Sudoku Problem in Python

# A Backtracking program
# in Python to solve Sudoku problem

# 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], end=" "),
        print()


# 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")

# The above code has been contributed by Harshit Sidhwa.