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# Lab 5: Constraint satisfaction solution

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Lab 5: Constraint satisfaction
The task in this assignment is to create a classic sudoku solver. If you are not familiar with
the rules of classic sudoku, visit this website and become an expert before you start:
http://www.conceptispuzzles.com/?uri=puzzle/sudoku/rules
Your program will receive a 9×9 board with numbers from 0 to 9 and should return the
number of permutations performed to solve the puzzle. During the execution it also should
replace the entries with value 0 with number from 1 to 9 according to the rules of the game.
Remember your program can only change the cells with value 0 (it represents a blank
square). The board:

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## Description

Lab 5: Constraint satisfaction
The task in this assignment is to create a classic sudoku solver. If you are not familiar with
the rules of classic sudoku, visit this website and become an expert before you start:
http://www.conceptispuzzles.com/?uri=puzzle/sudoku/rules
Your program will receive a 9×9 board with numbers from 0 to 9 and should return the
number of permutations performed to solve the puzzle. During the execution it also should
replace the entries with value 0 with number from 1 to 9 according to the rules of the game.
Remember your program can only change the cells with value 0 (it represents a blank
square). The board:
Will be represented by:
sudoku[0]=[7,8,0,4,0,0,1,2,0]
sudoku[1]=[6,0,0,0,7,5,0,0,9]
sudoku[2]=[0,0,0,6,0,1,0,7,8]
sudoku[3]=[0,0,7,0,4,0,2,6,0]
sudoku[4]=[0,0,1,0,5,0,9,3,0]
sudoku[5]=[9,0,4,0,6,0,0,0,5]
sudoku[6]=[0,7,0,3,0,0,0,1,2]
sudoku[7]=[1,2,0,0,0,7,4,0,0]
sudoku[8]=[0,4,9,2,0,6,0,0,7]
Part 1: Sequential solution
For this first part you are to complete two functions:
● sudoku_backtracking that returns an integer representing the number of recursive
function calls performed to solve the board using a simple backtracking algorithm.
Your implementation should not make any recursive calls for assignments that violate
constraints.
● Sudoku_forwardchecking that returns an integer representing the number of
recursive function calls performed to solve the board using a forward checking
algorithm. Your implementation should not make a recursive call unless the new
assignment under consideration does not leave any domains empty in the forward
check, and does not violate constraints.
To match the expected results, remember to explore values low to high, and variables left to
right, top to bottom, as shown here:
Your code should be run in Python3 and not include any extra modules other than common.
Considerations:
● We provide some boards to test your solution but grading will be done with another
set. All boards will have a solution.
● We provided a function for checking constraints in “common”: can_yx_be_z(), you
can use if you like, but it is not required.
● You cannot change cells in the board that start with a value different than 0.
● The running time of your functions cannot be longer than 1 min for any board,
otherwise it will fail the grading tests.
● All functions will be tested independently, so you will get credit for each one that
returns the right results, but you have to make sure your program compiles and runs
properly with python3.
● Make sure you follow the academic honesty and plagiarism rules given on the first
day of class and in the syllabus on canvas.