From 783b743520ffb81833e172c218cdcb4b867b3ac7 Mon Sep 17 00:00:00 2001
From: TOM <tom.schmidt@physik.uni-giessen.de>
Date: Sat, 18 May 2024 11:28:07 +0200
Subject: [PATCH] finished 05 06
---
Tom/{ => 01}/HA_01_Schmidt.ipynb | 0
Tom/{ => 01}/HA_01_Schmidt.md | 0
Tom/{ => 01}/HS1.pdf | Bin
.../HA_03_04_Schmidt - Kopie.ipynb | 0
Tom/03_04/HA_03_04_Schmidt.aux | 27 +
Tom/03_04/HA_03_04_Schmidt.fdb_latexmk | 106 ++++
Tom/03_04/HA_03_04_Schmidt.fls | 273 ++++++++++
Tom/{ => 03_04}/HA_03_04_Schmidt.ipynb | 262 +++++++---
Tom/03_04/HA_03_04_Schmidt.log | 438 ++++++++++++++++
Tom/{ => 03_04}/HA_03_04_Schmidt.pdf | Bin 640935 -> 643201 bytes
Tom/03_04/HA_03_04_Schmidt.synctex.gz | Bin 0 -> 49360 bytes
Tom/{ => 03_04}/HA_03_04_Schmidt.tex | 22 +-
Tom/{ => 03_04}/initial_states.yaml | 0
Tom/{ => 03_04}/results.csv | 0
Tom/{ => 03_04}/results_4.csv | 0
Tom/03_04/results_5.csv | 201 ++++++++
Tom/05_06/HA_05_06_Schmidt.aux | 6 +
Tom/05_06/HA_05_06_Schmidt.fdb_latexmk | 96 ++++
Tom/05_06/HA_05_06_Schmidt.fls | 170 ++++++
Tom/05_06/HA_05_06_Schmidt.log | 482 ++++++++++++++++++
Tom/05_06/HA_05_06_Schmidt.pdf | Bin 0 -> 175924 bytes
Tom/05_06/HA_05_06_Schmidt.synctex.gz | Bin 0 -> 47249 bytes
Tom/05_06/HA_05_06_Schmidt.tex | 218 ++++++++
Tom/HA_03_04_Schmidt.synctex.gz | Bin 45155 -> 0 bytes
24 files changed, 2227 insertions(+), 74 deletions(-)
rename Tom/{ => 01}/HA_01_Schmidt.ipynb (100%)
rename Tom/{ => 01}/HA_01_Schmidt.md (100%)
rename Tom/{ => 01}/HS1.pdf (100%)
rename Tom/{ => 03_04}/HA_03_04_Schmidt - Kopie.ipynb (100%)
create mode 100644 Tom/03_04/HA_03_04_Schmidt.aux
create mode 100644 Tom/03_04/HA_03_04_Schmidt.fdb_latexmk
create mode 100644 Tom/03_04/HA_03_04_Schmidt.fls
rename Tom/{ => 03_04}/HA_03_04_Schmidt.ipynb (93%)
create mode 100644 Tom/03_04/HA_03_04_Schmidt.log
rename Tom/{ => 03_04}/HA_03_04_Schmidt.pdf (94%)
create mode 100644 Tom/03_04/HA_03_04_Schmidt.synctex.gz
rename Tom/{ => 03_04}/HA_03_04_Schmidt.tex (84%)
rename Tom/{ => 03_04}/initial_states.yaml (100%)
rename Tom/{ => 03_04}/results.csv (100%)
rename Tom/{ => 03_04}/results_4.csv (100%)
create mode 100644 Tom/03_04/results_5.csv
create mode 100644 Tom/05_06/HA_05_06_Schmidt.aux
create mode 100644 Tom/05_06/HA_05_06_Schmidt.fdb_latexmk
create mode 100644 Tom/05_06/HA_05_06_Schmidt.fls
create mode 100644 Tom/05_06/HA_05_06_Schmidt.log
create mode 100644 Tom/05_06/HA_05_06_Schmidt.pdf
create mode 100644 Tom/05_06/HA_05_06_Schmidt.synctex.gz
create mode 100644 Tom/05_06/HA_05_06_Schmidt.tex
delete mode 100644 Tom/HA_03_04_Schmidt.synctex.gz
diff --git a/Tom/HA_01_Schmidt.ipynb b/Tom/01/HA_01_Schmidt.ipynb
similarity index 100%
rename from Tom/HA_01_Schmidt.ipynb
rename to Tom/01/HA_01_Schmidt.ipynb
diff --git a/Tom/HA_01_Schmidt.md b/Tom/01/HA_01_Schmidt.md
similarity index 100%
rename from Tom/HA_01_Schmidt.md
rename to Tom/01/HA_01_Schmidt.md
diff --git a/Tom/HS1.pdf b/Tom/01/HS1.pdf
similarity index 100%
rename from Tom/HS1.pdf
rename to Tom/01/HS1.pdf
diff --git a/Tom/HA_03_04_Schmidt - Kopie.ipynb b/Tom/03_04/HA_03_04_Schmidt - Kopie.ipynb
similarity index 100%
rename from Tom/HA_03_04_Schmidt - Kopie.ipynb
rename to Tom/03_04/HA_03_04_Schmidt - Kopie.ipynb
diff --git a/Tom/03_04/HA_03_04_Schmidt.aux b/Tom/03_04/HA_03_04_Schmidt.aux
new file mode 100644
index 0000000..e05cb0d
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@@ -0,0 +1,27 @@
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+INPUT C:\Users\Tom\Desktop\Dateien\Uni\Gießen\KI_II\Hausaufgaben\gitlab_ki_ii_ha\Tom\images\3_19.png
+INPUT HA_03_04_Schmidt.aux
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+INPUT C:\Users\Tom\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmbx10.pfb
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diff --git a/Tom/HA_03_04_Schmidt.ipynb b/Tom/03_04/HA_03_04_Schmidt.ipynb
similarity index 93%
rename from Tom/HA_03_04_Schmidt.ipynb
rename to Tom/03_04/HA_03_04_Schmidt.ipynb
index 4a8e87d..310d68a 100644
--- a/Tom/HA_03_04_Schmidt.ipynb
+++ b/Tom/03_04/HA_03_04_Schmidt.ipynb
@@ -1224,7 +1224,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -1797,30 +1797,7 @@
"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: "
- ]
- }
- ],
+ "outputs": [],
"source": [
"ARRAY = np.array(((4, 8, 3),\n",
" (7, 6, 2),\n",
@@ -1832,15 +1809,124 @@
"\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",
+ "visited_nodes_bfs = []"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
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+ "94\n",
+ "95\n",
+ "96\n",
+ "97\n",
+ "98\n",
+ "99\n"
+ ]
+ }
+ ],
+ "source": [
"for i in range(100):\n",
- " print(f\"i: {i}\")\n",
+ " print(i)\n",
" np.random.shuffle(ARRAY)\n",
" bfs_start = NodeBFS(ARRAY)\n",
" bfs_final = NodeBFS(ARRAY_SOLVED)\n",
@@ -1849,48 +1935,88 @@
" 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",
+ " solvable_bfs.append(n == -1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
"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"
+ "results_5.to_csv(\"results_5.csv\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "107"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "results_5[\"Lösbarkeit BFS\"].sum()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0\n",
+ "1\n",
+ "2\n",
+ "3\n",
+ "4\n",
+ "5\n",
+ "6\n",
+ "7\n",
+ "8\n",
+ "9\n",
+ "10\n"
+ ]
+ },
+ {
+ "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[24], line 6\u001b[0m\n\u001b[0;32m 4\u001b[0m greedy_start \u001b[38;5;241m=\u001b[39m NodeGreedy(ARRAY, manhatten_distance(ARRAY, ARRAY_SOLVED))\n\u001b[0;32m 5\u001b[0m greedy_final \u001b[38;5;241m=\u001b[39m NodeGreedy(ARRAY_SOLVED, \u001b[38;5;241m0\u001b[39m)\n\u001b[1;32m----> 6\u001b[0m n, path \u001b[38;5;241m=\u001b[39m \u001b[43minformed_search\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgreedy_start\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mgreedy_final\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmanhatten_distance\u001b[49m\u001b[43m)\u001b[49m\n",
+ "Cell \u001b[1;32mIn[11], line 27\u001b[0m, in \u001b[0;36minformed_search\u001b[1;34m(initial, final, cost_estimator)\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m pq\u001b[38;5;241m.\u001b[39mempty():\n\u001b[0;32m 26\u001b[0m current \u001b[38;5;241m=\u001b[39m pq\u001b[38;5;241m.\u001b[39mget()\n\u001b[1;32m---> 27\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[43mcurrent\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mnext_nodes\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfinal\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcost_estimator\u001b[49m\u001b[43m)\u001b[49m\u001b[43m:\u001b[49m\n\u001b[0;32m 28\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 29\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[10], line 52\u001b[0m, in \u001b[0;36mNodeGreedy.next_nodes\u001b[1;34m(self, final, cost_estimator)\u001b[0m\n\u001b[0;32m 50\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[0;32m 51\u001b[0m buffer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_make_new_state(pos_new)\n\u001b[1;32m---> 52\u001b[0m \u001b[38;5;28;01myield\u001b[39;00m \u001b[38;5;28mtype\u001b[39m(\u001b[38;5;28mself\u001b[39m)(buffer\u001b[38;5;241m.\u001b[39mcopy(), cost_estimator(buffer, \n\u001b[0;32m 53\u001b[0m final\u001b[38;5;241m.\u001b[39mstate))\n",
+ "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
+ ]
+ }
+ ],
+ "source": [
+ "for i in range(100):\n",
+ " print(i)\n",
+ " np.random.shuffle(ARRAY)\n",
+ " greedy_start = NodeGreedy(ARRAY, manhatten_distance(ARRAY, ARRAY_SOLVED))\n",
+ " greedy_final = NodeGreedy(ARRAY_SOLVED, 0)\n",
+ " n, path = informed_search(greedy_start, greedy_final, manhatten_distance)"
]
}
],
diff --git a/Tom/03_04/HA_03_04_Schmidt.log b/Tom/03_04/HA_03_04_Schmidt.log
new file mode 100644
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diff --git a/Tom/HA_03_04_Schmidt.tex b/Tom/03_04/HA_03_04_Schmidt.tex
similarity index 84%
rename from Tom/HA_03_04_Schmidt.tex
rename to Tom/03_04/HA_03_04_Schmidt.tex
index ff14fd9..0c3de4b 100644
--- a/Tom/HA_03_04_Schmidt.tex
+++ b/Tom/03_04/HA_03_04_Schmidt.tex
@@ -90,7 +90,7 @@ Algoritmus & Heuristik & Anzahl besuchter Knoten & Länge des Pfades \\
& Manhattan-Abstand & 143 & 17 \\
\hline
\end{tabular}
-\caption{Durchschnittswerte der unterschiedlichen Such-Algorithmen}
+\caption{Ergebnisse für die unterschiedlichen Such-Algorithmen}
\end{table}
@@ -107,13 +107,13 @@ Es ist deutlich zu sehen, dass die Ausführungszeiten der Greedy-Suche und A* au
\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.
+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 Tiefe entfernt liegen. Während die euklidische- und die Manhattan-Heuristik dabei einen fast identischen 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 \[\text{Ausführungszeit(Knoten, Tiefe)} = c \cdot \text{Knoten} \cdot b^{\text{Tiefe}}\]
+Alternativ könnte in der Aufgabenstellung auch ein einziges Skalierungsgesetz der Ausführungszeit in Abhängigkeit sowohl der besuchten Konten als auch der optimalen 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]
@@ -208,7 +208,7 @@ Hier die Ergebnisse für den mittleren Zusammenhang der Form $\text{Ausführungs
\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).
+Der vorgeschlagenen Algorithmus ist für alle Werte von $\omega$ vollständig, da die A*-Suche unabhängig von der Gesamtkostenfunktion den gesamten Suchbaum exploriert.
\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.
@@ -242,10 +242,20 @@ Für $\omega = 3$ wird $9-\omega^2$ zu Null und der vorgeschlagenen Algorithmus
\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.
-
+Die besten Werte in allen drei Metriken (Zeit, Besuchte Knoten, Pfadlänge) werden 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.
+\newpage
\section*{Aufgabe 5: 8er Puzzle - Lösbarkeit}
+In meinen Tests sind aus 200 zufälligen Puzzles 107 lösbar. Ich schätze deswegen, dass knapp unter 50\% aller möglichen Puzzles nicht lösbar sind.
+
+\vspace{2.5mm}
+Beim Überprüfen der Lösbarkeit mir A* rechnet mein Computer sehr lang und stürzt schließlich ab. Problem ist hier, dass der Algorithmen in unserer Implementierung für unlösbare Puzzles niemals terminiert und dadurch solange läuft, bis Arbeitsspeicher und Swap-Partition aufgebraucht sind. Das liegt an unserem Zyklencheck, welcher nur dann einen Knoten verwirft, wenn sein Zustand, seine akkumulierten Kosten und seine geschätzten Kosten übereinstimmen. Ein unlösbares Puzzle wird auf tieferer Ebene immer wieder Knoten mit bereits bekannten Zustände, aber höheren akkumulierten Kosten produzieren.
+
+\vspace{2.5mm}
+Zur Lösung dieses Problems könnten Knoten auch dann durch den Zyklencheck verworfen werden, wenn ihr Zustand bereits bekannt und ihre akkumulierten Kosten höher als frühere Knoten mit gleichem Zustand sind. Dadurch müsste der Algorithmus terminieren, wenn alle möglichen Zustände erreicht sowie der günstigste Weg zu diesen Zuständen gefunden wurde.
+
+\vspace{2.5mm}
+Das gleiche Problem tritt nicht für die Greedy-Suche auf, da hier Knoten nur basierend auf Zustand und erwarteten Kosten verworfen werden.
\end{document}
diff --git a/Tom/initial_states.yaml b/Tom/03_04/initial_states.yaml
similarity index 100%
rename from Tom/initial_states.yaml
rename to Tom/03_04/initial_states.yaml
diff --git a/Tom/results.csv b/Tom/03_04/results.csv
similarity index 100%
rename from Tom/results.csv
rename to Tom/03_04/results.csv
diff --git a/Tom/results_4.csv b/Tom/03_04/results_4.csv
similarity index 100%
rename from Tom/results_4.csv
rename to Tom/03_04/results_4.csv
diff --git a/Tom/03_04/results_5.csv b/Tom/03_04/results_5.csv
new file mode 100644
index 0000000..2ae53ca
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diff --git a/Tom/05_06/HA_05_06_Schmidt.aux b/Tom/05_06/HA_05_06_Schmidt.aux
new file mode 100644
index 0000000..41b441e
--- /dev/null
+++ b/Tom/05_06/HA_05_06_Schmidt.aux
@@ -0,0 +1,6 @@
+\relax
+\providecommand\babel@aux[2]{}
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new file mode 100644
index 0000000..3003d62
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diff --git a/Tom/05_06/HA_05_06_Schmidt.tex b/Tom/05_06/HA_05_06_Schmidt.tex
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+\documentclass{article}
+\usepackage{parskip}
+\setlength{\parindent}{0in}
+\setlength{\parskip}{\baselineskip}
+\usepackage{changepage}
+\usepackage{multirow}
+\usepackage[table]{xcolor}
+\usepackage{tabulary}
+\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, multicol}
+\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 05 und 06}
+\author{Tom Schmidt}
+\date{Mai 2024}
+\begin{document}
+\maketitle
+\subsection*{Aufgabe 01: Aussagenlogik}
+\subsubsection*{a)}
+Korrekt. 'wahr' ist eine Tautologie und folgt somit unabhängig von der Wissensbasis.
+\subsubsection*{b)}
+Nicht korrekt. 'falsch' hat keine Modelle und kann somit aus keiner Wissensbasis folgen.
+\subsubsection*{c)}
+Korrekt. $(A \land B)$ hat nur ein Modell ($A = w, B = w$) und dies ist auch ein Modell von $(A \iff B)$.
+\subsubsection*{d)}
+Nicht korrekt. $A = f, B = f$ ist ein Modell von $(A \iff B)$ aber kein Modell von $(A \lor B)$.
+\subsubsection*{e)}
+Korrekt. $(A = f, B = f)$ und $(A = w, B = w)$ sind sämtliche Modelle von $A \iff B$ und auch Modelle von $\lnot A \lor B$.
+\subsubsection*{f)}
+Korrekt. Die rechte Seite der Formel lässt sich syntaktisch umformen zu $(A \lor B \lor C) \land (\lnot(B \land C \land D) \lor E)$ und weiter zu $(A \lor B \lor C) \land (\lnot B \lor \lnot C \lor \lnot D \lor E)$. Dann wird ersichtlich, dass bei jedem Modell von $(A \lor B) \lor (\lnot C \lor \lnot D \lor E)$ entweder A oder B sowie eine der drei Formeln $\lnot C, \lnot D, \lnot E$ wahr sein müssen und dass in diesen Fällen auch $(A \lor B \lor C) \land (\lnot B \lor \lnot C \lor \lnot D \lor E)$
+\subsubsection*{g)}
+Nicht korrekt. Die jeweils linken Seiten der beiden UND-Verknüpfungen sind identisch, wir betrachten deswegen nur die beiden rechten Seiten. Dabei ist $C = f, D = w, E = f$ ein Modell von $(\lnot C \lor \lnot D \lor E)$, aber kein Modell von $(\lnot D \lor E)$.
+\subsubsection*{h)}
+Korrekt. $A = w, B = f$ ist ein Modell der Formel. Diese ist somit erfüllbar.
+\subsubsection*{i)}
+Korrekt. Die einzige Belegung, die kein Modell der rechten Seite der Formel ist, ist $A = w, B = w, C = f$. Diese Belegung ist auch kein Modell der linken Seite der Formel. Es existiert somit keine Belegung, die ein Modell der linken Seite ist und kein Modell der rechten Seite.
+\subsubsection*{j)}
+Korrekt. Die rechte Seite der Formel lässt sich syntaktisch umformen zu $((\lnot A \lor C)\land(\lnot B \lor C))$ und durch Ausklammern weiter zu $(C \lor (\lnot A \lor \lnot B))$. Das entspricht der linken Seite der Formel und aus syntaktischer Äquivalenz ($\iff$) folgt auch semantische Äquivalenz ($\equiv$).
+\subsubsection*{k)}
+Korrekt. $A = w, B = w$ ist ein Modell der Formel, sie ist somit erfüllbar.
+\subsection*{Aufgabe 02: Modelle}
+Vorüberlegung: Es sind stets $2^4 = 16$ Welten möglich, da es vier Aussagevariablen gibt.
+\subsubsection*{a)}
+15 Modelle. Nur eine der 16 möglichen Welten ist kein Modell der Formel (nämlich $B = f, C = f$).
+\subsubsection*{b)}
+15 Modelle. Nur eine der 16 möglichen Welten ist kein Modell der Formel (nämlich $A = w, B = w, C = w, D = w$).
+\subsubsection*{c)}
+Kein Modell, die Formel ist nicht erfüllbar. Dies ist sofort ersichtlich, wenn die syntaktische Umformung per Kontraposition zu $(\lnot B \implies \lnot A) \land A \land \lnot B \land C \land D$ durchgeführt wird. $\lnot B$ muss erfüllt sein, dies impliziert $\lnot A$, aber $A$ muss auch erfüllt sein $\to$ ein Widerspruch.
+\subsection*{Aufgabe 03: Einhorn}
+Ich treffe die Annahme, dass 'unsterblich' und 'sterblich' disjunkt sind d.h. die jeweils verneinte Formel der gleichen Aussage sind. Dies ist eine sprachliche Interpretation, die nicht aus der logischen Struktur der Aussage folgt.
+
+Ich definiere die Aussagevariablen:\\
+$MW$ (Einhorn ist ein mystisches Wesen)\\
+$U$ (Einhorn ist unsterblich)\\
+$S$ (Einhorn ist ein Säugetier)\\
+$B$ (Einhorn ist behörnt)\\
+$MA$ (Einhorn ist magisch)
+
+Die Aussagen ergeben nun folgende Wissensbasis:\\
+$(MW \implies U) \land(\lnot MW \implies (\lnot U \land S)) \land((U \lor S) \implies B) \land(B \implies MA)$
+
+In KNF umgeformt:\\
+$(\lnot MW \lor U)_1 \land (MW \lor \lnot U)_2 \land (MW \lor S)_3 \land (\lnot U \lor \lnot S \lor B)_4 \land (\lnot B \lor MA)_5$
+
+Per Resolution mit Faktorisierung ergibt sich:\\
+Res(1, 3) = $(U \lor S)_6$\\
+Res(6, 4) = $(\lnot S \lor B)_7$ sowie $(\lnot U \lor B)_8$\\
+Res(6, 7) = $(U \lor B)_9$\\
+Res(8, 9) = $(B)_10$\\
+Res(10, 5) = $(MA)$
+
+Das Einhorn ist somit behornt (c) und magisch (b). Für die Aussage, dass das Einhorn mystisch ist ($MW$), lässt sich aufgrund der Wissensbasis nichts sagen. Die Resolutionen mit den entsprechenden Klauseln 1, 2 und 3 führen entweder in Tautologien (Res(1,2) = $(U \lor \lnot U)$ und $(\lnot MW \lor MW)$) oder bereits bekannte Formeln (Res(1,3) = $(U \lor S)$).
+\subsection*{Aufgabe 04: Party}
+\subsubsection*{a)}
+\begin{table}[H]
+ \centering
+ \rowcolors{2}{gray!25}{white}
+ \begin{adjustwidth}{-1.5cm}{}
+ \begin{tabulary}{1\pdfpagewidth}[H]{||C|C|C|C|C|C|C||}
+ \hline
+ Essen & Party & Getraenke & $Essen \implies Party$ & $Getraenke \implies Party$ & $(Essen \land Getraenke) \implies Party$ & Gesamte Formel\\
+ \hline \hline
+ Wahr & Wahr & Wahr & Wahr & Wahr & Wahr & Wahr\\
+ Wahr & Wahr & Falsch & Wahr & Wahr & Wahr & Wahr\\
+ Wahr & Falsch & Wahr & Falsch & Falsch & Falsch & Wahr\\
+ Wahr & Falsch & Falsch & Falsch & Wahr & Wahr & Wahr\\
+ Falsch & Wahr & Wahr & Wahr & Wahr & Wahr & Wahr\\
+ Falsch & Wahr & Falsch & Wahr & Wahr & Wahr & Wahr \\
+ Falsch & Falsch & Wahr & Wahr & Falsch & Wahr & Wahr \\
+ Falsch & Falsch & Falsch & Wahr & Wahr & Wahr & Wahr\\
+ \hline
+ \end{tabulary}
+ \end{adjustwidth}
+\end{table}
+Die Formel ist somit in jeder möglichen Belegung wahr (d.i. eine Tautologie).
+\subsubsection*{b)}
+Linke Seite in KNF:
+$(\lnot Essen \lor Party \lor \lnot Getraenke)$
+
+Rechte Seite in KNF:
+$(\lnot Essen \lor Party \lor \lnot Getraenke)$
+
+Es fällt auf, dass die beiden Seiten identisch sind.
+
+\subsubsection*{c)}
+Um Resolution anwenden zu können, muss die Formel zunächst weiter umgeformt werden. Ausgehend von der KNF-Form beider Seiten:\\
+$(\lnot Essen \lor Party \lor \lnot Getraenke)\implies(\lnot Essen \lor Party \lor \lnot Getraenke)$\\
+Formen wir per Kontraposition um zu:\\
+$\lnot(\lnot Essen \lor Party \lor \lnot Getraenke)\implies \lnot(\lnot Essen \lor Party \lor \lnot Getraenke)$\\
+Nun lösen wir die letzte Implikation auf:\\
+$\lnot(\lnot(\lnot Essen \lor Party \lor \lnot Getraenke))\lor \lnot(\lnot Essen \lor Party \lor \lnot Getraenke)$\\
+Und wenden die De Morgan'schen Regeln an:\\
+$\lnot(\lnot(\lnot Essen \lor Party \lor \lnot Getraenke)\land (\lnot Essen \lor Party \lor \lnot Getraenke))$\\
+Und abschließend erneut die De Morgan'schen Regeln:\\
+$\lnot(Essen_1 \land \lnot Party_2 \land Getraenke_3 \land (\lnot Essen \lor Party \lor \lnot Getraenke)_4))$\\
+Wir sind nun bei einer verneinten KNF-Form der gesamten Formel angelangt und können den inneren Teil der Verneinung per Resolution untersuchen:\\
+Res(1,4) = $\emptyset$\\
+Res(2,4) = $\emptyset$\\
+Res(3,4) = $\emptyset$\\
+Wir enden somit bei $\lnot(\emptyset)$. D.i. der Tautologie und damit bei dem Ergebnis aus a).
+\subsection*{Aufgabe 05: Logikschaltungen}
+\subsubsection*{a)}
+\begin{table}[H]
+ \rowcolors{2}{gray!25}{white}
+ \begin{tabulary}{1\linewidth}{||C|C|C|C|C|C|C|C||}
+ \hline
+ $E_1$ & $E_2$ & $E_3$ & $=1$ & \& & \& & $A_1$ & $A_2$\\
+ \hline
+ w & w & w & f & w & f & w & w\\
+ \hline
+ w & f & f & w & f & f & w & f\\
+ \hline
+ w & f & w & w & f & w & f & w\\
+ \hline
+ w & w & f & f & w & f & f & w\\
+ \hline
+ f & w & w & w & f & w & f & w\\
+ \hline
+ f & f & w & f & f & f & w & f\\
+ \hline
+ f & w & f & w & f & f & w & f\\
+ \hline
+ f & f & f & f & f & f & f & f\\
+ \hline
+ \end{tabulary}
+\end{table}
+\subsubsection*{b)}
+Die KNF kann einfach aus der in a) erstellten Wahrheitstabelle ausgelesen werden: Für jede Zeile, die zu dem Ergebnis "f" führt wird eine Klausel gebildet. Dabei ist nur zu beachten, dass Variablen mit dem Wert "w" verneint werden.
+
+A1: $(\lnot E_1 \lor E_2 \lnot E_3) \land (\lnot E_1 \lor \lnot E_2 \land E_3) \land (E_1 \lor \lnot E_2 \lor \lnot E_3) \land (E_1 \lor E_2 \lor E_3)$
+
+A2: $(\lnot E_1 \lor E_2 \lor E_3) \land (E_1 \lor E_2 \lor \lnot E_3) \land (E_1 \lor \lnot E_2 \lor E_3) \land (E_1 \lor E_2 \lor E_3)$
+\subsection*{Aufgabe 06: Prädikatenlogik erster Stufe 1}
+\begin{table}[H]
+ \centering
+ \small
+ \begin{adjustwidth}{-0.5cm}{}
+ \begin{tabulary}{1\linewidth}{|C|C|C|C|C|J|}
+ \hline
+ \multicolumn{2}{|c|}{Aufgabe} & Syntax korrekt & Syntax falsch & Inhalt korrekt & Begründung\\
+ \hline \hline
+
+ \multirow{3}{*}{a)} & (i) & & x & & aus $Mother (x) \lor Father(x)$ resultiert ein Wahrheitswert, der syntaktisch $Loves()$ nicht übergeben werden kann.\\ \cline{2-6}
+ & (ii) & x & & x & Kann einfach in die korrekte Implikation überführt werden.\\ \cline{2-6}
+ & (iii) & x & & & $\land$ zusammen mit $\forall$ is nicht sinnvoll - hier müssten z.B. alle x Katzen sein\\ \cline{2-6}
+ \hline
+
+ \multirow{3}{*}{b)} & (i) & x & & x & Ist wahr, wenn jeder Hund, der \textbf{mindestens} einen Bruder hat, den er liebt, glücklich ist. Die Aussage in deutscher Sprache ist nicht eindeutig dahingehend, ob nur mindestens oder auch höchsten (d.i. genau ein einziger) Bruder gemeint ist. Falls letzteres der Fall ist (unwahrscheinlich), ist der logische Ausdruck inhaltlich nicht korrekt.\\ \cline{2-6}
+ & (ii) & x & & x & Auch hier gilt wie oben, dass inhaltliche Korrektheit nur dann gegeben ist, wenn auch Hunde, die mehrere ihrer Brüder lieben, glücklich sind. \\\cline{2-6}
+ & (iii) & x & & & Inhaltlich nicht korrekt, da hier impliziert wird, dass Hunde, die \textbf{alle} ihre Brüder lieben, glücklich sind.\\
+ \hline
+
+ \multirow{3}{*}{c)} & (i) & & x & & Syntaktisch falsch, da dem zweistelligen Prädikat $Child$ nur ein Term übergeben wird.\\ \cline{2-6}
+ & (ii) & x & & x & Schließt aus, dass es einen Hund x gibt, der ein Kind seiner Besitzers y beißt.\\ \cline{2-6}
+ & (iii) & x & & & Syntaktisch falsch, da in der dritten Implikation kein Quantor für y existiert und y somit nicht definiert ist.\\\cline{2-6}
+ & (iv) & x & & x & Ohne Verneinung wäre der Ausdruck wahr, wenn ein Hund existiert, der das Kind seines Besitzers beißt. Mit Verneinung ist ein solcher Hund ausgeschlossen.\\
+ \hline
+
+ \multirow{3}{*}{d)} & (i) & x & & x & Die rechte Seite der ersten Implikation sagt aus, dass die ersten Ziffern der Postleitzahlen übereinstimmen, wenn y in s lebt und die linke Seite sagt aus, dass dies nur impliziert ist, wenn auch x in s lebt.\\ \cline{2-6}
+ & (ii) & & x & & Syntaktisch falsch, da das letzte $=$ zwischen einem Wahrheitswert auf der linken Seite und einer Zahl auf der rechten Seite steht und dafür nicht definiert ist. \\ \cline{2-6}
+ & (iii) & & x & & Das Prädikat $Digit$ ist für $Digit(1, Zip(x) = Zip(y))$ nicht definiert.\\ \cline{2-6}
+ & (iv) & x & & x & Die linke Seite der Implikation ist wahr für alle x und y, die in einem Bundesland leben und die rechte Seite ist wahr, wenn die erste Ziffer ihrer Postleitzahlen gleich ist.\\
+ \hline
+
+ \end{tabulary}
+ \end{adjustwidth}
+\end{table}
+\end{document}
\ No newline at end of file
diff --git a/Tom/HA_03_04_Schmidt.synctex.gz b/Tom/HA_03_04_Schmidt.synctex.gz
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