Solve the Sudoku Python

PROGRAM TO SOLVE SUDOKU



# A Utility Function to print the Grid
def print_grid(arr):
    for i in range(9):
        for j in range(9):
            print arr[i][j],
        print ('n')
 
         
# Function to Find the entry in
# the Grid that is still  not used
# Searches the grid to find an
# entry that is still unassigned. If
# found, the reference parameters
# row, col will be set the location
# that is unassigned, and true is
# returned. If no unassigned entries
# remains, false is returned.
# 'l' is a list  variable that has
# been passed from the solve_sudoku function
# to keep track of incrementation
# of Rows and Columns
def find_empty_location(arr, l):
    for row in range(9):
        for col in range(9):
            if(arr[row][col]== 0):
                l[0]= row
                l[1]= col
                return True
    return False
 
# Returns a boolean which indicates
# whether any assigned entry
# in the specified row matches
# the given number.
def used_in_row(arr, row, num):
    for i in range(9):
        if(arr[row][i] == num):
            return True
    return False
 
# Returns a boolean which indicates
# whether any assigned entry
# in the specified column matches
# the given number.
def used_in_col(arr, col, num):
    for i in range(9):
        if(arr[i][col] == num):
            return True
    return False
 
# Returns a boolean which indicates
# whether any assigned entry
# within the specified 3x3 box
# matches the given number
def used_in_box(arr, row, col, num):
    for i in range(3):
        for j in range(3):
            if(arr[i + row][j + col] == num):
                return True
    return False
 
# Checks whether it will be legal
# to assign num to the given row, col
# Returns a boolean which indicates
# whether it will be legal to assign
# num to the given row, col location.
def check_location_is_safe(arr, row, col, num):
     
    # Check if 'num' is not already
    # placed in current row,
    # current column and current 3x3 box
    return not used_in_row(arr, row, num) and
           not used_in_col(arr, col, num) and
           not used_in_box(arr, row - row % 3,
                           col - col % 3, num)
 
# Takes a partially filled-in grid
# and attempts to assign values to
# all unassigned locations in such a
# way to meet the requirements
# for Sudoku solution (non-duplication
# across rows, columns, and boxes)
def solve_sudoku(arr):
     
    # 'l' is a list variable that keeps the
    # record of row and col in
    # find_empty_location Function   
    l =[0, 0]
     
    # If there is no unassigned
    # location, we are done   
    if(not find_empty_location(arr, l)):
        return True
     
    # Assigning list values to row and col
    # that we got from the above Function
    row = l[0]
    col = l[1]
     
    # consider digits 1 to 9
    for num in range(1, 10):
         
        # if looks promising
        if(check_location_is_safe(arr,
                          row, col, num)):
             
            # make tentative assignment
            arr[row][col]= num
 
            # return, if success,
            # ya !
            if(solve_sudoku(arr)):
                return True
 
            # failure, unmake & try again
            arr[row][col] = 0
             
    # this triggers backtracking       
    return False
 
# Driver main function to test above functions
if __name__=="__main__":
     
    # creating a 2D array for the grid
    grid =[[0 for x in range(9)]for y in range(9)]
     
    # assigning values to the grid
    grid =[[3, 0, 6, 5, 0, 8, 4, 0, 0],
          [5, 2, 0, 0, 0, 0, 0, 0, 0],
          [0, 8, 7, 0, 0, 0, 0, 3, 1],
          [0, 0, 3, 0, 1, 0, 0, 8, 0],
          [9, 0, 0, 8, 6, 3, 0, 0, 5],
          [0, 5, 0, 0, 9, 0, 6, 0, 0],
          [1, 3, 0, 0, 0, 0, 2, 5, 0],
          [0, 0, 0, 0, 0, 0, 0, 7, 4],
          [0, 0, 5, 2, 0, 6, 3, 0, 0]]
     
    # if success print the grid
    if(solve_sudoku(grid)):
        print_grid(grid)
    else:
        print "No solution exists"


OUTPUT:
3 1 6 5 7 8 4 9 2 
5 2 9 1 3 4 7 6 8 
4 8 7 6 2 9 5 3 1 
2 6 3 4 1 5 9 8 7 
9 7 4 8 6 3 1 2 5 
8 5 1 7 9 2 6 4 3 
1 3 8 9 4 7 2 5 6 
6 9 2 3 5 1 8 7 4 
7 4 5 2 8 6 3 1 9

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