>2.446751e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>93.795337</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.3</th>\n",
+ " <td>3.581351e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>139.738342</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.4</th>\n",
+ " <td>4.551088e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>173.209845</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.5</th>\n",
+ " <td>5.609567e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>211.722798</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.6</th>\n",
+ " <td>6.585994e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>242.126943</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.7</th>\n",
+ " <td>9.558220e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>341.976684</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.8</th>\n",
+ " <td>9.739779e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>411.865285</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1.9</th>\n",
+ " <td>5.600187e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>453.119171</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.0</th>\n",
+ " <td>7.719742e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>619.689119</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.1</th>\n",
+ " <td>8.059190e+07</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>640.450777</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.2</th>\n",
+ " <td>1.036646e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>809.481865</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.3</th>\n",
+ " <td>1.103883e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>855.191710</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.4</th>\n",
+ " <td>1.356776e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1044.380829</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.5</th>\n",
+ " <td>1.720562e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1319.230570</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.6</th>\n",
+ " <td>2.225932e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1504.556995</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.7</th>\n",
+ " <td>2.514645e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1679.178756</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.8</th>\n",
+ " <td>2.930559e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1901.264249</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2.9</th>\n",
+ " <td>2.920653e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>1901.590674</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3.0</th>\n",
+ " <td>3.956456e+08</td>\n",
+ " <td>12.000000</td>\n",
+ " <td>2707.658031</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Zeit Pfadlaenge Besuchte Knoten\n",
+ "W \n",
+ "0.0 5.454133e+07 26.590674 175.404145\n",
+ "0.1 2.759089e+08 16.958549 960.067358\n",
+ "0.2 1.095760e+08 14.414508 396.108808\n",
+ "0.3 5.963669e+07 13.145078 225.645078\n",
+ "0.4 3.127483e+07 12.336788 128.031088\n",
+ "0.5 2.345782e+07 12.217617 99.404145\n",
+ "0.6 1.861436e+07 12.051813 80.841969\n",
+ "0.7 1.657493e+07 12.036269 72.950777\n",
+ "0.8 1.490684e+07 12.000000 66.808290\n",
+ "0.9 1.523352e+07 12.000000 66.808290\n",
+ "1.0 1.911567e+07 12.000000 82.173575\n",
+ "1.1 1.955509e+07 12.000000 84.215026\n",
+ "1.2 2.446751e+07 12.000000 93.795337\n",
+ "1.3 3.581351e+07 12.000000 139.738342\n",
+ "1.4 4.551088e+07 12.000000 173.209845\n",
+ "1.5 5.609567e+07 12.000000 211.722798\n",
+ "1.6 6.585994e+07 12.000000 242.126943\n",
+ "1.7 9.558220e+07 12.000000 341.976684\n",
+ "1.8 9.739779e+07 12.000000 411.865285\n",
+ "1.9 5.600187e+07 12.000000 453.119171\n",
+ "2.0 7.719742e+07 12.000000 619.689119\n",
+ "2.1 8.059190e+07 12.000000 640.450777\n",
+ "2.2 1.036646e+08 12.000000 809.481865\n",
+ "2.3 1.103883e+08 12.000000 855.191710\n",
+ "2.4 1.356776e+08 12.000000 1044.380829\n",
+ "2.5 1.720562e+08 12.000000 1319.230570\n",
+ "2.6 2.225932e+08 12.000000 1504.556995\n",
+ "2.7 2.514645e+08 12.000000 1679.178756\n",
+ "2.8 2.930559e+08 12.000000 1901.264249\n",
+ "2.9 2.920653e+08 12.000000 1901.590674\n",
+ "3.0 3.956456e+08 12.000000 2707.658031"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "( \n",
+ " results_4\n",
+ " .groupby([\"W\"])\n",
+ " .agg(\"mean\")\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Aufgabe 5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "KeyboardInterrupt",
+ "evalue": "",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[1;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[1;32mIn[15], line 23\u001b[0m\n\u001b[0;32m 21\u001b[0m bfs_final \u001b[38;5;241m=\u001b[39m NodeBFS(ARRAY_SOLVED)\n\u001b[0;32m 22\u001b[0m start_time \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mperf_counter_ns()\n\u001b[1;32m---> 23\u001b[0m n, path \u001b[38;5;241m=\u001b[39m \u001b[43mfind_target_bfs\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbfs_start\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbfs_final\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 24\u001b[0m final_time \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mperf_counter_ns()\n\u001b[0;32m 25\u001b[0m runtime_bfs\u001b[38;5;241m.\u001b[39mappend(final_time\u001b[38;5;241m-\u001b[39mstart_time)\n",
+ "Cell \u001b[1;32mIn[8], line 26\u001b[0m, in \u001b[0;36mfind_target_bfs\u001b[1;34m(initial, final)\u001b[0m\n\u001b[0;32m 24\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m q\u001b[38;5;241m.\u001b[39mempty():\n\u001b[0;32m 25\u001b[0m node \u001b[38;5;241m=\u001b[39m q\u001b[38;5;241m.\u001b[39mget()\n\u001b[1;32m---> 26\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mchild\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mnext_nodes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m:\u001b[49m\n\u001b[0;32m 27\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mchild\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mnot\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mparent\u001b[49m\u001b[43m:\u001b[49m\n\u001b[0;32m 28\u001b[0m \u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\n",
+ "Cell \u001b[1;32mIn[6], line 20\u001b[0m, in \u001b[0;36mNodeBFS.next_nodes\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Generate other state nodes that from the current node.\u001b[39;00m\n\u001b[0;32m 10\u001b[0m \u001b[38;5;124;03m\u001b[39;00m\n\u001b[0;32m 11\u001b[0m \u001b[38;5;124;03mParameters:\u001b[39;00m\n\u001b[1;32m (...)\u001b[0m\n\u001b[0;32m 17\u001b[0m \u001b[38;5;124;03m a single move of the empty spot in the current state.\u001b[39;00m\n\u001b[0;32m 18\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m 19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m pos_new \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_next_positions():\n\u001b[1;32m---> 20\u001b[0m \u001b[38;5;28;01myield\u001b[39;00m \u001b[38;5;28;43mtype\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_make_new_state\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpos_new\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
+ "Cell \u001b[1;32mIn[4], line 16\u001b[0m, in \u001b[0;36mNode.__init__\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m 14\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstate \u001b[38;5;241m=\u001b[39m state\n\u001b[0;32m 15\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mempty_pos \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_empty_pos()\n\u001b[1;32m---> 16\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mhash_value \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mhash\u001b[39m(\u001b[38;5;28mrepr\u001b[39m(\u001b[38;5;28mself\u001b[39m))\n",
+ "Cell \u001b[1;32mIn[6], line 5\u001b[0m, in \u001b[0;36mNodeBFS.__repr__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__repr__\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m----> 5\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNodeBFS(\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstate\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m)\u001b[39m\u001b[38;5;124m\"\u001b[39m\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:1612\u001b[0m, in \u001b[0;36m_array_str_implementation\u001b[1;34m(a, max_line_width, precision, suppress_small, array2string)\u001b[0m\n\u001b[0;32m 1606\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m a\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m==\u001b[39m ():\n\u001b[0;32m 1607\u001b[0m \u001b[38;5;66;03m# obtain a scalar and call str on it, avoiding problems for subclasses\u001b[39;00m\n\u001b[0;32m 1608\u001b[0m \u001b[38;5;66;03m# for which indexing with () returns a 0d instead of a scalar by using\u001b[39;00m\n\u001b[0;32m 1609\u001b[0m \u001b[38;5;66;03m# ndarray's getindex. Also guard against recursive 0d object arrays.\u001b[39;00m\n\u001b[0;32m 1610\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m _guarded_repr_or_str(np\u001b[38;5;241m.\u001b[39mndarray\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__getitem__\u001b[39m(a, ()))\n\u001b[1;32m-> 1612\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43marray2string\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_line_width\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprecision\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msuppress_small\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m \u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:736\u001b[0m, in \u001b[0;36marray2string\u001b[1;34m(a, max_line_width, precision, suppress_small, separator, prefix, style, formatter, threshold, edgeitems, sign, floatmode, suffix, legacy)\u001b[0m\n\u001b[0;32m 733\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m a\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[0;32m 734\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m[]\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m--> 736\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_array2string\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moptions\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseparator\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprefix\u001b[49m\u001b[43m)\u001b[49m\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:513\u001b[0m, in \u001b[0;36m_recursive_guard.<locals>.decorating_function.<locals>.wrapper\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 511\u001b[0m repr_running\u001b[38;5;241m.\u001b[39madd(key)\n\u001b[0;32m 512\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m--> 513\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 514\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[0;32m 515\u001b[0m repr_running\u001b[38;5;241m.\u001b[39mdiscard(key)\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:539\u001b[0m, in \u001b[0;36m_array2string\u001b[1;34m(a, options, separator, prefix)\u001b[0m\n\u001b[0;32m 536\u001b[0m summary_insert \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m 538\u001b[0m \u001b[38;5;66;03m# find the right formatting function for the array\u001b[39;00m\n\u001b[1;32m--> 539\u001b[0m format_function \u001b[38;5;241m=\u001b[39m \u001b[43m_get_format_function\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43moptions\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 541\u001b[0m \u001b[38;5;66;03m# skip over \"[\"\u001b[39;00m\n\u001b[0;32m 542\u001b[0m next_line_prefix \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m\"\u001b[39m\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:467\u001b[0m, in \u001b[0;36m_get_format_function\u001b[1;34m(data, **options)\u001b[0m\n\u001b[0;32m 465\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m formatdict[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtimedelta\u001b[39m\u001b[38;5;124m'\u001b[39m]()\n\u001b[0;32m 466\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m--> 467\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mformatdict\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mint\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 468\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;28missubclass\u001b[39m(dtypeobj, _nt\u001b[38;5;241m.\u001b[39mfloating):\n\u001b[0;32m 469\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28missubclass\u001b[39m(dtypeobj, _nt\u001b[38;5;241m.\u001b[39mlongfloat):\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:410\u001b[0m, in \u001b[0;36m_get_formatdict.<locals>.<lambda>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 403\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_get_formatdict\u001b[39m(data, \u001b[38;5;241m*\u001b[39m, precision, floatmode, suppress, sign, legacy,\n\u001b[0;32m 404\u001b[0m formatter, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m 405\u001b[0m \u001b[38;5;66;03m# note: extra arguments in kwargs are ignored\u001b[39;00m\n\u001b[0;32m 406\u001b[0m \n\u001b[0;32m 407\u001b[0m \u001b[38;5;66;03m# wrapped in lambdas to avoid taking a code path with the wrong type of data\u001b[39;00m\n\u001b[0;32m 408\u001b[0m formatdict \u001b[38;5;241m=\u001b[39m {\n\u001b[0;32m 409\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mbool\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: BoolFormat(data),\n\u001b[1;32m--> 410\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mint\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: \u001b[43mIntegerFormat\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdata\u001b[49m\u001b[43m)\u001b[49m,\n\u001b[0;32m 411\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfloat\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: FloatingFormat(\n\u001b[0;32m 412\u001b[0m data, precision, floatmode, suppress, sign, legacy\u001b[38;5;241m=\u001b[39mlegacy),\n\u001b[0;32m 413\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlongfloat\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: FloatingFormat(\n\u001b[0;32m 414\u001b[0m data, precision, floatmode, suppress, sign, legacy\u001b[38;5;241m=\u001b[39mlegacy),\n\u001b[0;32m 415\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcomplexfloat\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: ComplexFloatingFormat(\n\u001b[0;32m 416\u001b[0m data, precision, floatmode, suppress, sign, legacy\u001b[38;5;241m=\u001b[39mlegacy),\n\u001b[0;32m 417\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlongcomplexfloat\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: ComplexFloatingFormat(\n\u001b[0;32m 418\u001b[0m data, precision, floatmode, suppress, sign, legacy\u001b[38;5;241m=\u001b[39mlegacy),\n\u001b[0;32m 419\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mdatetime\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: DatetimeFormat(data, legacy\u001b[38;5;241m=\u001b[39mlegacy),\n\u001b[0;32m 420\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtimedelta\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: TimedeltaFormat(data),\n\u001b[0;32m 421\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mobject\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: _object_format,\n\u001b[0;32m 422\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mvoid\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: str_format,\n\u001b[0;32m 423\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mnumpystr\u001b[39m\u001b[38;5;124m'\u001b[39m: \u001b[38;5;28;01mlambda\u001b[39;00m: repr_format}\n\u001b[0;32m 425\u001b[0m \u001b[38;5;66;03m# we need to wrap values in `formatter` in a lambda, so that the interface\u001b[39;00m\n\u001b[0;32m 426\u001b[0m \u001b[38;5;66;03m# is the same as the above values.\u001b[39;00m\n\u001b[0;32m 427\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mindirect\u001b[39m(x):\n",
+ "File \u001b[1;32m~\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\arrayprint.py:1229\u001b[0m, in \u001b[0;36mIntegerFormat.__init__\u001b[1;34m(self, data)\u001b[0m\n\u001b[0;32m 1227\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m 1228\u001b[0m max_str_len \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n\u001b[1;32m-> 1229\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mformat \u001b[38;5;241m=\u001b[39m \u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m%\u001b[39;49m\u001b[38;5;132;43;01m{}\u001b[39;49;00m\u001b[38;5;124;43md\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mformat\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmax_str_len\u001b[49m\u001b[43m)\u001b[49m\n",
+ "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
+ ]
+ }
+ ],
+ "source": [
+ "ARRAY = np.array(((4, 8, 3),\n",
+ " (7, 6, 2),\n",
+ " (5, 1, 0)), dtype=int)\n",
+ "\n",
+ "ARRAY_SOLVED = np.array(((1, 2, 3),\n",
+ " (4, 5, 6),\n",
+ " (7, 8, 0)), dtype=int)\n",
+ "\n",
+ "solvable_bfs = []\n",
+ "runtime_bfs = []\n",
+ "visited_nodes_bfs = []\n",
+ "solvable_greedy = []\n",
+ "runtime_greedy = []\n",
+ "visited_nodes_greedy = []\n",
+ "solvable_astar = []\n",
+ "runtime_astar = []\n",
+ "visited_nodes_astar = []\n",
+ "for i in range(100):\n",
+ " print(f\"i: {i}\")\n",
+ " np.random.shuffle(ARRAY)\n",
+ " bfs_start = NodeBFS(ARRAY)\n",
+ " bfs_final = NodeBFS(ARRAY_SOLVED)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = find_target_bfs(bfs_start, bfs_final)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_bfs.append(final_time-start_time)\n",
+ " visited_nodes_bfs.append(n)\n",
+ " solvable_bfs.append(n == -1)\n",
+ " if n == -1:\n",
+ " greedy_start = NodeGreedy(ARRAY, manhatten_distance(ARRAY, ARRAY_SOLVED))\n",
+ " greedy_final = NodeGreedy(ARRAY_SOLVED, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(greedy_start, greedy_final, manhatten_distance)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_greedy.append(final_time-start_time)\n",
+ " visited_nodes_greedy.append(n)\n",
+ " solvable_greedy.append(n == -1)\n",
+ "\n",
+ " astar_start = NodeAstar(ARRAY, 0, manhatten_distance(ARRAY, ARRAY_SOLVED))\n",
+ " astar_final = NodeAstar(ARRAY_SOLVED, -1, 0)\n",
+ " start_time = time.perf_counter_ns()\n",
+ " n, path = informed_search(astar_start, astar_final, manhatten_distance)\n",
+ " final_time = time.perf_counter_ns()\n",
+ " runtime_astar.append(final_time-start_time)\n",
+ " visited_nodes_astar.append(n)\n",
+ " solvable_astar.append(n == -1)\n",
+ " runtime_greedy.append(None)\n",
+ " visited_nodes_greedy.append(None)\n",
+ " solvable_greedy.append(None)\n",
+ " runtime_astar.append(None)\n",
+ " visited_nodes_astar.append(None)\n",
+ " solvable_astar.append(None)\n",
+ "\n",
+ "results_5 = pd.DataFrame({\n",
+ " \"Lösbarkeit BFS\": solvable_bfs,\n",
+ " \"Besuchte Knoten BFS\": visited_nodes_bfs,\n",
+ " \"Laufzeit BFS\": runtime_bfs,\n",
+ "\n",
+ " \"Lösbarkeit Greedy\": solvable_greedy,\n",
+ " \"Besuchte Knoten Greedy\": visited_nodes_greedy,\n",
+ " \"Laufzeit Greedy\": runtime_greedy,\n",
+ "\n",
+ " \"Lösbarkeit A*\": solvable_astar,\n",
+ " \"Besuchte Knoten A*\": visited_nodes_astar,\n",
+ " \"Laufzeit A*\": runtime_astar,\n",
+ "})\n",
+ "\n",
+ "\n",
+ "results_5.to_csv(\"results_5.csv\")\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
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+\documentclass{article}
+\usepackage[utf8]{inputenc}
+\usepackage[ngerman]{babel}
+\usepackage{float}
+\usepackage{graphicx}
+\graphicspath{{C:/Users/Tom/Desktop/Dateien/Uni/Gießen/KI_II/Hausaufgaben/gitlab_ki_ii_ha/Tom/images}}
+\usepackage{geometry}
+\usepackage{listings}
+\usepackage{multirow}
+\geometry{left=2cm, right=2cm, top=2.5cm, bottom=2cm}
+\usepackage{xcolor}
+\usepackage{amsmath}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.95}
+\lstdefinestyle{mystyle}{
+ backgroundcolor=\color{backcolour},
+ commentstyle=\color{codegreen},
+ keywordstyle=\color{magenta},
+ numberstyle=\tiny\color{codegray},
+ stringstyle=\color{codepurple},
+ basicstyle=\ttfamily\footnotesize,
+ breakatwhitespace=false,
+ breaklines=true,
+ captionpos=b,
+ keepspaces=true,
+ numbers=left,
+ numbersep=5pt,
+ showspaces=false,
+ showstringspaces=false,
+ showtabs=false,
+ tabsize=2
+}
+\lstset{style=mystyle}
+\title{KI II: Hausaufgabe 03 und 04}
+\author{Tom Schmidt}
+\date{Mai 2024}
+\begin{document}
+\maketitle
+\section*{Aufgabe 1: 8er Puzzle - andere Heuristiken}
+\subsection*{Quellcode für die beiden neuen Heuristiken}
+\begin{lstlisting}[language=Python]
+def manhatten_distance(state, final_state):
+ """Compute the manhattan distance between two arrays of identical shape"""
+ distance = 0
+ for i, row in enumerate(state):
+ for j, value in enumerate(row):
+ if value != 0:
+ x, y = np.where(final_state == value)
+ distance += abs(x[0]-i) + abs(y[0]-j)
+ return distance
+
+def euclidian_distance(state, final_state):
+ """Compute the euclidian distance between two arrays of identical shape"""
+ distance = 0
+ for i, row in enumerate(state):
+ for j, value in enumerate(row):
+ if value != 0:
+ x, y = np.where(final_state == value)
+ distance += m.sqrt(pow((x[0]-i), 2) + pow((y[0]-j),2))
+ return distance
+\end{lstlisting}
+\subsection*{Ergebnisse}
+\begin{table}[h!]
+\centering
+\begin{tabular}{| c | c |}
+\hline
+Heuristik & Wert für die beiden oben angegebenen Zustände\\
+\hline
+Anzahl falscher Positionen (siehe VL) & 7 \\
+Euklidischer Abstand & 14 \\
+Manhatten-Abstand & 11.30056307974577 \\
+\hline
+\end{tabular}
+\caption{Abstands-Heuristiken für die vorgegebenen ARRAY\_INITIAL und ARRAY\_FINAL}
+\end{table}
+\begin{table}[h!]
+\centering
+\begin{tabular}{| c | c | c | c |}
+\hline
+Algoritmus & Heuristik & Anzahl besuchter Knoten & Länge des Pfades \\
+\hline
+\multirow{3}{2.5em}{Greedy} & Anzahl falscher Positionen (siehe VL) & 490 & 27 \\
+& Euklidischer Abstand & 333 & 41 \\
+& Manhattan-Abstand & 83 & 33 \\
+\hline
+\multirow{3}{1em}{A*} & Anzahl falscher Positionen (siehe VL) & 1048 & 17 \\
+& Euklidischer Abstand & 107 & 17 \\
+& Manhattan-Abstand & 143 & 17 \\
+\hline
+\end{tabular}
+\caption{Durchschnittswerte der unterschiedlichen Such-Algorithmen}
+\end{table}
+
+
+\section*{Aufgabe 2: 8er Puzzle - Benchmark}
+Dargestellt werden stets Durchschnittswerte über alle in der Datenbank verfügbaren Puzzel einer bestimmten Tiefe.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_1}
+ \caption{Ausführungszeiten in Abhängigkeit der Lösungstiefe}
+\end{figure}
+Es ist deutlich zu sehen, dass die Ausführungszeiten der Greedy-Suche und A* auf der logarithmischen Skala mit der Tiefe linear (d.h. in echt exponentiell) steigen. A* beginnt dabei deutlich niedriger und behält diesen Abstand (d.h. auch dieser nimmt auf einer nicht logarithmischen Skala exponentiell zu). Die Ausführungszeiten der Greedy-Suche hingegen flachen nach einer Tiefe von 8 deutlich ab (auf einer nicht logarithmischen Skala würden sie linear zunehmen).
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_2}
+ \caption{Anzahl an Schritten der gefunden Lösung in Abhängigkeit der Lösungstiefe}
+\end{figure}
+Die BFS-Suche wurde hier nur zum Vergleich dargestellt. Sie ist optimal und bildet damit die Funktion $f(x) = x$ ab. Die nicht-optimale Greedy-Suche beginnt ca. ab Tiefe 7 Lösungen zu finden, die immer weiter von der optimalen Lösung entfernt liegen. Während die euklidische- und die Manhattan-Heuristik dabei einen fast identisch Verlauf zeigen, findet die Difference-Heuristik auch im Vergleich zu diesen zunehmend schlechtere Lösungen.
+
+\newpage
+Da A* optimal ist, aber längere Ausführungszeiten aufweist (die dazu auch noch exponentiell mit der Lösungstiefe steigen) und die Greedy-Suche deutlich kürzere Ausführungszeiten benötigt, aber zunehmend schlechtere Lösungen findet, ist die Auswahl des `besten` Algorithmus eine Frage der Gewichtung zwischen diesen beiden Faktoren. Ich würde aufgrund der Optimalität zu A* tendieren, da die durchschnittliche Ausführungszeit selbst bei Tiefe 20 sehr kurz ist (0,1379561 Sekunden für Manhattan-Abstand). Die beste Heuristik ist der Manhattan-Abstand, da er hinsichtlich Ausführungszeit deutlich überlegen und hinsichtlich Pfadlänge zur zweitbesten Heuristik, dem euklidischen Abstand, praktisch identisch ist.
+\section*{Aufgabe 3: 8er Puzzle - Skalierung}
+Ich nehme an, dass wir für die Bestimmung des mittleren Skalierungsgesetzes zunächst selbst einen grundlegenden Funktionszusammenhang wählen müssen. Für die Tiefe lege ich diesen analytisch durch die Überlegungen zur Komplexität der Such-Algorithmen in der Vorlesung als $f(x) = c \cdot b^x$ fest (Ergebnisse in (1)). Für die besuchten Knoten entscheide ich mich nach einer kurzen explorativen Datenanalyse für einen linearen Zusammenhang der Form $f(x) = bx + c$ (Ergebnisse in (2)).
+Alternativ könnte auch ein Skalierungsgesetz der Ausführungszeit in Abhängigkeit von besuchten Konten und optimale Tiefe gemeint sein. Der grundlegende Zusammenhang wäre dann \[\text{Ausführungszeit(Knoten, Tiefe)} = c \cdot \text{Knoten} \cdot b^{\text{Tiefe}}\]
+Diese dreidimensionalen Funktionen lassen sich schlechter darstellen, aber ich bestimme sie trotzdem und gebe sie im letzten Abschnitt (3) dieser Aufgabe an.
+\subsection*{(1) Mittlere Skalierungsgesetze in Abhängigkeit der besuchten Konten}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_4}
+ \caption{\large{$f(x) = 84248,22970039019 \cdot x + 32320045.70097196$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_5}
+ \caption{\large{$f(x) = 97793.62881363 \cdot x -734727.1035676643$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_6}
+ \caption{\large{$f(x) = 132767.73454286708 \cdot x -348828.474575256$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_7}
+ \caption{\large{$f(x) = 128448.46390735488 \cdot x -390310.96235161996$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_8}
+ \caption{\large{$f(x) = 93936.09172683966 \cdot x -3340801.1885135137$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_9}
+ \caption{\large{$f(x) = 123092.8176687587 \cdot x -2135648.050355018$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_10}
+ \caption{\large{$f(x) = 118732.83441765835 \cdot x -1825991.1906389832$}}
+\end{figure}
+
+\subsection*{(2) Mittlere Skalierungsgesetze in Abhängigkeit der optimalen Tiefe}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_3}
+ \caption{\large{$f(x) = 1397078,4256394417 \cdot 1,4934757474967757^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_11}
+ \caption{\large{$f(x) = 15829449.91762724 \cdot 1.1040853671478799^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_12}
+ \caption{\large{$f(x) = 6647786.303387479 \cdot 1.1245066542998425^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_13}
+ \caption{\large{$f(x) = 4085261.428709779 \cdot 1.141818450947134^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_!4}
+ \caption{\large{$f(x) = 99969.87525556808 \cdot 1.5692736067710622^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_15}
+ \caption{\large{$f(x) = 82799.55093950704 \cdot 1.4813236373618255^x$}}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_16}
+ \caption{\large{$f(x) = 126997.29495831158 \cdot 1.4180160045233512^x$}}
+\end{figure}
+
+\subsection*{(3) Mittlere Skalierungsgesetze in Abhängigkeit der besuchten Konten UND optimalen Tiefe}
+Hier die Ergebnisse für den mittleren Zusammenhang der Form $\text{Ausführungszeit(Knoten, Tiefe)} = c \cdot \text{Knoten} \cdot b^{\text{Tiefe}}$ für alle Algorithmen und Heuristiken.
+\subsubsection*{Zusammenhang für BFS:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 77039,43719692642 \cdot \text{Knoten} \cdot 1,0055919559514195^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für Greedy mit Difference Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 97266,1288263614 \cdot \text{Knoten} \cdot 0,9999131616926763^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für Greedy mit Euklidisch Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 131654,15115619134 \cdot \text{Knoten} \cdot 1,0001474034274616^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für Greedy mit Manhattan Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 127231,03942668319 \cdot \text{Knoten} \cdot 1,0001122266989912^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für A* mit Difference Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 73891,13778835062 \cdot \text{Knoten} \cdot 1,012228255704712^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für A* mit Euklidisch Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 94983,46672895551 \cdot \text{Knoten} \cdot 1,0129346800844947^{\text{Tiefe}}\]
+\subsubsection*{Zusammenhang für A* mit Manhattan Heuristik:}
+\[\text{Ausführungszeit(Knoten, Tiefe)} = 92500,85226522778 \cdot \text{Knoten} \cdot 1,0123224209580304^{\text{Tiefe}}\]
+
+\section*{Aufgabe 4: 8er Puzzle - alternative Heuristik}
+\subsection*{a)}
+Der vorgeschlagenen Algorithmus ist für alle Werte von $\omega$ vollständig, da die A*-Suche unabhängig von der Gesamtkostenfunktion den gesamten Suchbaum exploriert (falls nicht früher eine Lösung gefunden wird).
+\subsection*{b)}
+Die A*-Suche ist optimal, wenn $h(s)$ zulässig ist. Die Gesamtkostenfunktion wird verwendet, um potentiell zu explorierende Blattknoten zu vergleichen d.h. ihr Absolutwert spielt keine Rolle. Wir können somit den vorgeschlagenen Algorithmus anhand des Verhältnisses zwischen $8\omega$ und $9-\omega^2$ untersuchen. Eine stärkere Gewichtung von $g(s)$ ist dabei unproblematisch, aber eine stärkere Gewichtung von $h(s)$ führt zu einer potentiellen Überschätzung der Kosten durch den Heuristik-Anteil der Gesamtkostenfunktion und damit zu einer nicht garantiert optimalen Suche.
+
+Für $\omega < 0$ wird $8\omega$ negativ und der vorgeschlagenen Algorithmus somit nicht optimal.
+
+Für $\omega = 0$ wird $8\omega$ zu Null und der vorgeschlagenen Algorithmus somit nicht optimal.
+
+Für $0 < \omega < 1$ wird $8\omega$ kleiner als $9-\omega^2$ und der vorgeschlagenen Algorithmus somit nicht optimal.
+
+\textbf{Für $1\leq \omega \leq 3$ wird $8\omega$ größer als $9-\omega^2$ und der vorgeschlagenen Algorithmus somit optimal.}
+
+Für $\omega > 3$ wird $9-\omega^2$ negativ und der vorgeschlagenen Algorithmus somit nicht optimal.
+
+\subsection*{c)}
+Für $\omega = 3$ wird $9-\omega^2$ zu Null und der vorgeschlagenen Algorithmus somit äquivalent zur Uniform-Cost-Search.
+
+\subsection*{d)}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_17}
+ \caption{Pfadlänge in Abhängigkeit von $\omega$}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_18}
+ \caption{Zeit in Abhängigkeit von $\omega$}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\linewidth]{3_19}
+ \caption{Besuchte Knoten in Abhängigkeit von $\omega$}
+\end{figure}
+
+Die besten Werte in allen drei Metriken (Zeit, Besuchte Knoten, Pfadlänge) wird mit $\omega = 0,8$ erreicht. Allerdings ist $\omega = 0,8$ nicht garantiert optimal (siehe oben) und $\omega = 1$ nur knapp unterlegen. Deswegen halte ich $\omega = 1$ für die `beste` Wahl.
+
+
+\section*{Aufgabe 5: 8er Puzzle - Lösbarkeit}
+\end{document}
+
+
+
+
+
+
+
+
+
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diff --git a/Tom/results.csv b/Tom/results.csv
new file mode 100644
index 0000000000000000000000000000000000000000..7cb7fd20703e95af137599b0f564a783f788cfbd
--- /dev/null
+++ b/Tom/results.csv
@@ -0,0 +1,13784 @@
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+4058,Greedy,Euklidisch,6,13,7,1286100
+4059,Greedy,Euklidisch,6,13,7,1298200
+4060,Greedy,Euklidisch,6,13,7,1366000
+4061,Greedy,Euklidisch,6,13,7,1213700
+4062,Greedy,Euklidisch,6,13,7,1211100
+4063,Greedy,Euklidisch,6,13,7,1286500
+4064,Greedy,Euklidisch,6,13,7,1292800
+4065,Greedy,Euklidisch,6,13,7,1279400
+4066,Greedy,Euklidisch,6,13,7,1324700
+4067,Greedy,Euklidisch,6,11,7,1215100
+4068,Greedy,Euklidisch,6,12,7,1214800
+4069,Greedy,Euklidisch,6,15,7,1438700
+4070,Greedy,Euklidisch,6,11,7,1126000
+4071,Greedy,Euklidisch,6,13,7,1237500
+4072,Greedy,Euklidisch,6,10,7,1138400
+4073,Greedy,Euklidisch,6,11,7,1070600
+4074,Greedy,Euklidisch,6,13,7,1286000
+4075,Greedy,Euklidisch,6,13,7,1289200
+4076,Greedy,Euklidisch,6,13,7,1284900
+4077,Greedy,Euklidisch,6,13,7,1316000
+4078,Greedy,Euklidisch,6,13,7,1288700
+4079,Greedy,Euklidisch,6,10,7,1001800
+4080,Greedy,Euklidisch,8,18,9,2037300
+4081,Greedy,Euklidisch,8,21,9,2186000
+4082,Greedy,Euklidisch,8,18,9,1882500
+4083,Greedy,Euklidisch,8,13,9,1486300
+4084,Greedy,Euklidisch,8,18,9,1837200
+4085,Greedy,Euklidisch,8,21,9,2204000
+4086,Greedy,Euklidisch,8,16,9,1659300
+4087,Greedy,Euklidisch,8,20,9,2112300
+4088,Greedy,Euklidisch,8,16,9,1659400
+4089,Greedy,Euklidisch,8,16,9,1875700
+4090,Greedy,Euklidisch,8,18,9,1807800
+4091,Greedy,Euklidisch,8,16,9,1726500
+4092,Greedy,Euklidisch,8,18,9,1794800
+4093,Greedy,Euklidisch,8,18,9,1833300
+4094,Greedy,Euklidisch,8,16,9,1666400
+4095,Greedy,Euklidisch,8,18,9,1835900
+4096,Greedy,Euklidisch,8,16,9,1663800
+4097,Greedy,Euklidisch,8,22,9,2289200
+4098,Greedy,Euklidisch,8,17,9,2204800
+4099,Greedy,Euklidisch,8,16,9,1789800
+4100,Greedy,Euklidisch,8,18,9,1945900
+4101,Greedy,Euklidisch,8,18,9,1857600
+4102,Greedy,Euklidisch,8,18,9,1921500
+4103,Greedy,Euklidisch,8,18,9,1933900
+4104,Greedy,Euklidisch,8,17,9,1769000
+4105,Greedy,Euklidisch,8,21,9,2516700
+4106,Greedy,Euklidisch,8,16,9,1784500
+4107,Greedy,Euklidisch,8,18,9,2174700
+4108,Greedy,Euklidisch,8,18,9,2171300
+4109,Greedy,Euklidisch,8,18,9,1879300
+4110,Greedy,Euklidisch,8,21,9,2329700
+4111,Greedy,Euklidisch,8,16,9,1826700
+4112,Greedy,Euklidisch,8,20,9,2275700
+4113,Greedy,Euklidisch,8,17,9,1897100
+4114,Greedy,Euklidisch,8,18,9,1991700
+4115,Greedy,Euklidisch,8,18,9,2011400
+4116,Greedy,Euklidisch,8,18,9,1928500
+4117,Greedy,Euklidisch,8,18,9,1953200
+4118,Greedy,Euklidisch,8,18,9,1954900
+4119,Greedy,Euklidisch,8,28,9,3200900
+4120,Greedy,Euklidisch,8,16,9,1836500
+4121,Greedy,Euklidisch,8,18,9,1953700
+4122,Greedy,Euklidisch,8,21,9,2451800
+4123,Greedy,Euklidisch,8,18,9,2014200
+4124,Greedy,Euklidisch,8,16,9,1698600
+4125,Greedy,Euklidisch,8,18,9,1936800
+4126,Greedy,Euklidisch,8,26,11,2894900
+4127,Greedy,Euklidisch,8,124,33,16051500
+4128,Greedy,Euklidisch,8,18,9,2206500
+4129,Greedy,Euklidisch,8,17,9,1849100
+4130,Greedy,Euklidisch,8,15,9,1609500
+4131,Greedy,Euklidisch,8,16,9,1816300
+4132,Greedy,Euklidisch,8,21,9,2559700
+4133,Greedy,Euklidisch,8,18,9,1951000
+4134,Greedy,Euklidisch,8,16,9,1764300
+4135,Greedy,Euklidisch,8,23,9,2697200
+4136,Greedy,Euklidisch,8,15,9,1620300
+4137,Greedy,Euklidisch,8,15,9,1623900
+4138,Greedy,Euklidisch,8,60,9,7526200
+4139,Greedy,Euklidisch,8,21,9,2330600
+4140,Greedy,Euklidisch,8,16,9,1878100
+4141,Greedy,Euklidisch,8,21,9,2475300
+4142,Greedy,Euklidisch,8,18,9,2072200
+4143,Greedy,Euklidisch,8,20,9,2205500
+4144,Greedy,Euklidisch,8,14,9,1614300
+4145,Greedy,Euklidisch,8,18,9,1983200
+4146,Greedy,Euklidisch,8,23,9,2816600
+4147,Greedy,Euklidisch,8,15,9,1722000
+4148,Greedy,Euklidisch,8,15,9,1624500
+4149,Greedy,Euklidisch,8,344,37,47077500
+4150,Greedy,Euklidisch,8,18,9,2043800
+4151,Greedy,Euklidisch,8,16,9,1754800
+4152,Greedy,Euklidisch,8,16,9,1700800
+4153,Greedy,Euklidisch,8,18,9,1984500
+4154,Greedy,Euklidisch,8,15,9,1620400
+4155,Greedy,Euklidisch,8,16,9,1725000
+4156,Greedy,Euklidisch,8,16,9,1964200
+4157,Greedy,Euklidisch,8,271,9,36351800
+4158,Greedy,Euklidisch,8,18,9,2132200
+4159,Greedy,Euklidisch,8,18,9,1941700
+4160,Greedy,Euklidisch,8,21,9,2338600
+4161,Greedy,Euklidisch,8,18,9,1921200
+4162,Greedy,Euklidisch,8,262,41,35182100
+4163,Greedy,Euklidisch,8,15,9,1678600
+4164,Greedy,Euklidisch,8,18,9,1928300
+4165,Greedy,Euklidisch,8,17,9,1817600
+4166,Greedy,Euklidisch,8,16,9,1772700
+4167,Greedy,Euklidisch,8,21,9,2518900
+4168,Greedy,Euklidisch,8,16,9,1906700
+4169,Greedy,Euklidisch,8,16,9,1774100
+4170,Greedy,Euklidisch,8,16,9,1775400
+4171,Greedy,Euklidisch,8,18,9,1953900
+4172,Greedy,Euklidisch,8,18,9,1903100
+4173,Greedy,Euklidisch,8,15,9,1691800
+4174,Greedy,Euklidisch,8,21,9,2319900
+4175,Greedy,Euklidisch,8,15,9,1821800
+4176,Greedy,Euklidisch,8,17,9,2044700
+4177,Greedy,Euklidisch,8,16,9,1782000
+4178,Greedy,Euklidisch,8,15,9,1694000
+4179,Greedy,Euklidisch,8,16,9,1815300
+4180,Greedy,Euklidisch,8,18,9,2022800
+4181,Greedy,Euklidisch,8,18,9,1936400
+4182,Greedy,Euklidisch,8,21,9,2317600
+4183,Greedy,Euklidisch,8,234,41,31334100
+4184,Greedy,Euklidisch,8,16,9,1962900
+4185,Greedy,Euklidisch,8,16,9,1719900
+4186,Greedy,Euklidisch,8,16,9,1772800
+4187,Greedy,Euklidisch,8,18,9,2065600
+4188,Greedy,Euklidisch,8,18,9,2079600
+4189,Greedy,Euklidisch,8,246,9,32957600
+4190,Greedy,Euklidisch,8,15,9,1692700
+4191,Greedy,Euklidisch,8,15,9,1624300
+4192,Greedy,Euklidisch,8,21,9,2373600
+4193,Greedy,Euklidisch,8,18,9,2059800
+4194,Greedy,Euklidisch,8,17,9,1870200
+4195,Greedy,Euklidisch,8,18,9,1946200
+4196,Greedy,Euklidisch,8,16,9,1765900
+4197,Greedy,Euklidisch,8,48,11,5922400
+4198,Greedy,Euklidisch,8,14,9,1658000
+4199,Greedy,Euklidisch,8,17,9,1909800
+4200,Greedy,Euklidisch,8,22,9,2484300
+4201,Greedy,Euklidisch,8,66,9,8238200
+4202,Greedy,Euklidisch,8,18,9,1921400
+4203,Greedy,Euklidisch,8,15,9,1726800
+4204,Greedy,Euklidisch,8,16,9,1760400
+4205,Greedy,Euklidisch,8,18,9,1924700
+4206,Greedy,Euklidisch,8,16,9,1761700
+4207,Greedy,Euklidisch,8,16,9,1777400
+4208,Greedy,Euklidisch,8,16,9,1770200
+4209,Greedy,Euklidisch,8,21,9,2458300
+4210,Greedy,Euklidisch,8,16,9,1731900
+4211,Greedy,Euklidisch,8,22,9,2568100
+4212,Greedy,Euklidisch,8,14,9,1629600
+4213,Greedy,Euklidisch,8,23,9,2547900
+4214,Greedy,Euklidisch,8,16,9,1766600
+4215,Greedy,Euklidisch,8,18,9,1922900
+4216,Greedy,Euklidisch,8,16,9,1765300
+4217,Greedy,Euklidisch,8,77,9,9945200
+4218,Greedy,Euklidisch,8,21,9,2356400
+4219,Greedy,Euklidisch,8,18,9,1936400
+4220,Greedy,Euklidisch,8,21,9,2325400
+4221,Greedy,Euklidisch,8,16,9,1790100
+4222,Greedy,Euklidisch,8,15,9,1989800
+4223,Greedy,Euklidisch,8,15,9,1745500
+4224,Greedy,Euklidisch,8,13,9,1469600
+4225,Greedy,Euklidisch,8,18,9,1991100
+4226,Greedy,Euklidisch,8,14,9,1597100
+4227,Greedy,Euklidisch,8,15,9,1865400
+4228,Greedy,Euklidisch,8,18,9,1891700
+4229,Greedy,Euklidisch,8,16,9,1810400
+4230,Greedy,Euklidisch,8,16,9,1864700
+4231,Greedy,Euklidisch,8,16,9,1848600
+4232,Greedy,Euklidisch,8,19,9,2170100
+4233,Greedy,Euklidisch,8,17,9,1843600
+4234,Greedy,Euklidisch,8,18,9,1949300
+4235,Greedy,Euklidisch,8,18,9,1929900
+4236,Greedy,Euklidisch,8,214,9,28816200
+4237,Greedy,Euklidisch,8,13,9,1543700
+4238,Greedy,Euklidisch,8,16,9,1790000
+4239,Greedy,Euklidisch,8,15,9,1617600
+4240,Greedy,Euklidisch,8,20,9,2518500
+4241,Greedy,Euklidisch,8,18,9,2020200
+4242,Greedy,Euklidisch,8,21,9,2626900
+4243,Greedy,Euklidisch,8,16,9,1770800
+4244,Greedy,Euklidisch,8,15,9,1616600
+4245,Greedy,Euklidisch,8,15,9,1726400
+4246,Greedy,Euklidisch,8,15,9,1690300
+4247,Greedy,Euklidisch,8,16,9,1754600
+4248,Greedy,Euklidisch,8,15,9,1735500
+4249,Greedy,Euklidisch,8,16,9,1753700
+4250,Greedy,Euklidisch,8,21,9,2506000
+4251,Greedy,Euklidisch,8,15,9,1771000
+4252,Greedy,Euklidisch,8,20,9,2194700
+4253,Greedy,Euklidisch,8,191,51,25221900
+4254,Greedy,Euklidisch,8,18,9,2057100
+4255,Greedy,Euklidisch,8,16,9,1872400
+4256,Greedy,Euklidisch,8,234,33,31293400
+4257,Greedy,Euklidisch,8,16,9,1706800
+4258,Greedy,Euklidisch,8,18,9,2222400
+4259,Greedy,Euklidisch,8,16,9,1827900
+4260,Greedy,Euklidisch,8,18,9,1931800
+4261,Greedy,Euklidisch,8,280,9,37460500
+4262,Greedy,Euklidisch,8,15,9,1624400
+4263,Greedy,Euklidisch,8,17,9,1874600
+4264,Greedy,Euklidisch,8,16,9,1695300
+4265,Greedy,Euklidisch,8,28,9,3203600
+4266,Greedy,Euklidisch,8,18,9,2011900
+4267,Greedy,Euklidisch,8,15,9,2145100
+4268,Greedy,Euklidisch,8,18,9,1990100
+4269,Greedy,Euklidisch,8,16,9,1754900
+4270,Greedy,Euklidisch,8,338,35,44641400
+4271,Greedy,Euklidisch,8,16,9,2031500
+4272,Greedy,Euklidisch,8,48,11,5760800
+4273,Greedy,Euklidisch,8,15,9,1705300
+4274,Greedy,Euklidisch,8,18,9,1951500
+4275,Greedy,Euklidisch,8,238,39,32130300
+4276,Greedy,Euklidisch,8,18,9,2028300
+4277,Greedy,Euklidisch,8,49,9,6128800
+4278,Greedy,Euklidisch,8,16,9,2029400
+4279,Greedy,Euklidisch,8,16,9,1772000
+4280,Greedy,Euklidisch,8,167,37,21745000
+4281,Greedy,Euklidisch,10,114,11,13995000
+4282,Greedy,Euklidisch,10,19,11,2409700
+4283,Greedy,Euklidisch,10,21,11,2350200
+4284,Greedy,Euklidisch,10,279,45,37046700
+4285,Greedy,Euklidisch,10,21,11,2247100
+4286,Greedy,Euklidisch,10,21,11,2328900
+4287,Greedy,Euklidisch,10,21,11,2637600
+4288,Greedy,Euklidisch,10,24,11,2715100
+4289,Greedy,Euklidisch,10,23,11,2659100
+4290,Greedy,Euklidisch,10,23,11,2467700
+4291,Greedy,Euklidisch,10,21,11,2330100
+4292,Greedy,Euklidisch,10,24,11,2690400
+4293,Greedy,Euklidisch,10,193,37,25019300
+4294,Greedy,Euklidisch,10,32,11,3595900
+4295,Greedy,Euklidisch,10,20,11,2255700
+4296,Greedy,Euklidisch,10,179,49,23749300
+4297,Greedy,Euklidisch,10,21,11,2424500
+4298,Greedy,Euklidisch,10,247,43,33096600
+4299,Greedy,Euklidisch,10,21,11,2421900
+4300,Greedy,Euklidisch,10,282,39,38333200
+4301,Greedy,Euklidisch,10,21,11,2383300
+4302,Greedy,Euklidisch,10,182,39,24163100
+4303,Greedy,Euklidisch,10,18,11,2249100
+4304,Greedy,Euklidisch,10,24,11,2962900
+4305,Greedy,Euklidisch,10,23,11,2524500
+4306,Greedy,Euklidisch,10,267,41,35762300
+4307,Greedy,Euklidisch,10,24,11,2784600
+4308,Greedy,Euklidisch,10,321,41,43109300
+4309,Greedy,Euklidisch,10,20,11,2219500
+4310,Greedy,Euklidisch,10,19,11,2661800
+4311,Greedy,Euklidisch,10,289,41,37994600
+4312,Greedy,Euklidisch,10,20,11,2212300
+4313,Greedy,Euklidisch,10,19,11,2224000
+4314,Greedy,Euklidisch,10,23,11,2510900
+4315,Greedy,Euklidisch,10,20,11,2419600
+4316,Greedy,Euklidisch,10,19,11,2238000
+4317,Greedy,Euklidisch,10,18,11,2157600
+4318,Greedy,Euklidisch,10,70,23,8994300
+4319,Greedy,Euklidisch,10,21,11,2453700
+4320,Greedy,Euklidisch,10,21,11,2277300
+4321,Greedy,Euklidisch,10,21,11,2404700
+4322,Greedy,Euklidisch,10,23,11,2849900
+4323,Greedy,Euklidisch,10,23,11,2691600
+4324,Greedy,Euklidisch,10,21,11,2369400
+4325,Greedy,Euklidisch,10,23,11,2690500
+4326,Greedy,Euklidisch,10,240,39,32731800
+4327,Greedy,Euklidisch,10,18,11,2131300
+4328,Greedy,Euklidisch,10,21,11,2362200
+4329,Greedy,Euklidisch,10,24,11,2758000
+4330,Greedy,Euklidisch,10,26,11,2916900
+4331,Greedy,Euklidisch,10,60,19,7597100
+4332,Greedy,Euklidisch,10,29,13,3328900
+4333,Greedy,Euklidisch,10,20,11,2205000
+4334,Greedy,Euklidisch,10,23,11,2550800
+4335,Greedy,Euklidisch,10,21,11,2769100
+4336,Greedy,Euklidisch,10,26,11,2915400
+4337,Greedy,Euklidisch,10,19,11,2151200
+4338,Greedy,Euklidisch,10,24,11,2712800
+4339,Greedy,Euklidisch,10,250,31,33913300
+4340,Greedy,Euklidisch,10,21,11,2416500
+4341,Greedy,Euklidisch,10,19,11,2236800
+4342,Greedy,Euklidisch,10,63,13,7847100
+4343,Greedy,Euklidisch,10,19,11,2160700
+4344,Greedy,Euklidisch,10,238,39,30729400
+4345,Greedy,Euklidisch,10,231,39,30830900
+4346,Greedy,Euklidisch,10,28,11,3280500
+4347,Greedy,Euklidisch,10,21,11,2472100
+4348,Greedy,Euklidisch,10,24,11,2763200
+4349,Greedy,Euklidisch,10,154,41,19774100
+4350,Greedy,Euklidisch,10,21,11,2375000
+4351,Greedy,Euklidisch,10,512,35,66580300
+4352,Greedy,Euklidisch,10,268,41,36260700
+4353,Greedy,Euklidisch,10,511,45,67275400
+4354,Greedy,Euklidisch,10,76,23,9550200
+4355,Greedy,Euklidisch,10,21,11,2401100
+4356,Greedy,Euklidisch,10,69,11,8508200
+4357,Greedy,Euklidisch,10,21,11,2369100
+4358,Greedy,Euklidisch,10,23,11,2858400
+4359,Greedy,Euklidisch,10,21,11,2353900
+4360,Greedy,Euklidisch,10,72,11,9137300
+4361,Greedy,Euklidisch,10,24,11,2902800
+4362,Greedy,Euklidisch,10,21,11,2259600
+4363,Greedy,Euklidisch,10,19,11,2270100
+4364,Greedy,Euklidisch,10,300,23,40115400
+4365,Greedy,Euklidisch,10,24,11,2863600
+4366,Greedy,Euklidisch,10,23,11,2562300
+4367,Greedy,Euklidisch,10,249,31,33491200
+4368,Greedy,Euklidisch,10,128,37,16670200
+4369,Greedy,Euklidisch,10,21,11,2385800
+4370,Greedy,Euklidisch,10,33,11,3813700
+4371,Greedy,Euklidisch,10,21,11,2413000
+4372,Greedy,Euklidisch,10,21,11,2505200
+4373,Greedy,Euklidisch,10,21,11,2304500
+4374,Greedy,Euklidisch,10,24,11,2779800
+4375,Greedy,Euklidisch,10,250,53,33248800
+4376,Greedy,Euklidisch,10,20,11,2189100
+4377,Greedy,Euklidisch,10,250,41,34129900
+4378,Greedy,Euklidisch,10,21,11,2282800
+4379,Greedy,Euklidisch,10,96,17,12577300
+4380,Greedy,Euklidisch,10,23,11,2551900
+4381,Greedy,Euklidisch,10,19,11,2223200
+4382,Greedy,Euklidisch,10,160,41,21032100
+4383,Greedy,Euklidisch,10,59,17,7495000
+4384,Greedy,Euklidisch,10,21,11,2282800
+4385,Greedy,Euklidisch,10,69,25,8420000
+4386,Greedy,Euklidisch,10,230,35,31131600
+4387,Greedy,Euklidisch,10,21,11,2348800
+4388,Greedy,Euklidisch,10,353,51,47325000
+4389,Greedy,Euklidisch,10,21,11,2387600
+4390,Greedy,Euklidisch,10,30,11,3713200
+4391,Greedy,Euklidisch,10,24,11,2785100
+4392,Greedy,Euklidisch,10,21,11,2475500
+4393,Greedy,Euklidisch,10,313,33,39561000
+4394,Greedy,Euklidisch,10,240,23,30718900
+4395,Greedy,Euklidisch,10,25,11,3023800
+4396,Greedy,Euklidisch,10,249,41,31637800
+4397,Greedy,Euklidisch,10,26,11,2861500
+4398,Greedy,Euklidisch,10,21,11,2369500
+4399,Greedy,Euklidisch,10,20,11,2219500
+4400,Greedy,Euklidisch,10,20,11,2066800
+4401,Greedy,Euklidisch,10,21,11,2325100
+4402,Greedy,Euklidisch,10,19,11,2067000
+4403,Greedy,Euklidisch,10,120,31,14792800
+4404,Greedy,Euklidisch,10,24,11,2630000
+4405,Greedy,Euklidisch,10,317,37,40858700
+4406,Greedy,Euklidisch,10,19,11,2137200
+4407,Greedy,Euklidisch,10,26,11,2868900
+4408,Greedy,Euklidisch,10,320,29,40734500
+4409,Greedy,Euklidisch,10,21,11,2446700
+4410,Greedy,Euklidisch,10,60,13,7113700
+4411,Greedy,Euklidisch,10,131,37,15837900
+4412,Greedy,Euklidisch,10,23,11,2595200
+4413,Greedy,Euklidisch,10,18,11,1987500
+4414,Greedy,Euklidisch,10,65,21,7623500
+4415,Greedy,Euklidisch,10,23,11,2552400
+4416,Greedy,Euklidisch,10,23,11,2388700
+4417,Greedy,Euklidisch,10,255,35,33207000
+4418,Greedy,Euklidisch,10,21,11,2276900
+4419,Greedy,Euklidisch,10,21,11,2236100
+4420,Greedy,Euklidisch,10,21,11,2353100
+4421,Greedy,Euklidisch,10,24,11,2623400
+4422,Greedy,Euklidisch,10,165,35,20051100
+4423,Greedy,Euklidisch,10,241,33,30748000
+4424,Greedy,Euklidisch,10,239,33,30441100
+4425,Greedy,Euklidisch,10,19,11,2219200
+4426,Greedy,Euklidisch,10,260,37,33486600
+4427,Greedy,Euklidisch,10,21,11,2238100
+4428,Greedy,Euklidisch,10,21,11,2409800
+4429,Greedy,Euklidisch,10,136,39,16469300
+4430,Greedy,Euklidisch,10,302,31,38811000
+4431,Greedy,Euklidisch,10,24,11,2580300
+4432,Greedy,Euklidisch,10,451,55,58423300
+4433,Greedy,Euklidisch,10,23,11,2676600
+4434,Greedy,Euklidisch,10,23,11,2484200
+4435,Greedy,Euklidisch,10,322,23,41159100
+4436,Greedy,Euklidisch,10,25,11,2915300
+4437,Greedy,Euklidisch,10,17,11,1954300
+4438,Greedy,Euklidisch,10,236,35,30148700
+4439,Greedy,Euklidisch,10,239,35,30292900
+4440,Greedy,Euklidisch,10,21,11,2155500
+4441,Greedy,Euklidisch,10,20,11,2085600
+4442,Greedy,Euklidisch,10,24,11,2739100
+4443,Greedy,Euklidisch,10,26,11,2758600
+4444,Greedy,Euklidisch,10,264,63,33213400
+4445,Greedy,Euklidisch,10,21,11,2262800
+4446,Greedy,Euklidisch,10,21,11,2231700
+4447,Greedy,Euklidisch,10,23,11,2452700
+4448,Greedy,Euklidisch,10,258,41,32529200
+4449,Greedy,Euklidisch,10,310,19,39827700
+4450,Greedy,Euklidisch,10,21,11,2176300
+4451,Greedy,Euklidisch,10,24,11,2629000
+4452,Greedy,Euklidisch,10,23,11,2806300
+4453,Greedy,Euklidisch,10,21,11,2250500
+4454,Greedy,Euklidisch,10,553,59,72087300
+4455,Greedy,Euklidisch,10,196,35,24446300
+4456,Greedy,Euklidisch,10,26,11,2890300
+4457,Greedy,Euklidisch,10,23,11,2456000
+4458,Greedy,Euklidisch,10,18,11,2212600
+4459,Greedy,Euklidisch,10,19,11,2106700
+4460,Greedy,Euklidisch,10,231,23,29707000
+4461,Greedy,Euklidisch,10,59,11,7440700
+4462,Greedy,Euklidisch,10,20,11,2103300
+4463,Greedy,Euklidisch,10,26,11,2860000
+4464,Greedy,Euklidisch,10,21,11,2244800
+4465,Greedy,Euklidisch,10,21,11,2251300
+4466,Greedy,Euklidisch,10,19,11,2075000
+4467,Greedy,Euklidisch,10,17,11,2144800
+4468,Greedy,Euklidisch,10,195,33,24142600
+4469,Greedy,Euklidisch,10,21,11,2232200
+4470,Greedy,Euklidisch,10,181,47,22618300
+4471,Greedy,Euklidisch,10,21,11,2258500
+4472,Greedy,Euklidisch,10,18,11,2152700
+4473,Greedy,Euklidisch,10,21,11,2237900
+4474,Greedy,Euklidisch,10,246,45,31835300
+4475,Greedy,Euklidisch,10,21,11,2371100
+4476,Greedy,Euklidisch,10,21,11,2476300
+4477,Greedy,Euklidisch,10,35,11,3951000
+4478,Greedy,Euklidisch,10,21,11,2234100
+4479,Greedy,Euklidisch,10,132,41,16062300
+4480,Greedy,Euklidisch,10,21,11,2184200
+4481,Greedy,Euklidisch,10,24,11,2614600
+4482,Greedy,Euklidisch,10,21,11,2161100
+4483,Greedy,Euklidisch,10,76,27,9278400
+4484,Greedy,Euklidisch,10,258,33,33228200
+4485,Greedy,Euklidisch,10,21,11,2270500
+4486,Greedy,Euklidisch,10,24,11,2614500
+4487,Greedy,Euklidisch,10,18,11,2130000
+4488,Greedy,Euklidisch,10,20,11,2090800
+4489,Greedy,Euklidisch,10,26,11,2767000
+4490,Greedy,Euklidisch,10,25,11,3006300
+4491,Greedy,Euklidisch,10,19,11,2081400
+4492,Greedy,Euklidisch,10,23,11,2566600
+4493,Greedy,Euklidisch,10,23,11,2557900
+4494,Greedy,Euklidisch,10,63,23,7276100
+4495,Greedy,Euklidisch,10,23,11,2659200
+4496,Greedy,Euklidisch,10,35,11,4135900
+4497,Greedy,Euklidisch,10,21,11,2275300
+4498,Greedy,Euklidisch,10,23,11,2389900
+4499,Greedy,Euklidisch,10,21,11,2224000
+4500,Greedy,Euklidisch,10,24,11,2634200
+4501,Greedy,Euklidisch,10,21,11,2288900
+4502,Greedy,Euklidisch,10,29,13,3249900
+4503,Greedy,Euklidisch,10,30,11,3430900
+4504,Greedy,Euklidisch,10,259,45,33390200
+4505,Greedy,Euklidisch,10,105,27,12793300
+4506,Greedy,Euklidisch,10,19,11,2260100
+4507,Greedy,Euklidisch,10,322,53,39987900
+4508,Greedy,Euklidisch,10,21,11,2266100
+4509,Greedy,Euklidisch,10,255,39,32553700
+4510,Greedy,Euklidisch,10,289,39,37227100
+4511,Greedy,Euklidisch,10,21,11,2248700
+4512,Greedy,Euklidisch,10,274,23,36092800
+4513,Greedy,Euklidisch,10,19,11,2258300
+4514,Greedy,Euklidisch,10,269,41,36594300
+4515,Greedy,Euklidisch,10,26,11,3046400
+4516,Greedy,Euklidisch,10,29,11,3601200
+4517,Greedy,Euklidisch,10,246,35,33172400
+4518,Greedy,Euklidisch,10,17,11,2277700
+4519,Greedy,Euklidisch,10,20,11,2362600
+4520,Greedy,Euklidisch,10,126,39,16157800
+4521,Greedy,Euklidisch,10,250,47,33964300
+4522,Greedy,Euklidisch,10,26,11,3073100
+4523,Greedy,Euklidisch,10,24,11,2703300
+4524,Greedy,Euklidisch,10,18,11,2098600
+4525,Greedy,Euklidisch,10,21,11,2241800
+4526,Greedy,Euklidisch,10,19,11,2374500
+4527,Greedy,Euklidisch,10,18,11,2076400
+4528,Greedy,Euklidisch,10,245,41,33450200
+4529,Greedy,Euklidisch,10,26,11,3006300
+4530,Greedy,Euklidisch,10,21,11,2405500
+4531,Greedy,Euklidisch,10,21,11,2327800
+4532,Greedy,Euklidisch,10,21,11,2136300
+4533,Greedy,Euklidisch,10,235,33,30434500
+4534,Greedy,Euklidisch,10,20,11,2276700
+4535,Greedy,Euklidisch,10,24,11,2571200
+4536,Greedy,Euklidisch,10,20,11,2027300
+4537,Greedy,Euklidisch,10,91,17,10812500
+4538,Greedy,Euklidisch,10,21,11,2235900
+4539,Greedy,Euklidisch,10,26,11,2763500
+4540,Greedy,Euklidisch,10,18,11,1979500
+4541,Greedy,Euklidisch,10,21,11,2173900
+4542,Greedy,Euklidisch,10,145,37,17563500
+4543,Greedy,Euklidisch,10,18,11,2118400
+4544,Greedy,Euklidisch,10,240,31,30095100
+4545,Greedy,Euklidisch,10,245,33,31191900
+4546,Greedy,Euklidisch,10,24,11,2520600
+4547,Greedy,Euklidisch,10,313,27,38978700
+4548,Greedy,Euklidisch,10,21,11,2214800
+4549,Greedy,Euklidisch,10,24,11,2630100
+4550,Greedy,Euklidisch,10,18,11,1956600
+4551,Greedy,Euklidisch,10,21,11,2103600
+4552,Greedy,Euklidisch,10,57,15,6461400
+4553,Greedy,Euklidisch,10,261,43,32492400
+4554,Greedy,Euklidisch,10,293,37,36897100
+4555,Greedy,Euklidisch,10,268,39,33708500
+4556,Greedy,Euklidisch,10,23,11,2555300
+4557,Greedy,Euklidisch,10,289,37,36107900
+4558,Greedy,Euklidisch,10,22,11,2578500
+4559,Greedy,Euklidisch,10,141,27,17196500
+4560,Greedy,Euklidisch,10,23,11,2420200
+4561,Greedy,Euklidisch,10,19,11,2004200
+4562,Greedy,Euklidisch,10,20,11,2035300
+4563,Greedy,Euklidisch,10,26,11,2800400
+4564,Greedy,Euklidisch,10,122,25,14878800
+4565,Greedy,Euklidisch,10,29,11,3225000
+4566,Greedy,Euklidisch,10,20,11,2041000
+4567,Greedy,Euklidisch,10,21,11,2271000
+4568,Greedy,Euklidisch,10,679,33,84595100
+4569,Greedy,Euklidisch,10,604,63,76170700
+4570,Greedy,Euklidisch,10,19,11,2190000
+4571,Greedy,Euklidisch,10,585,45,74233500
+4572,Greedy,Euklidisch,10,29,13,3095600
+4573,Greedy,Euklidisch,10,236,37,29549400
+4574,Greedy,Euklidisch,10,77,11,9420500
+4575,Greedy,Euklidisch,10,24,11,2571100
+4576,Greedy,Euklidisch,10,20,11,2113800
+4577,Greedy,Euklidisch,10,19,11,2148100
+4578,Greedy,Euklidisch,10,292,35,36803600
+4579,Greedy,Euklidisch,10,29,11,3117900
+4580,Greedy,Euklidisch,10,285,45,35812700
+4581,Greedy,Euklidisch,10,26,11,2729900
+4582,Greedy,Euklidisch,10,252,35,31770800
+4583,Greedy,Euklidisch,10,340,45,42436600
+4584,Greedy,Euklidisch,10,20,11,2070000
+4585,Greedy,Euklidisch,10,227,11,28145600
+4586,Greedy,Euklidisch,10,222,11,27839000
+4587,Greedy,Euklidisch,10,20,11,2047000
+4588,Greedy,Euklidisch,10,18,11,2136800
+4589,Greedy,Euklidisch,10,20,11,2032200
+4590,Greedy,Euklidisch,10,286,39,36121400
+4591,Greedy,Euklidisch,10,365,39,45162000
+4592,Greedy,Euklidisch,10,21,11,2328000
+4593,Greedy,Euklidisch,10,338,23,41754200
+4594,Greedy,Euklidisch,10,21,11,2184400
+4595,Greedy,Euklidisch,10,24,11,2808400
+4596,Greedy,Euklidisch,10,23,11,2352700
+4597,Greedy,Euklidisch,10,19,11,2025900
+4598,Greedy,Euklidisch,10,305,25,37951500
+4599,Greedy,Euklidisch,10,361,35,44879900
+4600,Greedy,Euklidisch,10,282,43,35545900
+4601,Greedy,Euklidisch,10,44,11,4778700
+4602,Greedy,Euklidisch,10,21,11,2123600
+4603,Greedy,Euklidisch,10,236,41,29832500
+4604,Greedy,Euklidisch,10,18,11,1897000
+4605,Greedy,Euklidisch,10,17,11,1881600
+4606,Greedy,Euklidisch,10,26,11,2769600
+4607,Greedy,Euklidisch,10,340,53,41388400
+4608,Greedy,Euklidisch,10,19,11,2116600
+4609,Greedy,Euklidisch,10,20,11,2040400
+4610,Greedy,Euklidisch,10,21,11,2109100
+4611,Greedy,Euklidisch,10,21,11,2308800
+4612,Greedy,Euklidisch,10,21,11,2205700
+4613,Greedy,Euklidisch,10,23,11,2339400
+4614,Greedy,Euklidisch,10,20,11,2233800
+4615,Greedy,Euklidisch,10,482,71,60358500
+4616,Greedy,Euklidisch,10,29,13,3130200
+4617,Greedy,Euklidisch,10,19,11,2054500
+4618,Greedy,Euklidisch,10,20,11,2110600
+4619,Greedy,Euklidisch,10,142,39,17498200
+4620,Greedy,Euklidisch,10,21,11,2129500
+4621,Greedy,Euklidisch,10,20,11,2114800
+4622,Greedy,Euklidisch,10,19,11,2189000
+4623,Greedy,Euklidisch,10,238,31,29701000
+4624,Greedy,Euklidisch,10,21,11,2191000
+4625,Greedy,Euklidisch,12,583,71,72180300
+4626,Greedy,Euklidisch,12,31,13,3584400
+4627,Greedy,Euklidisch,12,288,39,35804300
+4628,Greedy,Euklidisch,12,29,13,3082100
+4629,Greedy,Euklidisch,12,34,15,3924300
+4630,Greedy,Euklidisch,12,24,13,2561700
+4631,Greedy,Euklidisch,12,24,13,2654600
+4632,Greedy,Euklidisch,12,28,13,3056600
+4633,Greedy,Euklidisch,12,26,13,2822000
+4634,Greedy,Euklidisch,12,239,35,29951800
+4635,Greedy,Euklidisch,12,83,27,10358600
+4636,Greedy,Euklidisch,12,22,13,2414800
+4637,Greedy,Euklidisch,12,299,41,37356500
+4638,Greedy,Euklidisch,12,126,27,15958400
+4639,Greedy,Euklidisch,12,64,15,7917400
+4640,Greedy,Euklidisch,12,314,43,40657700
+4641,Greedy,Euklidisch,12,291,33,38545800
+4642,Greedy,Euklidisch,12,29,13,3256700
+4643,Greedy,Euklidisch,12,26,13,3449900
+4644,Greedy,Euklidisch,12,29,13,3324600
+4645,Greedy,Euklidisch,12,24,13,2714700
+4646,Greedy,Euklidisch,12,381,35,50557100
+4647,Greedy,Euklidisch,12,248,29,32809600
+4648,Greedy,Euklidisch,12,20,13,2400500
+4649,Greedy,Euklidisch,12,33,15,4016800
+4650,Greedy,Euklidisch,12,290,39,38469800
+4651,Greedy,Euklidisch,12,23,13,2575900
+4652,Greedy,Euklidisch,12,24,13,2712400
+4653,Greedy,Euklidisch,12,40,15,4965900
+4654,Greedy,Euklidisch,12,292,25,37709600
+4655,Greedy,Euklidisch,12,274,49,36200500
+4656,Greedy,Euklidisch,12,39,19,5035800
+4657,Greedy,Euklidisch,12,266,45,35609700
+4658,Greedy,Euklidisch,12,279,49,36329700
+4659,Greedy,Euklidisch,12,141,25,17322400
+4660,Greedy,Euklidisch,12,279,31,36949900
+4661,Greedy,Euklidisch,12,576,65,75509100
+4662,Greedy,Euklidisch,12,47,13,5669300
+4663,Greedy,Euklidisch,12,897,61,117560000
+4664,Greedy,Euklidisch,12,499,49,65093900
+4665,Greedy,Euklidisch,12,34,13,3948200
+4666,Greedy,Euklidisch,12,267,25,35914600
+4667,Greedy,Euklidisch,12,25,13,2844100
+4668,Greedy,Euklidisch,12,25,13,2936600
+4669,Greedy,Euklidisch,12,26,13,3127600
+4670,Greedy,Euklidisch,12,22,13,2564200
+4671,Greedy,Euklidisch,12,602,49,80495500
+4672,Greedy,Euklidisch,12,241,39,32330900
+4673,Greedy,Euklidisch,12,22,13,2794000
+4674,Greedy,Euklidisch,12,37,15,4286800
+4675,Greedy,Euklidisch,12,26,13,2896900
+4676,Greedy,Euklidisch,12,294,29,38920600
+4677,Greedy,Euklidisch,12,24,13,2743500
+4678,Greedy,Euklidisch,12,79,17,9755900
+4679,Greedy,Euklidisch,12,31,13,3724300
+4680,Greedy,Euklidisch,12,859,73,113322200
+4681,Greedy,Euklidisch,12,388,55,51578900
+4682,Greedy,Euklidisch,12,22,13,2521600
+4683,Greedy,Euklidisch,12,121,29,15344300
+4684,Greedy,Euklidisch,12,24,13,2722300
+4685,Greedy,Euklidisch,12,26,13,2892500
+4686,Greedy,Euklidisch,12,535,37,72330700
+4687,Greedy,Euklidisch,12,26,13,2901500
+4688,Greedy,Euklidisch,12,434,57,55874800
+4689,Greedy,Euklidisch,12,24,13,2910100
+4690,Greedy,Euklidisch,12,289,39,38488800
+4691,Greedy,Euklidisch,12,27,13,3223100
+4692,Greedy,Euklidisch,12,20,13,2394900
+4693,Greedy,Euklidisch,12,66,25,8218200
+4694,Greedy,Euklidisch,12,214,45,27314700
+4695,Greedy,Euklidisch,12,271,51,35448400
+4696,Greedy,Euklidisch,12,23,13,2658700
+4697,Greedy,Euklidisch,12,249,29,33391700
+4698,Greedy,Euklidisch,12,273,27,35353000
+4699,Greedy,Euklidisch,12,58,15,7047300
+4700,Greedy,Euklidisch,12,80,13,10000500
+4701,Greedy,Euklidisch,12,29,13,3691400
+4702,Greedy,Euklidisch,12,224,33,29983000
+4703,Greedy,Euklidisch,12,26,13,2972300
+4704,Greedy,Euklidisch,12,271,35,35836700
+4705,Greedy,Euklidisch,12,233,37,30848400
+4706,Greedy,Euklidisch,12,302,41,40498700
+4707,Greedy,Euklidisch,12,249,41,32913700
+4708,Greedy,Euklidisch,12,29,13,3496100
+4709,Greedy,Euklidisch,12,249,33,33234400
+4710,Greedy,Euklidisch,12,21,13,2718800
+4711,Greedy,Euklidisch,12,26,13,2875900
+4712,Greedy,Euklidisch,12,320,39,42295200
+4713,Greedy,Euklidisch,12,26,13,3275800
+4714,Greedy,Euklidisch,12,542,61,71970700
+4715,Greedy,Euklidisch,12,24,13,2762200
+4716,Greedy,Euklidisch,12,186,15,23567300
+4717,Greedy,Euklidisch,12,29,13,3278600
+4718,Greedy,Euklidisch,12,24,13,2846400
+4719,Greedy,Euklidisch,12,24,13,3158900
+4720,Greedy,Euklidisch,12,24,13,2817900
+4721,Greedy,Euklidisch,12,35,13,4089300
+4722,Greedy,Euklidisch,12,298,23,40514500
+4723,Greedy,Euklidisch,12,101,21,13116100
+4724,Greedy,Euklidisch,12,580,79,75829200
+4725,Greedy,Euklidisch,12,311,31,42063000
+4726,Greedy,Euklidisch,12,332,27,42730300
+4727,Greedy,Euklidisch,12,267,41,35426000
+4728,Greedy,Euklidisch,12,516,57,70140500
+4729,Greedy,Euklidisch,12,31,13,3618300
+4730,Greedy,Euklidisch,12,127,27,16622000
+4731,Greedy,Euklidisch,12,227,37,30492300
+4732,Greedy,Euklidisch,12,253,41,34125500
+4733,Greedy,Euklidisch,12,22,13,2597900
+4734,Greedy,Euklidisch,12,62,25,7796800
+4735,Greedy,Euklidisch,12,261,61,33894700
+4736,Greedy,Euklidisch,12,34,17,4018500
+4737,Greedy,Euklidisch,12,26,13,2882400
+4738,Greedy,Euklidisch,12,24,13,2889700
+4739,Greedy,Euklidisch,12,24,13,2656500
+4740,Greedy,Euklidisch,12,24,13,2826400
+4741,Greedy,Euklidisch,12,593,53,76208500
+4742,Greedy,Euklidisch,12,24,13,2607500
+4743,Greedy,Euklidisch,12,27,13,2873400
+4744,Greedy,Euklidisch,12,128,35,15376000
+4745,Greedy,Euklidisch,12,27,13,2971500
+4746,Greedy,Euklidisch,12,24,13,2496300
+4747,Greedy,Euklidisch,12,750,61,93031900
+4748,Greedy,Euklidisch,12,23,13,2722900
+4749,Greedy,Euklidisch,12,298,23,37546700
+4750,Greedy,Euklidisch,12,316,25,39482900
+4751,Greedy,Euklidisch,12,227,51,28106300
+4752,Greedy,Euklidisch,12,611,55,77945500
+4753,Greedy,Euklidisch,12,24,13,2684200
+4754,Greedy,Euklidisch,12,252,49,32168800
+4755,Greedy,Euklidisch,12,82,19,9661500
+4756,Greedy,Euklidisch,12,26,13,2718500
+4757,Greedy,Euklidisch,12,42,19,4929000
+4758,Greedy,Euklidisch,12,22,13,2535500
+4759,Greedy,Euklidisch,12,537,47,68396700
+4760,Greedy,Euklidisch,12,24,13,2599000
+4761,Greedy,Euklidisch,12,313,43,39529400
+4762,Greedy,Euklidisch,12,596,107,72711900
+4763,Greedy,Euklidisch,12,118,29,14501300
+4764,Greedy,Euklidisch,12,298,49,37599500
+4765,Greedy,Euklidisch,12,188,13,22543300
+4766,Greedy,Euklidisch,12,25,13,2773800
+4767,Greedy,Euklidisch,12,26,13,2971300
+4768,Greedy,Euklidisch,12,122,19,14505200
+4769,Greedy,Euklidisch,12,294,65,35988900
+4770,Greedy,Euklidisch,12,132,13,16174700
+4771,Greedy,Euklidisch,12,23,13,2549400
+4772,Greedy,Euklidisch,12,34,13,3930800
+4773,Greedy,Euklidisch,12,26,13,2727200
+4774,Greedy,Euklidisch,12,26,13,2742900
+4775,Greedy,Euklidisch,12,337,41,42448400
+4776,Greedy,Euklidisch,12,293,37,36734800
+4777,Greedy,Euklidisch,12,24,13,2815100
+4778,Greedy,Euklidisch,12,244,47,30789800
+4779,Greedy,Euklidisch,12,20,13,2328200
+4780,Greedy,Euklidisch,12,299,39,36718900
+4781,Greedy,Euklidisch,12,29,13,3239700
+4782,Greedy,Euklidisch,12,276,51,33651600
+4783,Greedy,Euklidisch,12,22,13,2614700
+4784,Greedy,Euklidisch,12,24,13,2570700
+4785,Greedy,Euklidisch,12,32,15,3477200
+4786,Greedy,Euklidisch,12,24,13,2596000
+4787,Greedy,Euklidisch,12,170,49,20631900
+4788,Greedy,Euklidisch,12,278,45,35071300
+4789,Greedy,Euklidisch,12,29,13,3139100
+4790,Greedy,Euklidisch,12,530,57,66293300
+4791,Greedy,Euklidisch,12,295,27,37197000
+4792,Greedy,Euklidisch,12,252,49,31968100
+4793,Greedy,Euklidisch,12,305,41,38468900
+4794,Greedy,Euklidisch,12,32,13,3420500
+4795,Greedy,Euklidisch,12,29,13,3287600
+4796,Greedy,Euklidisch,12,21,13,2287800
+4797,Greedy,Euklidisch,12,503,53,61878000
+4798,Greedy,Euklidisch,12,32,13,3733000
+4799,Greedy,Euklidisch,12,257,41,33072000
+4800,Greedy,Euklidisch,12,249,33,31338400
+4801,Greedy,Euklidisch,12,261,25,32962400
+4802,Greedy,Euklidisch,12,248,51,31686800
+4803,Greedy,Euklidisch,12,28,13,3052300
+4804,Greedy,Euklidisch,12,24,13,2592500
+4805,Greedy,Euklidisch,12,146,31,17953800
+4806,Greedy,Euklidisch,12,26,13,2880900
+4807,Greedy,Euklidisch,12,26,13,2725200
+4808,Greedy,Euklidisch,12,248,35,31380600
+4809,Greedy,Euklidisch,12,27,13,2896000
+4810,Greedy,Euklidisch,12,236,37,30078600
+4811,Greedy,Euklidisch,12,282,21,35391400
+4812,Greedy,Euklidisch,12,27,13,2986900
+4813,Greedy,Euklidisch,12,297,23,37420500
+4814,Greedy,Euklidisch,12,23,13,2439400
+4815,Greedy,Euklidisch,12,24,13,2601800
+4816,Greedy,Euklidisch,12,239,25,30525500
+4817,Greedy,Euklidisch,12,257,43,32440700
+4818,Greedy,Euklidisch,12,613,57,77783200
+4819,Greedy,Euklidisch,12,24,13,2610300
+4820,Greedy,Euklidisch,12,248,39,31317700
+4821,Greedy,Euklidisch,12,292,39,36770100
+4822,Greedy,Euklidisch,12,247,37,31538300
+4823,Greedy,Euklidisch,12,111,29,13053000
+4824,Greedy,Euklidisch,12,266,57,33505800
+4825,Greedy,Euklidisch,12,253,35,31920500
+4826,Greedy,Euklidisch,12,26,13,2987800
+4827,Greedy,Euklidisch,12,298,49,37640300
+4828,Greedy,Euklidisch,12,22,13,2455500
+4829,Greedy,Euklidisch,12,23,13,2451100
+4830,Greedy,Euklidisch,12,26,13,2880800
+4831,Greedy,Euklidisch,12,35,13,3806600
+4832,Greedy,Euklidisch,12,154,39,18557300
+4833,Greedy,Euklidisch,12,24,13,2589800
+4834,Greedy,Euklidisch,12,48,13,5672300
+4835,Greedy,Euklidisch,12,249,35,31819600
+4836,Greedy,Euklidisch,12,28,13,3272200
+4837,Greedy,Euklidisch,12,55,21,6246800
+4838,Greedy,Euklidisch,12,269,45,34285200
+4839,Greedy,Euklidisch,12,50,19,5819600
+4840,Greedy,Euklidisch,12,32,13,3597800
+4841,Greedy,Euklidisch,12,59,17,6855100
+4842,Greedy,Euklidisch,12,275,41,34714700
+4843,Greedy,Euklidisch,12,22,13,2573300
+4844,Greedy,Euklidisch,12,29,13,3106300
+4845,Greedy,Euklidisch,12,26,13,2722700
+4846,Greedy,Euklidisch,12,249,39,31426300
+4847,Greedy,Euklidisch,12,26,13,2920100
+4848,Greedy,Euklidisch,12,354,43,42985800
+4849,Greedy,Euklidisch,12,32,13,3499500
+4850,Greedy,Euklidisch,12,229,55,28778900
+4851,Greedy,Euklidisch,12,204,25,25153500
+4852,Greedy,Euklidisch,12,60,13,6980500
+4853,Greedy,Euklidisch,12,301,39,38245700
+4854,Greedy,Euklidisch,12,118,25,14523100
+4855,Greedy,Euklidisch,12,24,13,2584000
+4856,Greedy,Euklidisch,12,32,13,3628000
+4857,Greedy,Euklidisch,12,224,29,28246100
+4858,Greedy,Euklidisch,12,341,43,43210400
+4859,Greedy,Euklidisch,12,292,37,36589300
+4860,Greedy,Euklidisch,12,24,13,2659300
+4861,Greedy,Euklidisch,12,24,13,2605600
+4862,Greedy,Euklidisch,12,29,13,3312400
+4863,Greedy,Euklidisch,12,29,13,3102600
+4864,Greedy,Euklidisch,12,24,13,2568700
+4865,Greedy,Euklidisch,12,711,125,88379900
+4866,Greedy,Euklidisch,12,271,21,34071700
+4867,Greedy,Euklidisch,12,122,33,15024100
+4868,Greedy,Euklidisch,12,79,29,8891900
+4869,Greedy,Euklidisch,12,21,13,2807700
+4870,Greedy,Euklidisch,12,318,55,38909800
+4871,Greedy,Euklidisch,12,24,13,2598200
+4872,Greedy,Euklidisch,12,26,13,3015100
+4873,Greedy,Euklidisch,12,283,41,35955700
+4874,Greedy,Euklidisch,12,29,13,3111400
+4875,Greedy,Euklidisch,12,26,13,2948200
+4876,Greedy,Euklidisch,12,22,13,2348900
+4877,Greedy,Euklidisch,12,23,13,2616200
+4878,Greedy,Euklidisch,12,107,25,12638200
+4879,Greedy,Euklidisch,12,192,33,23875400
+4880,Greedy,Euklidisch,12,25,13,2601500
+4881,Greedy,Euklidisch,12,56,15,6493700
+4882,Greedy,Euklidisch,12,23,13,2436200
+4883,Greedy,Euklidisch,12,301,37,36826200
+4884,Greedy,Euklidisch,12,84,15,9990400
+4885,Greedy,Euklidisch,12,27,13,2939200
+4886,Greedy,Euklidisch,12,143,25,17157300
+4887,Greedy,Euklidisch,12,26,13,2687300
+4888,Greedy,Euklidisch,12,23,13,2538800
+4889,Greedy,Euklidisch,12,472,61,57868100
+4890,Greedy,Euklidisch,12,239,35,29326700
+4891,Greedy,Euklidisch,12,509,47,64737800
+4892,Greedy,Euklidisch,12,302,31,37882300
+4893,Greedy,Euklidisch,12,26,13,2855600
+4894,Greedy,Euklidisch,12,395,27,48588100
+4895,Greedy,Euklidisch,12,103,27,12261200
+4896,Greedy,Euklidisch,12,254,31,30630000
+4897,Greedy,Euklidisch,12,27,13,2942700
+4898,Greedy,Euklidisch,12,31,13,3352800
+4899,Greedy,Euklidisch,12,33,13,3606900
+4900,Greedy,Euklidisch,12,34,13,3737300
+4901,Greedy,Euklidisch,12,26,13,2799700
+4902,Greedy,Euklidisch,12,333,17,42228200
+4903,Greedy,Euklidisch,12,130,39,15669900
+4904,Greedy,Euklidisch,12,759,117,94624200
+4905,Greedy,Euklidisch,12,340,43,41801000
+4906,Greedy,Euklidisch,12,55,17,6727600
+4907,Greedy,Euklidisch,12,31,17,3468200
+4908,Greedy,Euklidisch,12,228,35,29000000
+4909,Greedy,Euklidisch,12,291,37,36588400
+4910,Greedy,Euklidisch,12,120,33,14152500
+4911,Greedy,Euklidisch,12,58,15,6860400
+4912,Greedy,Euklidisch,12,32,13,3424900
+4913,Greedy,Euklidisch,12,22,13,2350500
+4914,Greedy,Euklidisch,12,28,13,2975500
+4915,Greedy,Euklidisch,12,54,21,6372100
+4916,Greedy,Euklidisch,12,24,13,2526000
+4917,Greedy,Euklidisch,12,63,13,7213300
+4918,Greedy,Euklidisch,12,59,13,6775100
+4919,Greedy,Euklidisch,12,28,13,3336400
+4920,Greedy,Euklidisch,12,323,33,39581200
+4921,Greedy,Euklidisch,12,341,43,42833500
+4922,Greedy,Euklidisch,12,513,39,63470100
+4923,Greedy,Euklidisch,12,26,13,2730100
+4924,Greedy,Euklidisch,12,26,13,2840800
+4925,Greedy,Euklidisch,12,429,35,52373200
+4926,Greedy,Euklidisch,12,762,43,94826300
+4927,Greedy,Euklidisch,12,29,13,3430400
+4928,Greedy,Euklidisch,12,397,35,50256200
+4929,Greedy,Euklidisch,12,517,53,64675000
+4930,Greedy,Euklidisch,12,29,13,3173900
+4931,Greedy,Euklidisch,12,26,13,2718600
+4932,Greedy,Euklidisch,12,22,13,2571100
+4933,Greedy,Euklidisch,12,27,13,3000900
+4934,Greedy,Euklidisch,12,79,13,9437300
+4935,Greedy,Euklidisch,12,28,13,3024900
+4936,Greedy,Euklidisch,12,235,27,29065400
+4937,Greedy,Euklidisch,12,394,53,48840600
+4938,Greedy,Euklidisch,12,22,13,2438400
+4939,Greedy,Euklidisch,12,232,39,28806800
+4940,Greedy,Euklidisch,12,333,41,41766600
+4941,Greedy,Euklidisch,12,231,13,29260200
+4942,Greedy,Euklidisch,12,26,13,3056300
+4943,Greedy,Euklidisch,12,260,23,32940200
+4944,Greedy,Euklidisch,12,270,45,33682800
+4945,Greedy,Euklidisch,12,29,13,3207600
+4946,Greedy,Euklidisch,12,24,13,3010700
+4947,Greedy,Euklidisch,12,23,13,2632000
+4948,Greedy,Euklidisch,12,274,37,34832700
+4949,Greedy,Euklidisch,12,278,25,35520000
+4950,Greedy,Euklidisch,12,265,47,33759500
+4951,Greedy,Euklidisch,12,303,65,37673800
+4952,Greedy,Euklidisch,12,251,41,32292200
+4953,Greedy,Euklidisch,12,28,13,3024900
+4954,Greedy,Euklidisch,12,254,57,32049900
+4955,Greedy,Euklidisch,12,24,13,2643600
+4956,Greedy,Euklidisch,12,505,37,63352000
+4957,Greedy,Euklidisch,12,154,29,19821700
+4958,Greedy,Euklidisch,12,226,29,29123200
+4959,Greedy,Euklidisch,12,715,73,90285000
+4960,Greedy,Euklidisch,12,264,23,32833100
+4961,Greedy,Euklidisch,12,693,83,86635200
+4962,Greedy,Euklidisch,12,177,41,21678500
+4963,Greedy,Euklidisch,12,38,17,4349400
+4964,Greedy,Euklidisch,12,26,13,2953000
+4965,Greedy,Euklidisch,12,26,13,2929800
+4966,Greedy,Euklidisch,12,311,31,39860000
+4967,Greedy,Euklidisch,12,109,13,13039000
+4968,Greedy,Euklidisch,12,93,27,11449200
+4969,Greedy,Euklidisch,12,590,95,73300900
+4970,Greedy,Euklidisch,12,35,13,3980100
+4971,Greedy,Euklidisch,12,181,47,22638400
+4972,Greedy,Euklidisch,12,23,13,2560600
+4973,Greedy,Euklidisch,12,24,13,2617100
+4974,Greedy,Euklidisch,12,298,45,37736800
+4975,Greedy,Euklidisch,12,21,13,2331300
+4976,Greedy,Euklidisch,12,29,13,3279500
+4977,Greedy,Euklidisch,12,24,13,2603900
+4978,Greedy,Euklidisch,12,29,13,3287900
+4979,Greedy,Euklidisch,12,267,45,33703300
+4980,Greedy,Euklidisch,12,25,13,2709700
+4981,Greedy,Euklidisch,12,318,23,40526300
+4982,Greedy,Euklidisch,12,256,13,32682400
+4983,Greedy,Euklidisch,12,67,27,7919500
+4984,Greedy,Euklidisch,12,39,19,4609700
+4985,Greedy,Euklidisch,12,360,55,45277900
+4986,Greedy,Euklidisch,12,265,45,33741100
+4987,Greedy,Euklidisch,12,519,35,67111000
+4988,Greedy,Euklidisch,12,231,37,27970300
+4989,Greedy,Euklidisch,12,27,13,3017600
+4990,Greedy,Euklidisch,12,24,13,2528100
+4991,Greedy,Euklidisch,12,341,49,43395700
+4992,Greedy,Euklidisch,12,301,15,38289400
+4993,Greedy,Euklidisch,12,25,13,2635900
+4994,Greedy,Euklidisch,12,240,41,30459500
+4995,Greedy,Euklidisch,12,276,41,35043300
+4996,Greedy,Euklidisch,12,268,31,34660100
+4997,Greedy,Euklidisch,12,32,13,3602200
+4998,Greedy,Euklidisch,12,29,13,3074000
+4999,Greedy,Euklidisch,12,290,17,36882800
+5000,Greedy,Euklidisch,12,277,33,35545200
+5001,Greedy,Euklidisch,12,173,53,21282100
+5002,Greedy,Euklidisch,12,546,35,70328900
+5003,Greedy,Euklidisch,12,29,13,3160900
+5004,Greedy,Euklidisch,12,29,13,3298400
+5005,Greedy,Euklidisch,12,24,13,2537700
+5006,Greedy,Euklidisch,12,267,45,34248400
+5007,Greedy,Euklidisch,12,129,37,15700000
+5008,Greedy,Euklidisch,12,32,15,3567700
+5009,Greedy,Euklidisch,12,248,25,31807500
+5010,Greedy,Euklidisch,12,341,55,42932800
+5011,Greedy,Euklidisch,14,56,19,6452900
+5012,Greedy,Euklidisch,14,36,15,3977300
+5013,Greedy,Euklidisch,14,201,39,24415400
+5014,Greedy,Euklidisch,14,286,29,35883400
+5015,Greedy,Euklidisch,14,184,47,22440400
+5016,Greedy,Euklidisch,14,242,39,30455800
+5017,Greedy,Euklidisch,14,684,67,86046000
+5018,Greedy,Euklidisch,14,284,31,37595800
+5019,Greedy,Euklidisch,14,228,37,30597600
+5020,Greedy,Euklidisch,14,375,45,50097100
+5021,Greedy,Euklidisch,14,246,41,32707000
+5022,Greedy,Euklidisch,14,246,39,33002500
+5023,Greedy,Euklidisch,14,231,33,31098700
+5024,Greedy,Euklidisch,14,519,47,70210900
+5025,Greedy,Euklidisch,14,26,15,3022900
+5026,Greedy,Euklidisch,14,112,39,14166300
+5027,Greedy,Euklidisch,14,258,35,34816500
+5028,Greedy,Euklidisch,14,277,47,38293600
+5029,Greedy,Euklidisch,14,210,39,26301800
+5030,Greedy,Euklidisch,14,75,25,8924900
+5031,Greedy,Euklidisch,14,394,45,50657900
+5032,Greedy,Euklidisch,14,109,17,13210100
+5033,Greedy,Euklidisch,14,769,75,95933700
+5034,Greedy,Euklidisch,14,37,15,4387000
+5035,Greedy,Euklidisch,14,553,41,71048700
+5036,Greedy,Euklidisch,14,549,75,70961100
+5037,Greedy,Euklidisch,14,488,67,61547400
+5038,Greedy,Euklidisch,14,256,45,31453600
+5039,Greedy,Euklidisch,14,514,81,65733700
+5040,Greedy,Euklidisch,14,268,35,33395900
+5041,Greedy,Euklidisch,14,242,25,31154900
+5042,Greedy,Euklidisch,14,39,19,4455500
+5043,Greedy,Euklidisch,14,29,15,3260900
+5044,Greedy,Euklidisch,14,234,37,30049600
+5045,Greedy,Euklidisch,14,302,37,38351100
+5046,Greedy,Euklidisch,14,358,47,45297700
+5047,Greedy,Euklidisch,14,272,53,34759100
+5048,Greedy,Euklidisch,14,286,29,36949300
+5049,Greedy,Euklidisch,14,233,39,29816700
+5050,Greedy,Euklidisch,14,231,33,29822700
+5051,Greedy,Euklidisch,14,75,15,8996600
+5052,Greedy,Euklidisch,14,29,15,3145500
+5053,Greedy,Euklidisch,14,149,35,18589300
+5054,Greedy,Euklidisch,14,343,45,43693100
+5055,Greedy,Euklidisch,14,570,59,72445000
+5056,Greedy,Euklidisch,14,251,41,32818800
+5057,Greedy,Euklidisch,14,238,31,30723000
+5058,Greedy,Euklidisch,14,27,15,3041400
+5059,Greedy,Euklidisch,14,271,17,34637000
+5060,Greedy,Euklidisch,14,29,15,3278900
+5061,Greedy,Euklidisch,14,422,49,53313300
+5062,Greedy,Euklidisch,14,247,35,31650700
+5063,Greedy,Euklidisch,14,504,77,62421700
+5064,Greedy,Euklidisch,14,532,39,68856100
+5065,Greedy,Euklidisch,14,690,81,89687500
+5066,Greedy,Euklidisch,14,533,35,66125300
+5067,Greedy,Euklidisch,14,309,43,40156600
+5068,Greedy,Euklidisch,14,84,29,10214900
+5069,Greedy,Euklidisch,14,32,15,3561500
+5070,Greedy,Euklidisch,14,599,59,75701700
+5071,Greedy,Euklidisch,14,246,47,31533900
+5072,Greedy,Euklidisch,14,230,27,29850100
+5073,Greedy,Euklidisch,14,332,47,41355200
+5074,Greedy,Euklidisch,14,315,15,40012400
+5075,Greedy,Euklidisch,14,105,17,12620700
+5076,Greedy,Euklidisch,14,96,17,11474600
+5077,Greedy,Euklidisch,14,251,15,32424300
+5078,Greedy,Euklidisch,14,325,49,40658400
+5079,Greedy,Euklidisch,14,516,57,67152500
+5080,Greedy,Euklidisch,14,334,35,42667500
+5081,Greedy,Euklidisch,14,542,41,68448300
+5082,Greedy,Euklidisch,14,66,15,7570700
+5083,Greedy,Euklidisch,14,366,55,48351200
+5084,Greedy,Euklidisch,14,500,69,62334300
+5085,Greedy,Euklidisch,14,138,31,16890400
+5086,Greedy,Euklidisch,14,36,15,4219400
+5087,Greedy,Euklidisch,14,29,15,3234600
+5088,Greedy,Euklidisch,14,689,73,89659100
+5089,Greedy,Euklidisch,14,247,37,31765200
+5090,Greedy,Euklidisch,14,138,29,16702500
+5091,Greedy,Euklidisch,14,602,129,75489300
+5092,Greedy,Euklidisch,14,655,33,83309600
+5093,Greedy,Euklidisch,14,32,15,3929800
+5094,Greedy,Euklidisch,14,282,47,36107800
+5095,Greedy,Euklidisch,14,265,43,34320300
+5096,Greedy,Euklidisch,14,254,37,32661000
+5097,Greedy,Euklidisch,14,32,15,3737800
+5098,Greedy,Euklidisch,14,34,15,3848900
+5099,Greedy,Euklidisch,14,311,31,39895500
+5100,Greedy,Euklidisch,14,95,21,11514500
+5101,Greedy,Euklidisch,14,283,41,36404900
+5102,Greedy,Euklidisch,14,38,15,4256500
+5103,Greedy,Euklidisch,14,35,15,3883700
+5104,Greedy,Euklidisch,14,124,27,15888000
+5105,Greedy,Euklidisch,14,32,15,3660700
+5106,Greedy,Euklidisch,14,258,35,32954400
+5107,Greedy,Euklidisch,14,33,15,3744800
+5108,Greedy,Euklidisch,14,249,21,31975800
+5109,Greedy,Euklidisch,14,445,57,55491100
+5110,Greedy,Euklidisch,14,862,67,110444400
+5111,Greedy,Euklidisch,14,324,49,41334000
+5112,Greedy,Euklidisch,14,252,35,32077100
+5113,Greedy,Euklidisch,14,143,19,17050200
+5114,Greedy,Euklidisch,14,89,33,10896800
+5115,Greedy,Euklidisch,14,265,41,33579100
+5116,Greedy,Euklidisch,14,140,27,16931300
+5117,Greedy,Euklidisch,14,130,23,16166800
+5118,Greedy,Euklidisch,14,249,39,31880700
+5119,Greedy,Euklidisch,14,815,55,103710800
+5120,Greedy,Euklidisch,14,503,45,63095300
+5121,Greedy,Euklidisch,14,299,41,38563000
+5122,Greedy,Euklidisch,14,563,45,72266100
+5123,Greedy,Euklidisch,14,806,53,103926000
+5124,Greedy,Euklidisch,14,31,15,3570600
+5125,Greedy,Euklidisch,14,30,15,3408400
+5126,Greedy,Euklidisch,14,33,15,3587800
+5127,Greedy,Euklidisch,14,239,35,30927500
+5128,Greedy,Euklidisch,14,317,43,39455000
+5129,Greedy,Euklidisch,14,273,23,34950900
+5130,Greedy,Euklidisch,14,789,71,101602000
+5131,Greedy,Euklidisch,14,748,79,97103100
+5132,Greedy,Euklidisch,14,32,15,3626400
+5133,Greedy,Euklidisch,14,203,21,25209100
+5134,Greedy,Euklidisch,14,519,37,67435100
+5135,Greedy,Euklidisch,14,518,67,64895600
+5136,Greedy,Euklidisch,14,324,15,41003200
+5137,Greedy,Euklidisch,14,289,15,37289900
+5138,Greedy,Euklidisch,14,592,51,76909600
+5139,Greedy,Euklidisch,14,704,79,88746100
+5140,Greedy,Euklidisch,14,286,45,36983700
+5141,Greedy,Euklidisch,14,27,15,3111900
+5142,Greedy,Euklidisch,14,178,31,22172000
+5143,Greedy,Euklidisch,14,359,25,45939300
+5144,Greedy,Euklidisch,14,557,45,72329100
+5145,Greedy,Euklidisch,14,294,57,36864400
+5146,Greedy,Euklidisch,14,300,33,38224400
+5147,Greedy,Euklidisch,14,341,53,42513000
+5148,Greedy,Euklidisch,14,317,51,39619300
+5149,Greedy,Euklidisch,14,62,17,7356800
+5150,Greedy,Euklidisch,14,296,21,36582000
+5151,Greedy,Euklidisch,14,237,33,30357400
+5152,Greedy,Euklidisch,14,37,15,4453700
+5153,Greedy,Euklidisch,14,149,33,18578600
+5154,Greedy,Euklidisch,14,239,35,30693500
+5155,Greedy,Euklidisch,14,207,47,25839700
+5156,Greedy,Euklidisch,14,400,91,50044000
+5157,Greedy,Euklidisch,14,60,23,6971500
+5158,Greedy,Euklidisch,14,273,23,34809300
+5159,Greedy,Euklidisch,14,459,47,57615900
+5160,Greedy,Euklidisch,14,248,41,32170400
+5161,Greedy,Euklidisch,14,52,15,5903000
+5162,Greedy,Euklidisch,14,504,47,65719800
+5163,Greedy,Euklidisch,14,39,15,4367300
+5164,Greedy,Euklidisch,14,257,35,32175600
+5165,Greedy,Euklidisch,14,29,15,3182400
+5166,Greedy,Euklidisch,14,508,43,65784300
+5167,Greedy,Euklidisch,14,379,45,48552600
+5168,Greedy,Euklidisch,14,305,29,39264000
+5169,Greedy,Euklidisch,14,279,31,35552100
+5170,Greedy,Euklidisch,14,611,51,77637200
+5171,Greedy,Euklidisch,14,40,17,4493300
+5172,Greedy,Euklidisch,14,25,15,2864400
+5173,Greedy,Euklidisch,14,263,51,33646800
+5174,Greedy,Euklidisch,14,495,61,62181800
+5175,Greedy,Euklidisch,14,29,15,3117900
+5176,Greedy,Euklidisch,14,61,17,7079300
+5177,Greedy,Euklidisch,14,361,33,45790400
+5178,Greedy,Euklidisch,14,238,39,30440100
+5179,Greedy,Euklidisch,14,127,43,15665000
+5180,Greedy,Euklidisch,14,27,15,3228900
+5181,Greedy,Euklidisch,14,120,23,14322400
+5182,Greedy,Euklidisch,14,577,57,74731900
+5183,Greedy,Euklidisch,14,200,49,25933000
+5184,Greedy,Euklidisch,14,97,27,11612000
+5185,Greedy,Euklidisch,14,574,43,74092500
+5186,Greedy,Euklidisch,14,27,15,3048300
+5187,Greedy,Euklidisch,14,344,29,43005200
+5188,Greedy,Euklidisch,14,261,37,33466300
+5189,Greedy,Euklidisch,14,524,31,68171700
+5190,Greedy,Euklidisch,14,82,31,9990700
+5191,Greedy,Euklidisch,14,531,47,68912500
+5192,Greedy,Euklidisch,14,35,15,4122100
+5193,Greedy,Euklidisch,14,32,15,3658400
+5194,Greedy,Euklidisch,14,66,15,7557800
+5195,Greedy,Euklidisch,14,738,95,94680400
+5196,Greedy,Euklidisch,14,37,15,4685000
+5197,Greedy,Euklidisch,14,237,31,30584900
+5198,Greedy,Euklidisch,14,263,39,33835600
+5199,Greedy,Euklidisch,14,136,35,16424700
+5200,Greedy,Euklidisch,14,288,39,36180900
+5201,Greedy,Euklidisch,14,295,51,37366100
+5202,Greedy,Euklidisch,14,270,31,34432500
+5203,Greedy,Euklidisch,14,31,15,3394400
+5204,Greedy,Euklidisch,14,135,25,16613800
+5205,Greedy,Euklidisch,14,29,15,3190300
+5206,Greedy,Euklidisch,14,269,39,34186000
+5207,Greedy,Euklidisch,14,242,39,31245900
+5208,Greedy,Euklidisch,14,31,15,3566400
+5209,Greedy,Euklidisch,14,85,29,10175700
+5210,Greedy,Euklidisch,14,42,15,4877300
+5211,Greedy,Euklidisch,14,28,15,3118900
+5212,Greedy,Euklidisch,14,34,15,3879700
+5213,Greedy,Euklidisch,14,65,23,7873000
+5214,Greedy,Euklidisch,14,78,25,9691200
+5215,Greedy,Euklidisch,14,328,45,40943200
+5216,Greedy,Euklidisch,14,489,35,63509400
+5217,Greedy,Euklidisch,14,89,21,10773300
+5218,Greedy,Euklidisch,14,127,21,15529900
+5219,Greedy,Euklidisch,14,190,21,23331100
+5220,Greedy,Euklidisch,14,250,37,32066800
+5221,Greedy,Euklidisch,14,612,73,79097500
+5222,Greedy,Euklidisch,14,475,69,59420300
+5223,Greedy,Euklidisch,14,267,15,34598300
+5224,Greedy,Euklidisch,14,84,19,9977800
+5225,Greedy,Euklidisch,14,43,17,4820400
+5226,Greedy,Euklidisch,14,44,15,5190100
+5227,Greedy,Euklidisch,14,252,43,32048100
+5228,Greedy,Euklidisch,14,283,37,36688300
+5229,Greedy,Euklidisch,14,39,19,4627700
+5230,Greedy,Euklidisch,14,319,73,40038700
+5231,Greedy,Euklidisch,14,41,15,4840100
+5232,Greedy,Euklidisch,14,246,45,31748300
+5233,Greedy,Euklidisch,14,133,43,16608600
+5234,Greedy,Euklidisch,14,46,15,5236600
+5235,Greedy,Euklidisch,14,24,15,2768500
+5236,Greedy,Euklidisch,14,214,29,27724400
+5237,Greedy,Euklidisch,14,30,15,3330900
+5238,Greedy,Euklidisch,14,289,39,36368100
+5239,Greedy,Euklidisch,14,29,15,3315300
+5240,Greedy,Euklidisch,14,213,39,27672200
+5241,Greedy,Euklidisch,14,769,75,96770600
+5242,Greedy,Euklidisch,14,32,15,3574000
+5243,Greedy,Euklidisch,14,133,23,16271300
+5244,Greedy,Euklidisch,14,30,15,3404600
+5245,Greedy,Euklidisch,14,253,53,31378900
+5246,Greedy,Euklidisch,14,253,37,32449500
+5247,Greedy,Euklidisch,14,414,61,51729300
+5248,Greedy,Euklidisch,14,83,21,10502800
+5249,Greedy,Euklidisch,14,141,35,16956400
+5250,Greedy,Euklidisch,14,34,15,4019200
+5251,Greedy,Euklidisch,14,194,37,23884600
+5252,Greedy,Euklidisch,14,28,15,3179600
+5253,Greedy,Euklidisch,14,84,17,10263900
+5254,Greedy,Euklidisch,14,64,17,7349100
+5255,Greedy,Euklidisch,14,224,31,28976800
+5256,Greedy,Euklidisch,14,241,21,30116800
+5257,Greedy,Euklidisch,14,137,31,16563400
+5258,Greedy,Euklidisch,14,593,61,75701000
+5259,Greedy,Euklidisch,14,250,23,31537600
+5260,Greedy,Euklidisch,14,238,35,30584600
+5261,Greedy,Euklidisch,14,233,33,30595400
+5262,Greedy,Euklidisch,14,31,15,3481200
+5263,Greedy,Euklidisch,14,33,15,3634300
+5264,Greedy,Euklidisch,14,103,35,12504500
+5265,Greedy,Euklidisch,14,407,55,50680600
+5266,Greedy,Euklidisch,14,285,45,36946100
+5267,Greedy,Euklidisch,14,55,17,6605200
+5268,Greedy,Euklidisch,14,319,45,40223400
+5269,Greedy,Euklidisch,14,230,31,29108000
+5270,Greedy,Euklidisch,14,34,19,4050100
+5271,Greedy,Euklidisch,14,308,53,38459400
+5272,Greedy,Euklidisch,14,53,23,6285900
+5273,Greedy,Euklidisch,14,231,37,29475100
+5274,Greedy,Euklidisch,14,266,37,34046100
+5275,Greedy,Euklidisch,14,287,33,36920500
+5276,Greedy,Euklidisch,14,66,15,8131100
+5277,Greedy,Euklidisch,14,39,15,4450700
+5278,Greedy,Euklidisch,14,317,33,40653900
+5279,Greedy,Euklidisch,14,280,43,35522300
+5280,Greedy,Euklidisch,14,30,15,3943700
+5281,Greedy,Euklidisch,14,298,45,38075200
+5282,Greedy,Euklidisch,14,85,27,10185500
+5283,Greedy,Euklidisch,14,280,41,35841400
+5284,Greedy,Euklidisch,14,79,25,10070300
+5285,Greedy,Euklidisch,14,312,35,39527500
+5286,Greedy,Euklidisch,14,534,37,69352300
+5287,Greedy,Euklidisch,14,27,15,3028200
+5288,Greedy,Euklidisch,14,269,57,33398100
+5289,Greedy,Euklidisch,14,786,55,101139200
+5290,Greedy,Euklidisch,14,96,29,11405900
+5291,Greedy,Euklidisch,14,144,21,17557000
+5292,Greedy,Euklidisch,14,265,23,34080200
+5293,Greedy,Euklidisch,14,300,63,37811700
+5294,Greedy,Euklidisch,14,508,57,65300300
+5295,Greedy,Euklidisch,14,33,15,3712100
+5296,Greedy,Euklidisch,14,288,35,36669800
+5297,Greedy,Euklidisch,14,283,21,36238100
+5298,Greedy,Euklidisch,14,87,31,10648300
+5299,Greedy,Euklidisch,14,535,65,68946200
+5300,Greedy,Euklidisch,14,180,27,22525700
+5301,Greedy,Euklidisch,14,526,45,68441300
+5302,Greedy,Euklidisch,14,35,17,4205400
+5303,Greedy,Euklidisch,14,244,29,31223400
+5304,Greedy,Euklidisch,14,232,45,29975000
+5305,Greedy,Euklidisch,14,292,41,37644500
+5306,Greedy,Euklidisch,14,29,15,3366800
+5307,Greedy,Euklidisch,14,35,17,4224500
+5308,Greedy,Euklidisch,14,560,79,71684100
+5309,Greedy,Euklidisch,14,31,15,3609000
+5310,Greedy,Euklidisch,14,257,61,31995000
+5311,Greedy,Euklidisch,14,496,35,64067200
+5312,Greedy,Euklidisch,14,592,69,73999800
+5313,Greedy,Euklidisch,14,596,67,74128900
+5314,Greedy,Euklidisch,14,234,17,30062700
+5315,Greedy,Euklidisch,14,266,45,34066100
+5316,Greedy,Euklidisch,14,25,15,3030000
+5317,Greedy,Euklidisch,14,84,27,10341200
+5318,Greedy,Euklidisch,14,504,63,63808000
+5319,Greedy,Euklidisch,14,270,49,34657600
+5320,Greedy,Euklidisch,14,227,35,29475200
+5321,Greedy,Euklidisch,14,73,17,8691600
+5322,Greedy,Euklidisch,14,236,45,30442700
+5323,Greedy,Euklidisch,14,838,51,105664900
+5324,Greedy,Euklidisch,14,34,15,3831300
+5325,Greedy,Euklidisch,14,397,37,48763700
+5326,Greedy,Euklidisch,14,295,43,37290800
+5327,Greedy,Euklidisch,14,609,67,77226600
+5328,Greedy,Euklidisch,14,428,53,54099400
+5329,Greedy,Euklidisch,14,266,33,33102900
+5330,Greedy,Euklidisch,14,230,27,29393200
+5331,Greedy,Euklidisch,14,65,21,7555500
+5332,Greedy,Euklidisch,14,360,51,44702700
+5333,Greedy,Euklidisch,14,34,15,3710200
+5334,Greedy,Euklidisch,14,240,39,30630400
+5335,Greedy,Euklidisch,14,31,15,3856500
+5336,Greedy,Euklidisch,14,279,55,37677400
+5337,Greedy,Euklidisch,14,246,35,33163100
+5338,Greedy,Euklidisch,14,29,15,3331600
+5339,Greedy,Euklidisch,14,127,37,16586500
+5340,Greedy,Euklidisch,14,124,31,15852500
+5341,Greedy,Euklidisch,14,263,39,35563700
+5342,Greedy,Euklidisch,14,523,45,68292100
+5343,Greedy,Euklidisch,14,30,15,3562500
+5344,Greedy,Euklidisch,14,287,49,38820700
+5345,Greedy,Euklidisch,14,244,49,31669300
+5346,Greedy,Euklidisch,14,263,39,35373400
+5347,Greedy,Euklidisch,14,252,29,34008400
+5348,Greedy,Euklidisch,14,309,31,39944800
+5349,Greedy,Euklidisch,14,329,35,41975400
+5350,Greedy,Euklidisch,14,29,15,3176100
+5351,Greedy,Euklidisch,14,110,27,13529300
+5352,Greedy,Euklidisch,14,487,69,60338300
+5353,Greedy,Euklidisch,14,282,33,36231300
+5354,Greedy,Euklidisch,14,27,15,3136600
+5355,Greedy,Euklidisch,14,326,27,41989000
+5356,Greedy,Euklidisch,14,414,55,52737700
+5357,Greedy,Euklidisch,14,62,23,7425000
+5358,Greedy,Euklidisch,14,250,39,32357700
+5359,Greedy,Euklidisch,14,293,41,37494100
+5360,Greedy,Euklidisch,14,31,15,3504100
+5361,Greedy,Euklidisch,14,542,61,70408000
+5362,Greedy,Euklidisch,14,247,37,31672800
+5363,Greedy,Euklidisch,14,376,45,48105100
+5364,Greedy,Euklidisch,14,580,53,73728900
+5365,Greedy,Euklidisch,14,269,47,34634200
+5366,Greedy,Euklidisch,14,283,43,35901200
+5367,Greedy,Euklidisch,14,27,15,3269500
+5368,Greedy,Euklidisch,14,596,67,74628600
+5369,Greedy,Euklidisch,14,237,55,29618300
+5370,Greedy,Euklidisch,14,25,15,3174100
+5371,Greedy,Euklidisch,14,253,39,32210500
+5372,Greedy,Euklidisch,14,552,53,71701000
+5373,Greedy,Euklidisch,14,43,15,5311800
+5374,Greedy,Euklidisch,14,32,15,3474100
+5375,Greedy,Euklidisch,14,547,55,70743000
+5376,Greedy,Euklidisch,14,55,21,6318700
+5377,Greedy,Euklidisch,14,229,33,29684400
+5378,Greedy,Euklidisch,14,301,49,38062600
+5379,Greedy,Euklidisch,14,35,17,3973600
+5380,Greedy,Euklidisch,14,230,39,30016000
+5381,Greedy,Euklidisch,14,572,55,73104000
+5382,Greedy,Euklidisch,14,282,37,36099000
+5383,Greedy,Euklidisch,14,219,43,28469000
+5384,Greedy,Euklidisch,14,32,15,3683900
+5385,Greedy,Euklidisch,14,572,55,73445900
+5386,Greedy,Euklidisch,14,100,25,12169300
+5387,Greedy,Euklidisch,14,340,23,43300700
+5388,Greedy,Euklidisch,14,151,47,18784100
+5389,Greedy,Euklidisch,14,29,15,3172100
+5390,Greedy,Euklidisch,14,363,35,46615000
+5391,Greedy,Euklidisch,14,302,45,38824900
+5392,Greedy,Euklidisch,14,35,17,4121300
+5393,Greedy,Euklidisch,14,257,61,32111000
+5394,Greedy,Euklidisch,14,36,15,4073200
+5395,Greedy,Euklidisch,16,40,17,4483700
+5396,Greedy,Euklidisch,16,366,23,46468700
+5397,Greedy,Euklidisch,16,299,37,38552600
+5398,Greedy,Euklidisch,16,303,29,38158100
+5399,Greedy,Euklidisch,16,110,31,13407300
+5400,Greedy,Euklidisch,16,61,17,6911700
+5401,Greedy,Euklidisch,16,171,45,21389200
+5402,Greedy,Euklidisch,16,391,47,49972400
+5403,Greedy,Euklidisch,16,85,31,10819600
+5404,Greedy,Euklidisch,16,932,69,124377700
+5405,Greedy,Euklidisch,16,236,49,31303200
+5406,Greedy,Euklidisch,16,292,37,38799100
+5407,Greedy,Euklidisch,16,277,55,36298800
+5408,Greedy,Euklidisch,16,238,51,31182500
+5409,Greedy,Euklidisch,16,754,69,101622300
+5410,Greedy,Euklidisch,16,420,45,54667000
+5411,Greedy,Euklidisch,16,292,29,39271300
+5412,Greedy,Euklidisch,16,268,55,34995500
+5413,Greedy,Euklidisch,16,188,49,24228100
+5414,Greedy,Euklidisch,16,35,17,4483100
+5415,Greedy,Euklidisch,16,163,49,20580900
+5416,Greedy,Euklidisch,16,538,57,73429300
+5417,Greedy,Euklidisch,16,241,45,33190100
+5418,Greedy,Euklidisch,16,290,31,38163800
+5419,Greedy,Euklidisch,16,316,53,42155000
+5420,Greedy,Euklidisch,16,239,37,31841100
+5421,Greedy,Euklidisch,16,116,43,13903600
+5422,Greedy,Euklidisch,16,318,49,40170400
+5423,Greedy,Euklidisch,16,295,17,38055300
+5424,Greedy,Euklidisch,16,469,67,58987800
+5425,Greedy,Euklidisch,16,89,23,10362300
+5426,Greedy,Euklidisch,16,513,39,67038900
+5427,Greedy,Euklidisch,16,35,17,3857400
+5428,Greedy,Euklidisch,16,37,19,4203500
+5429,Greedy,Euklidisch,16,362,49,45958600
+5430,Greedy,Euklidisch,16,59,17,6952900
+5431,Greedy,Euklidisch,16,366,45,46692700
+5432,Greedy,Euklidisch,16,241,27,30860100
+5433,Greedy,Euklidisch,16,253,45,32526100
+5434,Greedy,Euklidisch,16,278,33,34916900
+5435,Greedy,Euklidisch,16,505,39,62738400
+5436,Greedy,Euklidisch,16,29,17,3342300
+5437,Greedy,Euklidisch,16,224,37,28710600
+5438,Greedy,Euklidisch,16,257,17,33091600
+5439,Greedy,Euklidisch,16,323,67,40194600
+5440,Greedy,Euklidisch,16,415,61,52062000
+5441,Greedy,Euklidisch,16,402,51,50313300
+5442,Greedy,Euklidisch,16,562,43,69745300
+5443,Greedy,Euklidisch,16,282,51,35044000
+5444,Greedy,Euklidisch,16,182,21,22569900
+5445,Greedy,Euklidisch,16,32,17,3666700
+5446,Greedy,Euklidisch,16,268,51,34469400
+5447,Greedy,Euklidisch,16,48,23,5499200
+5448,Greedy,Euklidisch,16,306,43,38375600
+5449,Greedy,Euklidisch,16,207,49,25924400
+5450,Greedy,Euklidisch,16,269,61,33831800
+5451,Greedy,Euklidisch,16,80,25,9054000
+5452,Greedy,Euklidisch,16,115,33,13917500
+5453,Greedy,Euklidisch,16,887,65,112972300
+5454,Greedy,Euklidisch,16,280,45,35263700
+5455,Greedy,Euklidisch,16,284,47,35216000
+5456,Greedy,Euklidisch,16,649,77,81416300
+5457,Greedy,Euklidisch,16,48,17,5437900
+5458,Greedy,Euklidisch,16,309,27,38992200
+5459,Greedy,Euklidisch,16,547,33,69988900
+5460,Greedy,Euklidisch,16,504,77,62278300
+5461,Greedy,Euklidisch,16,395,63,49519400
+5462,Greedy,Euklidisch,16,59,23,7218200
+5463,Greedy,Euklidisch,16,258,37,32368600
+5464,Greedy,Euklidisch,16,70,17,8400800
+5465,Greedy,Euklidisch,16,314,47,38241800
+5466,Greedy,Euklidisch,16,236,39,29048300
+5467,Greedy,Euklidisch,16,222,27,27605500
+5468,Greedy,Euklidisch,16,220,43,26735900
+5469,Greedy,Euklidisch,16,45,23,5058800
+5470,Greedy,Euklidisch,16,139,29,16844300
+5471,Greedy,Euklidisch,16,315,35,39921400
+5472,Greedy,Euklidisch,16,254,41,31624000
+5473,Greedy,Euklidisch,16,74,29,8904800
+5474,Greedy,Euklidisch,16,739,71,93523700
+5475,Greedy,Euklidisch,16,459,23,56787100
+5476,Greedy,Euklidisch,16,321,51,40066300
+5477,Greedy,Euklidisch,16,104,35,12251100
+5478,Greedy,Euklidisch,16,787,65,99319100
+5479,Greedy,Euklidisch,16,271,37,33645300
+5480,Greedy,Euklidisch,16,303,25,37600500
+5481,Greedy,Euklidisch,16,324,65,39369600
+5482,Greedy,Euklidisch,16,284,17,35988500
+5483,Greedy,Euklidisch,16,89,29,10495200
+5484,Greedy,Euklidisch,16,750,111,92263600
+5485,Greedy,Euklidisch,16,145,49,17746400
+5486,Greedy,Euklidisch,16,131,33,15918000
+5487,Greedy,Euklidisch,16,249,33,30565800
+5488,Greedy,Euklidisch,16,221,37,28057400
+5489,Greedy,Euklidisch,16,134,33,15935900
+5490,Greedy,Euklidisch,16,429,43,53268800
+5491,Greedy,Euklidisch,16,297,17,37567000
+5492,Greedy,Euklidisch,16,253,31,31727600
+5493,Greedy,Euklidisch,16,298,47,36743900
+5494,Greedy,Euklidisch,16,538,49,66112000
+5495,Greedy,Euklidisch,16,41,17,4681800
+5496,Greedy,Euklidisch,16,285,37,35857500
+5497,Greedy,Euklidisch,16,147,47,17826900
+5498,Greedy,Euklidisch,16,34,17,3926900
+5499,Greedy,Euklidisch,16,31,17,3515900
+5500,Greedy,Euklidisch,16,64,25,7493600
+5501,Greedy,Euklidisch,16,435,69,53596500
+5502,Greedy,Euklidisch,16,447,51,55332000
+5503,Greedy,Euklidisch,16,38,17,4282400
+5504,Greedy,Euklidisch,16,47,23,5213200
+5505,Greedy,Euklidisch,16,128,43,15037400
+5506,Greedy,Euklidisch,16,300,35,37741500
+5507,Greedy,Euklidisch,16,519,53,65351500
+5508,Greedy,Euklidisch,16,261,45,32458700
+5509,Greedy,Euklidisch,16,380,45,47277300
+5510,Greedy,Euklidisch,16,278,19,34607300
+5511,Greedy,Euklidisch,16,37,17,4037600
+5512,Greedy,Euklidisch,16,84,23,9929400
+5513,Greedy,Euklidisch,16,254,23,32340000
+5514,Greedy,Euklidisch,16,388,49,46794700
+5515,Greedy,Euklidisch,16,69,23,8025000
+5516,Greedy,Euklidisch,16,274,35,34583300
+5517,Greedy,Euklidisch,16,302,39,37129000
+5518,Greedy,Euklidisch,16,286,45,35208200
+5519,Greedy,Euklidisch,16,35,17,3903800
+5520,Greedy,Euklidisch,16,288,37,35935400
+5521,Greedy,Euklidisch,16,830,83,103717400
+5522,Greedy,Euklidisch,16,321,35,39032400
+5523,Greedy,Euklidisch,16,247,45,31453800
+5524,Greedy,Euklidisch,16,548,95,67310100
+5525,Greedy,Euklidisch,16,577,57,73474600
+5526,Greedy,Euklidisch,16,142,33,16940300
+5527,Greedy,Euklidisch,16,121,33,14336700
+5528,Greedy,Euklidisch,16,194,21,23490200
+5529,Greedy,Euklidisch,16,534,49,66690100
+5530,Greedy,Euklidisch,16,235,33,29533400
+5531,Greedy,Euklidisch,16,435,85,53810000
+5532,Greedy,Euklidisch,16,319,47,40322800
+5533,Greedy,Euklidisch,16,265,19,33274700
+5534,Greedy,Euklidisch,16,298,45,37010000
+5535,Greedy,Euklidisch,16,232,35,29496100
+5536,Greedy,Euklidisch,16,550,59,67411100
+5537,Greedy,Euklidisch,16,572,91,69654800
+5538,Greedy,Euklidisch,16,254,55,31286300
+5539,Greedy,Euklidisch,16,272,21,34263800
+5540,Greedy,Euklidisch,16,122,35,14397800
+5541,Greedy,Euklidisch,16,229,35,27757200
+5542,Greedy,Euklidisch,16,467,21,57457000
+5543,Greedy,Euklidisch,16,236,29,28685800
+5544,Greedy,Euklidisch,16,287,53,35846300
+5545,Greedy,Euklidisch,16,61,19,7017300
+5546,Greedy,Euklidisch,16,278,33,34395900
+5547,Greedy,Euklidisch,16,838,61,104837900
+5548,Greedy,Euklidisch,16,44,19,5213900
+5549,Greedy,Euklidisch,16,345,57,42774300
+5550,Greedy,Euklidisch,16,228,49,27532700
+5551,Greedy,Euklidisch,16,110,31,13134200
+5552,Greedy,Euklidisch,16,256,43,32192100
+5553,Greedy,Euklidisch,16,684,67,84755500
+5554,Greedy,Euklidisch,16,285,23,36275400
+5555,Greedy,Euklidisch,16,241,37,30415900
+5556,Greedy,Euklidisch,16,124,35,14740400
+5557,Greedy,Euklidisch,16,128,33,15467600
+5558,Greedy,Euklidisch,16,549,59,70595600
+5559,Greedy,Euklidisch,16,136,45,16233800
+5560,Greedy,Euklidisch,16,327,23,40774000
+5561,Greedy,Euklidisch,16,277,39,35123900
+5562,Greedy,Euklidisch,16,338,27,42446800
+5563,Greedy,Euklidisch,16,239,41,29054300
+5564,Greedy,Euklidisch,16,95,25,11853900
+5565,Greedy,Euklidisch,16,305,53,38087000
+5566,Greedy,Euklidisch,16,295,55,38072500
+5567,Greedy,Euklidisch,16,78,31,9205400
+5568,Greedy,Euklidisch,16,314,45,38778400
+5569,Greedy,Euklidisch,16,42,17,4661100
+5570,Greedy,Euklidisch,16,30,17,3340500
+5571,Greedy,Euklidisch,16,545,37,70014000
+5572,Greedy,Euklidisch,16,123,35,14773900
+5573,Greedy,Euklidisch,16,255,43,32315000
+5574,Greedy,Euklidisch,16,425,73,53627400
+5575,Greedy,Euklidisch,16,310,55,38283100
+5576,Greedy,Euklidisch,16,342,43,41901900
+5577,Greedy,Euklidisch,16,288,35,36951900
+5578,Greedy,Euklidisch,16,504,61,64329800
+5579,Greedy,Euklidisch,16,592,53,75584200
+5580,Greedy,Euklidisch,16,273,47,34615300
+5581,Greedy,Euklidisch,16,556,71,68041400
+5582,Greedy,Euklidisch,16,470,73,59763900
+5583,Greedy,Euklidisch,16,573,55,70930300
+5584,Greedy,Euklidisch,16,427,63,53273200
+5585,Greedy,Euklidisch,16,527,69,66794300
+5586,Greedy,Euklidisch,16,231,53,28233300
+5587,Greedy,Euklidisch,16,34,17,3720900
+5588,Greedy,Euklidisch,16,363,47,45248900
+5589,Greedy,Euklidisch,16,99,35,11924500
+5590,Greedy,Euklidisch,16,121,35,14414700
+5591,Greedy,Euklidisch,16,144,37,17013900
+5592,Greedy,Euklidisch,16,258,39,32328600
+5593,Greedy,Euklidisch,16,558,53,70260800
+5594,Greedy,Euklidisch,16,105,27,12633700
+5595,Greedy,Euklidisch,16,194,35,23773600
+5596,Greedy,Euklidisch,16,306,29,38063100
+5597,Greedy,Euklidisch,16,688,127,84655200
+5598,Greedy,Euklidisch,16,288,35,35849100
+5599,Greedy,Euklidisch,16,861,57,106347100
+5600,Greedy,Euklidisch,16,233,23,29625600
+5601,Greedy,Euklidisch,16,152,35,18259200
+5602,Greedy,Euklidisch,16,480,45,59210300
+5603,Greedy,Euklidisch,16,511,53,61806500
+5604,Greedy,Euklidisch,16,457,57,57928800
+5605,Greedy,Euklidisch,16,248,61,30407300
+5606,Greedy,Euklidisch,16,242,51,29500000
+5607,Greedy,Euklidisch,16,246,45,31119700
+5608,Greedy,Euklidisch,16,333,77,40669900
+5609,Greedy,Euklidisch,16,42,17,4880200
+5610,Greedy,Euklidisch,16,338,37,42370400
+5611,Greedy,Euklidisch,16,424,51,52096100
+5612,Greedy,Euklidisch,16,72,25,8235200
+5613,Greedy,Euklidisch,16,36,19,4019500
+5614,Greedy,Euklidisch,16,317,25,40066500
+5615,Greedy,Euklidisch,16,84,23,10000400
+5616,Greedy,Euklidisch,16,304,37,38149700
+5617,Greedy,Euklidisch,16,416,57,50381200
+5618,Greedy,Euklidisch,16,497,69,61191500
+5619,Greedy,Euklidisch,16,313,59,38269100
+5620,Greedy,Euklidisch,16,731,67,92982800
+5621,Greedy,Euklidisch,16,559,59,70343100
+5622,Greedy,Euklidisch,16,254,55,31136100
+5623,Greedy,Euklidisch,16,267,23,33582200
+5624,Greedy,Euklidisch,16,278,33,34595800
+5625,Greedy,Euklidisch,16,617,67,79271400
+5626,Greedy,Euklidisch,16,329,65,43019600
+5627,Greedy,Euklidisch,16,301,45,40644800
+5628,Greedy,Euklidisch,16,254,39,34026100
+5629,Greedy,Euklidisch,16,235,19,31523500
+5630,Greedy,Euklidisch,16,536,71,73831400
+5631,Greedy,Euklidisch,16,343,29,43872500
+5632,Greedy,Euklidisch,16,247,25,30738200
+5633,Greedy,Euklidisch,16,299,39,38082600
+5634,Greedy,Euklidisch,16,747,41,95384300
+5635,Greedy,Euklidisch,16,318,51,39612700
+5636,Greedy,Euklidisch,16,224,53,29669600
+5637,Greedy,Euklidisch,16,281,43,49087100
+5638,Greedy,Euklidisch,16,412,57,50088600
+5639,Greedy,Euklidisch,16,647,101,80427700
+5640,Greedy,Euklidisch,16,76,23,8788900
+5641,Greedy,Euklidisch,16,105,29,12613800
+5642,Greedy,Euklidisch,16,248,45,31019600
+5643,Greedy,Euklidisch,16,60,23,7020400
+5644,Greedy,Euklidisch,16,91,23,10893200
+5645,Greedy,Euklidisch,16,95,29,11353700
+5646,Greedy,Euklidisch,16,578,43,71009700
+5647,Greedy,Euklidisch,16,221,37,27507400
+5648,Greedy,Euklidisch,16,508,35,62931900
+5649,Greedy,Euklidisch,16,126,35,15067900
+5650,Greedy,Euklidisch,16,37,17,4022200
+5651,Greedy,Euklidisch,16,36,17,4103800
+5652,Greedy,Euklidisch,16,238,55,29083900
+5653,Greedy,Euklidisch,16,556,53,68446200
+5654,Greedy,Euklidisch,16,710,87,87479500
+5655,Greedy,Euklidisch,16,515,51,64954300
+5656,Greedy,Euklidisch,16,203,25,25063400
+5657,Greedy,Euklidisch,16,697,67,86302100
+5658,Greedy,Euklidisch,16,38,17,4351700
+5659,Greedy,Euklidisch,16,322,17,39130800
+5660,Greedy,Euklidisch,16,334,75,40862200
+5661,Greedy,Euklidisch,16,265,47,32401200
+5662,Greedy,Euklidisch,16,217,33,27134100
+5663,Greedy,Euklidisch,16,433,81,54639900
+5664,Greedy,Euklidisch,16,497,47,62664100
+5665,Greedy,Euklidisch,16,80,33,9279600
+5666,Greedy,Euklidisch,16,435,55,53184800
+5667,Greedy,Euklidisch,16,322,31,40042300
+5668,Greedy,Euklidisch,18,400,31,48797900
+5669,Greedy,Euklidisch,18,326,31,40446200
+5670,Greedy,Euklidisch,18,294,29,36781100
+5671,Greedy,Euklidisch,18,482,57,60174200
+5672,Greedy,Euklidisch,18,314,29,40394800
+5673,Greedy,Euklidisch,18,230,37,30134600
+5674,Greedy,Euklidisch,18,268,21,35753800
+5675,Greedy,Euklidisch,18,264,25,34652600
+5676,Greedy,Euklidisch,18,304,31,40759400
+5677,Greedy,Euklidisch,18,112,29,14224600
+5678,Greedy,Euklidisch,18,34,19,4170900
+5679,Greedy,Euklidisch,18,570,65,76568900
+5680,Greedy,Euklidisch,18,269,53,34981900
+5681,Greedy,Euklidisch,18,285,45,37682200
+5682,Greedy,Euklidisch,18,363,51,48896400
+5683,Greedy,Euklidisch,18,132,41,16882100
+5684,Greedy,Euklidisch,18,65,21,7829000
+5685,Greedy,Euklidisch,18,323,47,42824900
+5686,Greedy,Euklidisch,18,342,47,45120800
+5687,Greedy,Euklidisch,18,290,19,38211800
+5688,Greedy,Euklidisch,18,820,65,109148300
+5689,Greedy,Euklidisch,18,264,41,35475100
+5690,Greedy,Euklidisch,18,311,29,41791200
+5691,Greedy,Euklidisch,18,788,55,104188900
+5692,Greedy,Euklidisch,18,577,125,72531200
+5693,Greedy,Euklidisch,18,246,39,31470200
+5694,Greedy,Euklidisch,18,351,51,44376000
+5695,Greedy,Euklidisch,18,81,25,9579500
+5696,Greedy,Euklidisch,18,174,31,21105900
+5697,Greedy,Euklidisch,18,309,53,37673100
+5698,Greedy,Euklidisch,18,286,59,36015200
+5699,Greedy,Euklidisch,18,49,19,5441500
+5700,Greedy,Euklidisch,18,318,31,40393000
+5701,Greedy,Euklidisch,18,377,29,47282800
+5702,Greedy,Euklidisch,18,269,37,33594700
+5703,Greedy,Euklidisch,18,459,45,58708600
+5704,Greedy,Euklidisch,18,379,89,46681000
+5705,Greedy,Euklidisch,18,246,45,30357600
+5706,Greedy,Euklidisch,18,75,25,9096700
+5707,Greedy,Euklidisch,18,270,19,34574600
+5708,Greedy,Euklidisch,18,260,39,33487200
+5709,Greedy,Euklidisch,18,307,45,38210100
+5710,Greedy,Euklidisch,18,464,75,57976200
+5711,Greedy,Euklidisch,18,499,47,64570300
+5712,Greedy,Euklidisch,18,351,33,44883800
+5713,Greedy,Euklidisch,18,321,59,40113600
+5714,Greedy,Euklidisch,18,307,71,38691300
+5715,Greedy,Euklidisch,18,745,89,94402900
+5716,Greedy,Euklidisch,18,551,73,69092400
+5717,Greedy,Euklidisch,18,302,33,37937000
+5718,Greedy,Euklidisch,18,594,67,75248000
+5719,Greedy,Euklidisch,18,750,77,94850400
+5720,Greedy,Euklidisch,18,85,35,10267600
+5721,Greedy,Euklidisch,18,504,67,62238000
+5722,Greedy,Euklidisch,18,169,33,20980700
+5723,Greedy,Euklidisch,18,319,31,40010900
+5724,Greedy,Euklidisch,18,222,27,27769400
+5725,Greedy,Euklidisch,18,755,61,95432200
+5726,Greedy,Euklidisch,18,243,29,30370600
+5727,Greedy,Euklidisch,18,337,55,42246600
+5728,Greedy,Euklidisch,18,149,27,18171700
+5729,Greedy,Euklidisch,18,200,47,24273800
+5730,Greedy,Euklidisch,18,272,59,33191000
+5731,Greedy,Euklidisch,18,307,79,37079300
+5732,Greedy,Euklidisch,18,151,29,18522600
+5733,Greedy,Euklidisch,18,513,61,62735700
+5734,Greedy,Euklidisch,18,333,71,40255200
+5735,Greedy,Euklidisch,18,280,37,34264800
+5736,Greedy,Euklidisch,18,315,51,39214000
+5737,Greedy,Euklidisch,18,200,45,24160500
+5738,Greedy,Euklidisch,18,285,55,34717800
+5739,Greedy,Euklidisch,18,559,73,70529100
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diff --git a/Tom/results_4.csv b/Tom/results_4.csv
new file mode 100644
index 0000000000000000000000000000000000000000..3f2a1f411db7d835a29a3344353d302160556c13
--- /dev/null
+++ b/Tom/results_4.csv
@@ -0,0 +1,11967 @@
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