Boggle Game: Backtracking Algorithm Implementation

1
Boggle GameBacktracking Algorithm
Implementation

• CS 1501

2
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.html

3
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.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
4
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.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 I E N D

F R O O
Y I E S
L D N T
A E R E
5
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.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.
• R O S T E R

F R O O
Y I E S
L D N T
A E R E
6
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.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.
• E N D
• F I N E
• R E A L

F R O O
Y I E S
L D N T
A E R E
7
Boggle Game

• Read the assignment requirement
  carefully.http//www.cs.pitt.edu/kirk/cs1501/Ram
  irez/Summer2009/assigs/boggle/assig1a.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.
• X D E A D
• X F Y L D E R E

F R O O
Y I E S
L D N T
A E R E
8
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
A E R E
F R O O
Y I E S
L A N T
A E R E
F R O O
Y I E S
L B N T
A E R E
F R O O
Y I E S
L D N T
A E R E
F R O O
Y I E S
L Z N T
A E R E

9
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.

10
Board Search

• Start from any cube on the board
• Track where we are (current position)
• Track where we were (history)

F R O O
Y I E S
L D N T
A E R E
11
Board Search

• Start from any cube on the board
• Track where we are (current position)
• (i, j)
• Determine where we can go (next position)
• (i-1, j-1) (i-1, j) (i-1, j1)(i, j-1) curr
  (i, j1)(i1, j-1)(i1, j)(i1, j1)
• Track where we were (history)

j
F R O O
Y I E S
L D N T
A E R E
(0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3)
i
12
Backtracking Example

• Start from any cube on the board
• 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)

j
F R O O
Y I E S
L D N T
A E R E
(0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3)
i
13
Backtracking Example

• Start from any cube on the board
• 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)

j
F R O O
Y I E S
L D N T
A E R E
(0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3)
i
14
Backtracking Example

• Start from any cube on the board
• 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)
• .

j
F R O O
Y I E S
L D N T
A E R E
(0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3)
i
15
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.

16
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 (2d array) to mark the cubes
  visited.
• Advance step mark new cube
• Backtrack unmark cube