Boggle Game Backtracking Algorithm Implementation CS 1501 Boggle

Boggle Game: Backtracking Algorithm Implementation CS 1501

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html 2

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html • The boggle game is to form as many 3+ letter words as possible from a 2 -dimensional board of letters. – We want to form words by starting at any letter and traversing over adjacent cubes vertically, horizontally or diagonally. – Any cube may appear at most once in a word. – Only real words (from dictionary) are valid. – Words must be at least 3 letters long to be valid. F R O O Y I E S L D N T A E R E 3

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html • The boggle game is to form as many 3+ letter words as possible from a 2 -dimensional board of letters. – We want to form words by starting at any letter and traversing over adjacent cubes vertically, horizontally or diagonally. – Any cube may appear at most once in a word. – Only real words (from dictionary) are valid. – Words must be at least 3 letters long to be valid. F R O O Y I E S L D N T A E R E FRIEND 4

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html • The boggle game is to form as many 3+ letter words as possible from a 2 -dimensional board of letters. – We want to form words by starting at any letter and traversing over adjacent cubes vertically, horizontally or diagonally. – Any cube may appear at most once in a word. – Only real words (from dictionary) are valid. – Words must be at least 3 letters long to be valid. F R O O Y I E S L D N T A E ROSTER 5

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html • The boggle game is to form as many 3+ letter words as possible from a 2 -dimensional board of letters. – We want to form words by starting at any letter and traversing over adjacent cubes vertically, horizontally or diagonally. – Any cube may appear at most once in a word. – Only real words (from dictionary) are valid. – Words must be at least 3 letters long to be valid. F R O O Y I E S L D N T A E R E END FINE REAL 6

Boggle Game • Read the assignment requirement carefully. http: //www. cs. pitt. edu/~kirk/cs 1501/Ramirez/Summer 2009/assigs/boggle/assig 1 a. html • The boggle game is to form as many 3+ letter words as possible from a 2 -dimensional board of letters. – We want to form words by starting at any letter and traversing over adjacent cubes vertically, horizontally or diagonally. – Any cube may appear at most once in a word. – Only real words (from dictionary) are valid. – Words must be at least 3 letters long to be valid. F R O O Y I E S L D N T A E R E XDEAD XFYLDERE 7

Boggle Game • Wild card * – A * can represent any letter in the alphabet. – Wild card essentially causes more word possibilities in a given board. F R O O Y I E S L * N T L A N T L B N T A E R E F R O O Y I E S L D N T L Z N T A E R E …… 8

Requirement • Read board from text file. • Calculate all possible words (of length at least 3). • Allow the user to type words from the keyboard and tell him if each word is “valid” or not. • Show the user all of the words for the board by printing out all of the words in the board word list in alphabetical order. 9

Board Search • Start from any cube on the board F R O O Y I E S L D N T A E R E – Track where we are (current position) – Track where we were (history) 10

Board Search j • Start from any cube on the board F R O O (0, 0 ) (0, 1 ) (0, 2 ) (0, 3 ) Y I E S (1, 0 ) (1, 1 ) (1, 2 ) (1, 3 ) L D N T (2, 0 ) (2, 1 ) (2, 2 ) (2, 3 ) A E R E (3, 0 ) (3, 1 ) (3, 2 ) (3, 3 ) i – Track where we are (current position) • (i, j) – Determine where we can go (next position) • (i-1, j-1) (i-1, j+1) (i, j-1) curr (i, j+1) (i+1, j-1)(i+1, j+1) – Track where we were (history) 11

Backtracking Example j • Start from any cube on the board F R O O (0, 0 ) (0, 1 ) (0, 2 ) (0, 3 ) Y I E S (1, 0 ) (1, 1 ) (1, 2 ) (1, 3 ) L D N T (2, 0 ) (2, 1 ) (2, 2 ) (2, 3 ) A E R E (3, 0 ) (3, 1 ) (3, 2 ) (3, 3 ) i – Start from D • At (2, 1) • Next step can be: (1, 0) (1, 1) (1, 2) (2, 0) (2, 2) (3, 0) (3, 1) (3, 2) • Try (1, 0) – DY – Advance to (1, 0) 12

Backtracking Example j • Start from any cube on the board F R O O (0, 0 ) (0, 1 ) (0, 2 ) (0, 3 ) Y I E S (1, 0 ) (1, 1 ) (1, 2 ) (1, 3 ) L D N T (2, 0 ) (2, 1 ) (2, 2 ) (2, 3 ) A E R E (3, 0 ) (3, 1 ) (3, 2 ) (3, 3 ) i – Now at Y (1, 0)-(2, 1) • At (1, 0) • Next step can be: (0, 0) (0, 1) (1, 1) (2, 2) (2, 0) – (2, 1) is not allowed! • Try all possible steps and find no valid prefix or words – Backtrack to D (2, 1) 13

Backtracking Example j • Start from any cube on the board F R O O (0, 0 ) (0, 1 ) (0, 2 ) (0, 3 ) Y I E S (1, 0 ) (1, 1 ) (1, 2 ) (1, 3 ) L D N T (2, 0 ) (2, 1 ) (2, 2 ) (2, 3 ) A E R E (3, 0 ) (3, 1 ) (3, 2 ) (3, 3 ) i – Return to D • At (2, 1) • Next step can be: (1, 1) (1, 2) (2, 0) (2, 2) (3, 0) (3, 1) (3, 2) – (1, 0) has failed. • Try (1, 1) – DI – Advance to (1, 1) …. 14

New Step Situations • When we try a new step on the board, the composition with the new letter can have 4 possible situations: – Not a prefix, not a word • Give up, backtrack to the previous step (pruning) – Not a prefix, is a word • Save the word, backtrack to the previous step – Is a prefix, not a word • Explore the next possible step – Is a prefix, is a word • Save the word, explore the next possible step – The function to check a prefix or a word are provided. 15

Big Picture • Proceed forward to a solution until it becomes apparent that no solution can be achieved along the current path. • At that point UNDO the solution (backtrack) to a point where we can again proceed forward • Some hints: – Use a stack to track the history path. • Push stack: advance step • Pop stack: backtrack – Use a variable for each cube to track what is the next direction to explore. (stack) • Advance step: push the next direction into the stack • Backtrack: pop the next direction out of the stack – Use a boolean table (2 d array) to mark the cubes visited. • Advance step: mark new cube • Backtrack: unmark cube 16