Presentation Number 12

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Presentation Number 12

• C Programming Course

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The Final Project

• In the final project you are required to write a
  Sudoku solver.

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Sudoku

• Rules
• The puzzle is defined over a 9x9 grid made up of
  3x3 subgrids (called regions).
• The aim of the puzzle is to fill in the missing
  cells with the numbers 1 through 9.
• Each row, column and region must contain only one
  instance of each numeral.

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Sudoku

• Each cell is part of a region, row and column.
• When a cell is assigned a number, it effects the
  assignments of its region, row and column.

Assign a number to this cell
These cells are effected
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Possible Assignments

• The region eliminates the numbers
• The row eliminates the numbers
• The column eliminates the numbers

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Possible Assignments

• This leaves the numbers
• as possible assignments.

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These are the options that are left for each cell
after we update the board with the initial numbers
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These are the options that are left for each cell
after we update the board with the initial numbers
Notice that the red cells were automatically
solved
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Updating the board according to these cells
solves more cells
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
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And again ...
The puzzle is solved
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Updating the Board

• By repeatedly updating the board, setting numbers
  and eliminating options the puzzle (or at least
  most of the puzzle) can be solved.

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Updating the Board

• If a cell has only one option and we havent
  updated the board according to this cell
• We update the board and mark the cell
• (so we wont repeat the update again).
• We repeat this until we can no longer update the
  board.

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Cell Data Structure

• A cell is a struct that stores
• A flag for each one of the nine options.
• A flag that says if we used this cell to update
  the board.

Options Update Flag
Yes / No
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The Options That Remain

• Many of the puzzles cannot be solved by simply
  updating the board.
• Usually, we will have some cells that have more
  than one option.
• What do we do with them?

This cell can be 2, 4 or 9
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The Options That Remain

• Copy the board
• Find an unsolved cell
• Remove the first option for the cell in the
  original board.
• Remove all the options except the first in the
  copy of the board.

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The Options That Remain

• We will use recursion to solve the puzzle.
• If we can solve the puzzle using the new copy of
  the board then we found our solution.
• Otherwise, the original board is closer to the
  solution than before.

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Pseudo-Code

• flag SolveSudoku( board )
• UpdateBoard( board )
• solutionFlag CheckBoard( board )
• if ( solutionFlag SOLVED )
• PrintBoard( board )
• return SOLVED
• if ( solutionFlag NO_SOLUTION )
• return NO_SOLUTION

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Pseudo-Code

• CopyBoard( board, copy_board )
• id FindUnsolvedCell( board )
• SetOption( board, copy_board, id )
• solutionFlag SolveSudoku( copy_board )
• if ( solutionFlag SOLVED )
• return SOLVED
• else
• return SolveSudoku( board )

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Pseudo-Code

• Solve the board. If there is a solution print
  it, otherwise report that there is no solution.
• flag SolveSudoku( board )
• Update the board according to cells that have
  only one solution and were not used to update the
  board before.
• UpdateBoard( board )
• Checks if a board is solved, has no solution or
  has not been solved yet.
• CheckBoard( board )
• Prints the board.
• PrintBoard( board )

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Pseudo-Code

• Copies a board into another board.
• CopyBoard( board, copy_board )
• Finds a cell that has more than one option left
  and returns its id.
• id FindUnsolvedCell( board )
• The function updates a cell (given by an id
  number) in both boards. In the original board it
  removes the first option. In the copy_board it
  removes everything except the first option.
• SetOption( board, copy_board, id )

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Input / Output

• Input Output
• 5 3 0 0 7 0 0 0 0 5 3 4 6 7 8 9 1 2
• 6 0 0 1 9 5 0 0 0 6 7 2 1 9 5 3 4 8
• 0 9 8 0 0 0 0 6 0 1 9 8 3 4 2 5 6 7
• - - - - - - - - - - - - - - - - - -
• 8 0 0 0 0 0 0 0 3 8 5 9 7 6 1 4 2 3
• 4 0 0 8 0 3 0 0 1 4 2 6 8 5 3 7 9 1
• 7 0 0 0 2 0 0 0 6 7 1 3 9 2 4 8 5 6
• - - - - - - - - - - - - - - - - - -
• 0 6 0 0 0 0 2 8 0 9 6 1 5 3 7 2 8 4
• 0 0 0 4 1 9 0 0 5 2 8 7 4 1 9 6 3 5
• 0 0 0 0 8 0 0 7 9 3 4 5 2 8 6 1 7 9

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Input / Output

• The number 0 represents an empty cell.
• The signs , - and are region separators.
• All characters are separated by spaces.
• If the input board has no solution print
• This board has not solution!.
• If an error has occurred during the run of the
  program it should return -1 and print Error.
• You can assume that the initial input is correct
  (and legal).

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Solution

• The solution presented here is only a suggestion.
• Feel free to change whatever you like.

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Submission Date?
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Questions?

• about anything that was learned during the course