# Sudoku problems.
# The CSP.ac_3() and CSP.backtrack() methods need to be implemented

from csp import CSP, alldiff


def print_solution(solution):
    """
    Convert the representation of a Sudoku solution, as returned from
    the method CSP.backtracking_search(), into a Sudoku board.
    """
    for row in range(width):
        for col in range(width):
            print(solution[f'X{row+1}{col+1}'], end=" ")
            if col == 2 or col == 5:
                print('|', end=" ")
        print("")
        if row == 2 or row == 5:
            print('------+-------+------')


# Choose Sudoku problem
grid = open('sudoku_easy.txt').read().split()

width = 9
box_width = 3

domains = {}
for row in range(width):
    for col in range(width):
        if grid[row][col] == '0':
            domains[f'X{row+1}{col+1}'] = set(range(1, 10))
        else:
            domains[f'X{row+1}{col+1}'] = {int(grid[row][col])}

edges = []
for row in range(width):
    edges += alldiff([f'X{row+1}{col+1}' for col in range(width)])
for col in range(width):
    edges += alldiff([f'X{row+1}{col+1}' for row in range(width)])
for box_row in range(box_width):
    for box_col in range(box_width):
        cells = []
        edges += alldiff(
            [
                f'X{row+1}{col+1}' for row in range(box_row * box_width, (box_row + 1) * box_width)
                for col in range(box_col * box_width, (box_col + 1) * box_width)
            ]
        )

csp = CSP(
    variables=[f'X{row+1}{col+1}' for row in range(width) for col in range(width)],
    domains=domains,
    edges=edges,
)

print(csp.ac_3())
print_solution(csp.backtracking_search())

# Expected output after implementing csp.ac_3() and csp.backtracking_search():
# True
# 7 8 4 | 9 3 2 | 1 5 6
# 6 1 9 | 4 8 5 | 3 2 7
# 2 3 5 | 1 7 6 | 4 8 9
# ------+-------+------
# 5 7 8 | 2 6 1 | 9 3 4
# 3 4 1 | 8 9 7 | 5 6 2
# 9 2 6 | 5 4 3 | 8 7 1
# ------+-------+------
# 4 5 3 | 7 2 9 | 6 1 8
# 8 6 2 | 3 1 4 | 7 9 5
# 1 9 7 | 6 5 8 | 2 4 3