add notebook about A* search

Signed-off-by: Michael Leuschel <leuschel@uni-duesseldorf.de>

add notebook about A* search
8f99e088 · Michael Leuschel · 6d085e2f · 8f99e088
Commit 8f99e088 authored 2 years ago by Michael Leuschel
--- a/logic_programming/9_AStar_Search.ipynb
+++ b/logic_programming/9_AStar_Search.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "9eb5530a",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "source": [
+    "Empty Prolog Notebook"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "40ad6905",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": [
+    ":- consult('prolog_files/roumania.pl')."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "9c7e889c",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mDist = 75,\n",
+       "City = zerind"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?- s(arad,Dist,City)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "af6a9e4a",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "Dist | City | \n",
+       ":- | :- | \n",
+       "75 | zerind | \n",
+       "118 | timisoara | \n",
+       "140 | sibiu | "
+      ],
+      "text/plain": [
+       "Dist | City | \n",
+       ":- | :- | \n",
+       "75 | zerind | \n",
+       "118 | timisoara | \n",
+       "140 | sibiu | "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mtrue"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "jupyter:print_table(s(arad,Dist,City))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "55da475c",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "City | Dist | \n",
+       ":- | :- | \n",
+       "zerind | 75 | \n",
+       "timisoara | 118 | \n",
+       "sibiu | 140 | "
+      ],
+      "text/plain": [
+       "City | Dist | \n",
+       ":- | :- | \n",
+       "zerind | 75 | \n",
+       "timisoara | 118 | \n",
+       "sibiu | 140 | "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mtrue"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "jupyter:print_table(wkante(City,Dist,arad))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "c32206c4",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mSLDZ = 374,\n",
+       "SLDT = 329,\n",
+       "SLDS = 253"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?- h(zerind,SLDZ), h(timisoara,SLDT), h(sibiu,SLDS)."
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "id": "3e904005",
+   "metadata": {},
+   "source": [
+    "The following is the evaluation function we will use in the A* algorithm:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "e942f0d4",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "eval_function(G_SoFar,H_EstDist,F) :- F is G_SoFar+H_EstDist. % A*\n",
+    "%eval_function(_G_SoFar,H_EstDist,F) :- F =H_EstDist. % Greedy\n",
+    "%eval_function(G_SoFar,_,F) :- F=G_SoFar. % Dijkstra"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "242f4141",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mHZerind = 449,\n",
+       "HSibiu = 393,\n",
+       "HTimisoara = 447"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?- eval_function(75,374,HZerind), eval_function(140,253,HSibiu),\n",
+    "   eval_function(118,329,HTimisoara)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "78764141",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    ":- use_module(library(heaps)).\n",
+    "\n",
+    "add_states_to_heap([],H,H).\n",
+    "add_states_to_heap([st(G,State)|T],Heap,UpdHeap) :-\n",
+    "   (h(State,SH) -> true ; print(err(State)),nl,SH=1000),  % compute heuristic function\n",
+    "   eval_function(G,SH,F),  % Compute weight\n",
+    "   add_to_heap(Heap,F,st(G,State),H2),\n",
+    "   add_states_to_heap(T,H2,UpdHeap)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "b03ac6e7",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       " A* Heap = [393-st(140,sibiu),447-st(118,timisoara),449-st(75,zerind)]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mEH = heap(nil,0),\n",
+       "NewHeap = heap(t(st(140,sibiu),393,[t(st(118,timisoara),447,[]),t(st(75,zerind),449,[])]),3),\n",
+       "List = [393-st(140,sibiu),447-st(118,timisoara),449-st(75,zerind)]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?- empty_heap(EH), add_states_to_heap([st(75,zerind),st(140,sibiu),st(118,timisoara)],EH,NewHeap),\n",
+    "   heap_to_list(NewHeap,List), format(' A* Heap = ~w~n',[List])."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "f6f156a3",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "astar :- statistics(runtime,_),start(S), \n",
+    "         astar(S), \n",
+    "         statistics(runtime,[_,T]), print(T),print(' ms'),nl.\n",
+    "\n",
+    "astar(S) :- empty_heap(EH),\n",
+    "   add_states_to_heap([st(0,S)],EH,StartHeap),\n",
+    "   nl,print('Starting A* search'),nl, \n",
+    "   asearch(StartHeap,1).\n",
+    "\n",
+    "asearch(Heap,StepNr) :- \n",
+    "   heap_to_list(Heap,List), format(' ~w: A* Heap = ~w~n',[StepNr,List]),\n",
+    "  get_from_heap(Heap,_Heuristic,st(G,State),NewHeap),\n",
+    "  %print(StepNr),print(' ==> '), print(st(G,State)),nl,\n",
+    "  process_node(G,State,NewHeap,StepNr).\n",
+    "\n",
+    "% process_node(DistanceFromStart,State, Heap, StepNr)\n",
+    "process_node(G,State,_,StepNr) :-\n",
+    "   ziel(State),\n",
+    "   format('GOAL found at step ~w with distance ~w : ~w~n',[StepNr,G,State]).\n",
+    "process_node(G,State,Heap,StepNr) :-\n",
+    "   findall(st(G1,SuccState),\n",
+    "\t         (wkante(State,Weight,SuccState),G1 is G+Weight),SList),\n",
+    "\t% print(succs(SList)),nl,\n",
+    "    add_states_to_heap(SList,Heap,UpdatedHeap),\n",
+    "    S1 is StepNr+1,\n",
+    "    asearch(UpdatedHeap,S1)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "9639129f",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "'Starting A* search'\n",
+       " 1: A* Heap = [366-st(0,arad)]\n",
+       " 2: A* Heap = [393-st(140,sibiu),447-st(118,timisoara),449-st(75,zerind)]\n",
+       " 3: A* Heap = [413-st(220,rimnicu_vilcea),417-st(239,fagaras),447-st(118,timisoara),449-st(75,zerind),646-st(280,arad),671-st(291,oradea)]\n",
+       " 4: A* Heap = [415-st(317,pitesti),417-st(239,fagaras),447-st(118,timisoara),449-st(75,zerind),526-st(366,craiova),553-st(300,sibiu),646-st(280,arad),671-st(291,oradea)]\n",
+       " 5: A* Heap = [417-st(239,fagaras),418-st(418,bucharest),447-st(118,timisoara),449-st(75,zerind),526-st(366,craiova),553-st(300,sibiu),607-st(414,rimnicu_vilcea),615-st(455,craiova),646-st(280,arad),671-st(291,oradea)]\n",
+       " 6: A* Heap = [418-st(418,bucharest),447-st(118,timisoara),449-st(75,zerind),450-st(450,bucharest),526-st(366,craiova),553-st(300,sibiu),591-st(338,sibiu),607-st(414,rimnicu_vilcea),615-st(455,craiova),646-st(280,arad),671-st(291,oradea)]\n",
+       "GOAL found at step 6 with distance 418 : bucharest\n",
+       "0' ms'"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mtrue"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?-astar."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "943a1e1c",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "eval_function(_G_SoFar,H_EstDist,F) :- F =H_EstDist. % Greedy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "dab9377c",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "'Starting A* search'\n",
+       " 1: A* Heap = [366-st(0,arad)]\n",
+       " 2: A* Heap = [253-st(140,sibiu),329-st(118,timisoara),374-st(75,zerind)]\n",
+       " 3: A* Heap = [178-st(239,fagaras),193-st(220,rimnicu_vilcea),329-st(118,timisoara),366-st(280,arad),374-st(75,zerind),380-st(291,oradea)]\n",
+       " 4: A* Heap = [0-st(450,bucharest),193-st(220,rimnicu_vilcea),253-st(338,sibiu),329-st(118,timisoara),366-st(280,arad),374-st(75,zerind),380-st(291,oradea)]\n",
+       "GOAL found at step 4 with distance 450 : bucharest\n",
+       "0' ms'"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[1mtrue"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "?-astar."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ad76945b",
+   "metadata": {
+    "vscode": {
+     "languageId": "prolog"
+    }
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Prolog",
+   "language": "prolog",
+   "name": "prolog_kernel"
+  },
+  "language_info": {
+   "codemirror_mode": "prolog",
+   "file_extension": ".pl",
+   "mimetype": "text/x-prolog",
+   "name": "Prolog"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+%% Cell type:markdown id:9eb5530a tags:
+
+Empty Prolog Notebook
+
+%% Cell type:code id:40ad6905 tags:
+
+``` prolog
+:- consult('prolog_files/roumania.pl').
+```
+
+%% Cell type:code id:9c7e889c tags:
+
+``` prolog
+?- s(arad,Dist,City).
+```
+
+%% Output
+
+
+%% Cell type:code id:af6a9e4a tags:
+
+``` prolog
+jupyter:print_table(s(arad,Dist,City))
+```
+
+%% Output
+
+    Dist | City |
+    :- | :- |
+    75 | zerind |
+    118 | timisoara |
+    140 | sibiu |
+
+
+%% Cell type:code id:55da475c tags:
+
+``` prolog
+jupyter:print_table(wkante(City,Dist,arad))
+```
+
+%% Output
+
+    City | Dist |
+    :- | :- |
+    zerind | 75 |
+    timisoara | 118 |
+    sibiu | 140 |
+
+
+%% Cell type:code id:c32206c4 tags:
+
+``` prolog
+?- h(zerind,SLDZ), h(timisoara,SLDT), h(sibiu,SLDS).
+```
+
+%% Output
+
+
+%% Cell type:markdown id:3e904005 tags:
+
+The following is the evaluation function we will use in the A* algorithm:
+
+%% Cell type:code id:e942f0d4 tags:
+
+``` prolog
+eval_function(G_SoFar,H_EstDist,F) :- F is G_SoFar+H_EstDist. % A*
+%eval_function(_G_SoFar,H_EstDist,F) :- F =H_EstDist. % Greedy
+%eval_function(G_SoFar,_,F) :- F=G_SoFar. % Dijkstra
+```
+
+%% Cell type:code id:242f4141 tags:
+
+``` prolog
+?- eval_function(75,374,HZerind), eval_function(140,253,HSibiu),
+   eval_function(118,329,HTimisoara).
+```
+
+%% Output
+
+
+%% Cell type:code id:78764141 tags:
+
+``` prolog
+
+:- use_module(library(heaps)).
+
+add_states_to_heap([],H,H).
+add_states_to_heap([st(G,State)|T],Heap,UpdHeap) :-
+   (h(State,SH) -> true ; print(err(State)),nl,SH=1000),  % compute heuristic function
+   eval_function(G,SH,F),  % Compute weight
+   add_to_heap(Heap,F,st(G,State),H2),
+   add_states_to_heap(T,H2,UpdHeap).
+```
+
+%% Cell type:code id:b03ac6e7 tags:
+
+``` prolog
+?- empty_heap(EH), add_states_to_heap([st(75,zerind),st(140,sibiu),st(118,timisoara)],EH,NewHeap),
+   heap_to_list(NewHeap,List), format(' A* Heap = ~w~n',[List]).
+```
+
+%% Output
+
+
+
+%% Cell type:code id:f6f156a3 tags:
+
+``` prolog
+astar :- statistics(runtime,_),start(S),
+         astar(S),
+         statistics(runtime,[_,T]), print(T),print(' ms'),nl.
+
+astar(S) :- empty_heap(EH),
+   add_states_to_heap([st(0,S)],EH,StartHeap),
+   nl,print('Starting A* search'),nl,
+   asearch(StartHeap,1).
+
+asearch(Heap,StepNr) :-
+   heap_to_list(Heap,List), format(' ~w: A* Heap = ~w~n',[StepNr,List]),
+  get_from_heap(Heap,_Heuristic,st(G,State),NewHeap),
+  %print(StepNr),print(' ==> '), print(st(G,State)),nl,
+  process_node(G,State,NewHeap,StepNr).
+
+% process_node(DistanceFromStart,State, Heap, StepNr)
+process_node(G,State,_,StepNr) :-
+   ziel(State),
+   format('GOAL found at step ~w with distance ~w : ~w~n',[StepNr,G,State]).
+process_node(G,State,Heap,StepNr) :-
+   findall(st(G1,SuccState),
+	         (wkante(State,Weight,SuccState),G1 is G+Weight),SList),
+	% print(succs(SList)),nl,
+    add_states_to_heap(SList,Heap,UpdatedHeap),
+    S1 is StepNr+1,
+    asearch(UpdatedHeap,S1).
+```
+
+%% Cell type:code id:9639129f tags:
+
+``` prolog
+?-astar.
+```
+
+%% Output
+
+
+
+%% Cell type:code id:943a1e1c tags:
+
+``` prolog
+eval_function(_G_SoFar,H_EstDist,F) :- F =H_EstDist. % Greedy
+```
+
+%% Cell type:code id:dab9377c tags:
+
+``` prolog
+?-astar.
+```
+
+%% Output
+
+
+
+%% Cell type:code id:ad76945b tags:
+
+``` prolog
+```