/Searching-Algorithms

Artificial Intelligence course homework 1.

Primary LanguagePython

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{\f37\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}{\flomajor\f31500\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fdbmajor\f31501\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fhimajor\f31502\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0302020204030204}Calibri Light;}
{\fbimajor\f31503\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\flominor\f31504\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fdbminor\f31505\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fhiminor\f31506\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}
{\fbiminor\f31507\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f43\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\f44\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\f46\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\f47\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\f48\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\f49\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\f50\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\f51\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\f63\fbidi \fmodern\fcharset238\fprq1 Courier New CE;}{\f64\fbidi \fmodern\fcharset204\fprq1 Courier New Cyr;}
{\f66\fbidi \fmodern\fcharset161\fprq1 Courier New Greek;}{\f67\fbidi \fmodern\fcharset162\fprq1 Courier New Tur;}{\f68\fbidi \fmodern\fcharset177\fprq1 Courier New (Hebrew);}{\f69\fbidi \fmodern\fcharset178\fprq1 Courier New (Arabic);}
{\f70\fbidi \fmodern\fcharset186\fprq1 Courier New Baltic;}{\f71\fbidi \fmodern\fcharset163\fprq1 Courier New (Vietnamese);}{\f383\fbidi \froman\fcharset238\fprq2 Cambria Math CE;}{\f384\fbidi \froman\fcharset204\fprq2 Cambria Math Cyr;}
{\f386\fbidi \froman\fcharset161\fprq2 Cambria Math Greek;}{\f387\fbidi \froman\fcharset162\fprq2 Cambria Math Tur;}{\f390\fbidi \froman\fcharset186\fprq2 Cambria Math Baltic;}{\f391\fbidi \froman\fcharset163\fprq2 Cambria Math (Vietnamese);}
{\f413\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}{\f414\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\f416\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\f417\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}
{\f418\fbidi \fswiss\fcharset177\fprq2 Calibri (Hebrew);}{\f419\fbidi \fswiss\fcharset178\fprq2 Calibri (Arabic);}{\f420\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}{\f421\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}
{\flomajor\f31508\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\flomajor\f31509\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flomajor\f31511\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}
{\flomajor\f31512\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\flomajor\f31513\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flomajor\f31514\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\flomajor\f31515\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\flomajor\f31516\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbmajor\f31518\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\fdbmajor\f31519\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fdbmajor\f31521\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbmajor\f31522\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\fdbmajor\f31523\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fdbmajor\f31524\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbmajor\f31525\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\fdbmajor\f31526\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fhimajor\f31528\fbidi \fswiss\fcharset238\fprq2 Calibri Light CE;}{\fhimajor\f31529\fbidi \fswiss\fcharset204\fprq2 Calibri Light Cyr;}
{\fhimajor\f31531\fbidi \fswiss\fcharset161\fprq2 Calibri Light Greek;}{\fhimajor\f31532\fbidi \fswiss\fcharset162\fprq2 Calibri Light Tur;}{\fhimajor\f31533\fbidi \fswiss\fcharset177\fprq2 Calibri Light (Hebrew);}
{\fhimajor\f31534\fbidi \fswiss\fcharset178\fprq2 Calibri Light (Arabic);}{\fhimajor\f31535\fbidi \fswiss\fcharset186\fprq2 Calibri Light Baltic;}{\fhimajor\f31536\fbidi \fswiss\fcharset163\fprq2 Calibri Light (Vietnamese);}
{\fbimajor\f31538\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fbimajor\f31539\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fbimajor\f31541\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}
{\fbimajor\f31542\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fbimajor\f31543\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fbimajor\f31544\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\fbimajor\f31545\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fbimajor\f31546\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\flominor\f31548\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\flominor\f31549\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flominor\f31551\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\flominor\f31552\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\flominor\f31553\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flominor\f31554\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\flominor\f31555\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\flominor\f31556\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbminor\f31558\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fdbminor\f31559\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fdbminor\f31561\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbminor\f31562\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fdbminor\f31563\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fdbminor\f31564\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbminor\f31565\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fdbminor\f31566\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}
{\fhiminor\f31568\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}{\fhiminor\f31569\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\fhiminor\f31571\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\fhiminor\f31572\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}
{\fhiminor\f31573\fbidi \fswiss\fcharset177\fprq2 Calibri (Hebrew);}{\fhiminor\f31574\fbidi \fswiss\fcharset178\fprq2 Calibri (Arabic);}{\fhiminor\f31575\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}
{\fhiminor\f31576\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}{\fbiminor\f31578\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fbiminor\f31579\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fbiminor\f31581\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fbiminor\f31582\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fbiminor\f31583\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fbiminor\f31584\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fbiminor\f31585\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fbiminor\f31586\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}}
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\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14287828 Artificial Intelligence, Home Work 1: Search Algorithms
\par /*
\par Parth Khetarpal \endash  pxk170016
\par */
\par Language Used: Python 3.7.1
\par Python IDE used: Pycharm Version 2018.2
\par \lquote 8pp\rquote  Folder contents
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid14287828 \hich\af37\dbch\af0\loch\f37 -\tab}}\pard\plain \ltrpar\s15\ql \fi-360\li720\ri0\sa40\sl259\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin720\itap0\pararsid14287828\contextualspace \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid14287828 eightpuzzle.py
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid14287828 \hich\af37\dbch\af0\loch\f37 -\tab}main.py
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid14287828 \hich\af37\dbch\af0\loch\f37 -\tab}readme.rtf
\par }\pard\plain \ltrpar\ql \li0\ri0\sa40\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid14287828 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {
\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14287828 Run Via Cmd
\par Input format: 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \b\i\ul\insrsid14287828\charrsid14287828 python main.py
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14287828 
\par Please make sure both the python files are in the same folder. 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13859009 Additional Information:}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14287828 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13859009 We were asked to implement 3 searching algorithms, namely,
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid13859009 \hich\af37\dbch\af0\loch\f37 -\tab}}\pard\plain \ltrpar\s15\ql \fi-360\li720\ri0\sa40\sl259\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin720\itap0\pararsid13859009\contextualspace \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid13859009 BFS (Breadth First Search)
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid13859009 \hich\af37\dbch\af0\loch\f37 -\tab}IDS (Iterative Depth Search)
\par {\listtext\pard\plain\ltrpar \s15 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f37\fs22\insrsid13859009 \hich\af37\dbch\af0\loch\f37 -\tab}A* Informed Search (With 2 different heuristics)
\par }\pard\plain \ltrpar\ql \li0\ri0\sa40\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13859009 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {
\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13859009 For the A* algorithm, Number of misplaced tiles and Manhattan Distance were used for calculation of the heuristic distance. 
\par If the nodes expanded exceed the search space tree\rquote s depth of 10, an error is printed and the puzzle is left unsolved. 
\par Comments are added throughout the code for convenience. 
\par The User provides the input of the initial maze configuration. The final state of the maze is 
\par [ 1 2 3
\par   4 5 6
\par   7 8 0 ]
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \b\insrsid13859009\charrsid13859009 Where the \lquote 0\rquote  is the blank tile. }{\rtlch\fcs1 \af0 \ltrch\fcs0 \b\insrsid13859009 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid13859009 For }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1986684 the purpose of analysis,
\par Number of steps taken
\par Number of nodes in Queue
\par Number of nodes in visited
\par Time Performance : (Same as number of nodes popped of queue ie visited)
\par Space performance: (Max number of number of nodes in queue at it max length)
\par Time spent: Measured in seconds for the searching and solving of the puzzle)
\par 
\par 
\par 
\par 
\par 
\par 
\par 
\par Sample Output:
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1986684 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1986684 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:0
\par Element:1
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:7
\par Element:8
\par Element:6
\par ---------------------
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 1
\par step 0
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= None , depth= 0 , step cost= 0 , total_cost= 0
\par 
\par step 1
\par [[1 0 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= left , depth= 1 , step cost= 1 , total_cost= 1
\par 
\par step 2
\par [[1 2 3]
\par  [4 0 5]
\par  [7 8 6]]
\par action= up , depth= 2 , step cost= 2 , total_cost= 3
\par 
\par step 3
\par [[1 2 3]
\par  [4 5 0]
\par  [7 8 6]]
\par action= left , depth= 3 , step cost= 5 , total_cost= 8
\par 
\par step 4
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par action= up , depth= 4 , step cost= 6 , total_cost= 14
\par 
\par Total Number of steps:  4
\par number of Nodes in Queue:  17
\par number of Nodes in Visited:  29
\par Time performance: 29 nodes popped off the queue.
\par Space performance: 18 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\brdrb\brdrs\brdrw15\brsp20 \wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1986684 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1986684 Time spent: }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid1383574\charrsid1383574 0.011s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1986684 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1986684 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11468914 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11468914 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11468914 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:1
\par Element:0
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:6
\par Element:8
\par Element:7
\par ---------------------
\par [[1 0 3]
\par  [4 2 5]
\par  [6 8 7]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 1
\par Max depth exceeded
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid8418386\charrsid8418386 Time spent: 0.045s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid8418386 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11468914 
\par 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid8418386 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11468914 
\par 
\par 
\par 
\par 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15225499 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:0
\par Element:1
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:7
\par Element:8
\par Element:6
\par ---------------------
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 2
\par depth limit 0
\par depth limit 1
\par depth limit 2
\par depth limit 3
\par depth limit 4
\par step 0
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= None , depth= 0 , step cost= 0 , total_cost= 0
\par 
\par step 1
\par [[1 0 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= left , depth= 1 , step cost= 1 , total_cost= 1
\par 
\par step 2
\par [[1 2 3]
\par  [4 0 5]
\par  [7 8 6]]
\par action= up , depth= 2 , step cost= 2 , total_cost= 3
\par 
\par step 3
\par [[1 2 3]
\par  [4 5 0]
\par  [7 8 6]]
\par action= left , depth= 3 , step cost= 5 , total_cost= 8
\par 
\par step 4
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par action= up , depth= 4 , step cost= 6 , total_cost= 14
\par 
\par Total Number of steps:  4
\par number of Nodes in Queue:  4
\par Time performance: 35 nodes popped off the queue.
\par Space performance: 5 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\brdrb\brdrs\brdrw15\brsp20 \wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15225499 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 Time spent: }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid8009176\charrsid8009176 0.0088s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15225499 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 
\par (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:1
\par Element:0
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:6
\par Element:8
\par Element:7
\par ---------------------
\par [[1 0 3]
\par  [4 2 5]
\par  [6 8 7]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 2
\par depth limit 0
\par depth limit 1
\par depth limit 2
\par depth limit 3
\par depth limit 4
\par depth limit 5
\par depth limit 6
\par depth limit 7
\par depth limit 8
\par depth limit 9
\par depth limit 10
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\brdrb\brdrs\brdrw15\brsp20 \wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15225499 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 Max Limit Reached
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid2906864\charrsid2906864 Time spent: 0.061s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid2906864 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15225499 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15225499 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:0
\par Element:1
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:7
\par Element:8
\par Element:6
\par ---------------------
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 3
\par step 0
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= None , depth= 0 , step cost= 0 , total_cost= 0
\par 
\par step 1
\par [[1 0 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= left , depth= 1 , step cost= 1 , total_cost= 4
\par 
\par step 2
\par [[1 2 3]
\par  [4 0 5]
\par  [7 8 6]]
\par action= up , depth= 2 , step cost= 2 , total_cost= 5
\par 
\par step 3
\par [[1 2 3]
\par  [4 5 0]
\par  [7 8 6]]
\par action= left , depth= 3 , step cost= 5 , total_cost= 9
\par 
\par step 4
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par action= up , depth= 4 , step cost= 6 , total_cost= 14
\par 
\par Total Number of steps:  4
\par number of Nodes in Queue:  11
\par Time performance: 13 nodes popped off the queue.
\par Space performance: 12 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\brdrb\brdrs\brdrw15\brsp20 \wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 Time spent: 0.0093s}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15225499 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 
\par (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:1
\par Element:0
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:6
\par Element:8
\par Element:7
\par ---------------------
\par [[1 0 3]
\par  [4 2 5]
\par  [6 8 7]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 3
\par MAX DEPTH REACHED
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3692271 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid3692271 Time spent: 0.019s
\par Time performance: 165 nodes popped off the queue.
\par Space performance: 109 nodes in the queue at its max.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid333407 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:0
\par Element:1
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:7
\par Element:8
\par Element:6
\par ---------------------
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 4
\par step 0
\par [[0 1 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= None , depth= 0 , step cost= 0 , total_cost= 0
\par 
\par step 1
\par [[1 0 3]
\par  [4 2 5]
\par  [7 8 6]]
\par action= left , depth= 1 , step cost= 1 , total_cost= 4
\par 
\par step 2
\par [[1 2 3]
\par  [4 0 5]
\par  [7 8 6]]
\par action= up , depth= 2 , step cost= 2 , total_cost= 5
\par 
\par step 3
\par [[1 2 3]
\par  [4 5 0]
\par  [7 8 6]]
\par action= left , depth= 3 , step cost= 5 , total_cost= 9
\par 
\par step 4
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par action= up , depth= 4 , step cost= 6 , total_cost= 14
\par 
\par Total Number of steps:  4
\par number of Nodes in Queue:  12
\par Time performance: 14 nodes popped off the queue.
\par Space performance: 13 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\brdrb\brdrs\brdrw15\brsp20 \wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 Time spent: 0.0094s
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1383574 (venv) C:\\Users\\PARTH\\Documents\\PyCharm\\8pp.py>python main.py
\par Enter Input array
\par Element:1
\par Element:0
\par Element:3
\par Element:4
\par Element:2
\par Element:5
\par Element:6
\par Element:8
\par Element:7
\par ---------------------
\par [[1 0 3]
\par  [4 2 5]
\par  [6 8 7]]
\par GOAL
\par [[1 2 3]
\par  [4 5 6]
\par  [7 8 0]]
\par Enter algorithm for solving 8 puzzle problem
\par 1:'BFS',
\par 2:'IDS',
\par 3:'Astar with manhattan distance as heuristic',
\par 4:'Astar with misplaced tile as heuristic'
\par 4
\par MAX DEPTH REACHED
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1052505 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid1052505 Time spent: 0.022s
\par Time performance: 139 nodes popped off the queue.
\par Space performance: 90 nodes in the queue at its max.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15293733 
\par }\pard \ltrpar\ql \li0\ri0\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1383574 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15293733 
\par 
\par 
\par 
\par 
\par 
\par 
\par 
\par 
\par 
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 Analysis of the 2 Heuristics for the A* search algorithm. }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15293733 
\par \ltrrow}\trowd \irow0\irowband0\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738
\pard\plain \ltrpar\qc \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid14943913\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid14943913 Manhattan Distance\cell Number of misplaced tiles\cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 \trowd \irow0\irowband0\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr
\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid14943913\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 The }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 Manhattan}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid7751531 distance between tow points is defined as the sum of the differences between the x and the y coordinates of both those points. }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7751531\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 The number of misplaced tiles comparing the initial state (configuration) of the puzzle and how many
 tiles apart is that tile is from the goal state. }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14943913 \trowd \irow1\irowband1\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 
\trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid14943913\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7751531 Generic Formula used:
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7751531\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531  For every grid position:
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531\charrsid7751531 sum_manhattan += sum(abs(a-b) for a,b in zip((i,j), goal_position_dic[current[i,j]]))}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 \cell Generic Formula used:
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531\charrsid7751531 cost = np.sum(new_state != goal_state)-1 }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 
\trowd \irow2\irowband2\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 Total Number of steps:  4}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 
\par  (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 Total Number of steps:  4
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7751531 \trowd \irow3\irowband3\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 number of Nodes in Queue:  11}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761  
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 number of Nodes in Queue:  12
\par }\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7751531\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \trowd \irow4\irowband4\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 
\trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 Time performance: 13 nodes popped off the queue.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761  
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 Time performance: 14 nodes popped off the queue.
\par }\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7751531\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \trowd \irow5\irowband5\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 
\trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 Space performance: 12 nodes in the queue at its max.
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 Space performance: 13 nodes in the queue at its max.
\par }\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7751531\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \trowd \irow6\irowband6\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 
\trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 Time spent: 0.0093s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761  
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 Time spent: 0.009}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 4}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid7080032 s}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761      
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid11950761 (for input specified)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7080032 \trowd \irow7\irowband7\ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx5315\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5423\clshdrawnil \cellx10738\row \ltrrow
}\pard\plain \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid15541960 (for puzzled unsolved i.e Depth >= 10)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid3692271 
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid15541960\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15541960 Time spent: 0.019s
\par Time performance: 165 nodes popped off the queue.
\par Space performance: 109 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15541960 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15541960 (for puzzled unsolved i.e Depth 
>= 10)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid3692271 
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid15541960\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15541960 Time spent: 0.022s
\par Time performance: 139 nodes popped off the queue.
\par Space performance: 90 nodes in the queue at its max.
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7080032\yts20 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15541960 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid3692271 
\trowd \irow8\irowband8\lastrow \ltrrow\ts20\trgaph108\trrh330\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14943913\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
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