A simple backtracking sudoku solver

sudoku.py

def rows(puzzle):
    return [puzzle[9 * i:9 * i + 9] for i in range(9)]


def columns(puzzle):
    return [puzzle[i::9] for i in range(9)]


def boxes(puzzle):
    return [puzzle[i:i + 3] +
            puzzle[i + 9:i + 9 + 3] +
            puzzle[i + 9 + 9:i + 9 + 9 + 3] for i in
            (j * 3 + k * 27 for j in range(3) for k in range(3))]


def valid_group(group):
    digits = [d for d in group if d != '.']
    return len(set(digits)) == len(digits)


def valid(puzzle):
    return all(valid_group(group) for group in rows(puzzle)) and all(
        valid_group(group) for group in columns(puzzle)) and all(
        valid_group(group) for group in boxes(puzzle))


def solved(puzzle):
    return valid(puzzle) and '.' not in puzzle


def permutations(puzzle):
    return [puzzle.replace('.', f'{i + 1}', 1) for i in range(9)]


def solve(puzzle):
    stack = [puzzle]
    while stack:
        curr = stack.pop()
        if solved(curr):
            return curr
        stack.extend(perm for perm in permutations(curr) if valid(perm))


def valid_input(inp):
    return len(inp) == 81 and not set(inp) - set('.123456789')


def main():
    puzzle = input()
    if not valid_input(puzzle):
        print('Invalid input!')
        return
    solved_puzzle = solve(puzzle)
    if not solved_puzzle:
        print('No solution!')
        return
    print(solved_puzzle)


if __name__ == '__main__':
    main()