sudoku solver

solver.py

import os
from typing import List, Tuple
import itertools

possibilities = set([1, 2, 3, 4, 5, 6, 7, 8, 9])


def solve(board: List[List[int]]) -> List[List[int]] | None:

    if is_solved(board):
        return board

    moves, i, j = find_cell_with_least_moves(board)
    if len(moves) == 0:
        return None
    for move in sorted(moves):
        board[i][j] = move
        result = solve(board)
        if result != None:
            return result
        # we hit a dead end, backtrack.
        board[i][j] = 0

    return None


def find_cell_with_least_moves(board: List[List[int]]) -> Tuple[set, int, int]:
    result = (possibilities, -1, -1)
    n = len(board)
    for i in range(n):
        for j in range(n):
            if board[i][j] != 0:
                continue
            moves = calculate_moves(board, i, j)
            if len(moves) < len(result[0]):
                result = (moves, i, j)
            if len(moves) == 0:
                return moves, i, j
    return result


def calculate_moves(board: List[List[int]], i: int, j: int) -> set:
    return possibilities - set(
        row_nums(board, i) + col_nums(board, j) + inner_grid_nums(board, i, j)
    )


def filter_zeroes(ns: List[int]) -> List[int]:
    return [n for n in ns if n != 0]


def is_solved(board: List[List[int]]) -> bool:
    return 0 not in itertools.chain(*board)


def inner_grid_nums(board: List[List[int]], i, j) -> List[int]:
    r = (i // 3) * 3
    c = (j // 3) * 3

    row_section = board[r : r + 3]
    mini_board = [row[c : c + 3] for row in row_section]
    return filter_zeroes(list(itertools.chain(*mini_board)))


def row_nums(board: List[List[int]], i) -> List[int]:
    return filter_zeroes(board[i])


def col_nums(board: List[List[int]], j) -> List[int]:
    return filter_zeroes([row[j] for row in board])


def board_to_string(board):
    result = []
    for i in range(len(board)):
        if i % 3 == 0 and i != 0:
            result.append("- - - - - - - - - - - -")

        row = []
        for j in range(len(board[0])):
            if j % 3 == 0 and j != 0:
                row.append("|")

            row.append(str(board[i][j] if board[i][j] != 0 else "."))

        result.append(" ".join(row))

    return "\n".join(result)


def clear_screen():
    # For Windows
    if os.name == "nt":
        _ = os.system("cls")
    # For Unix/Linux/MacOS
    else:
        _ = os.system("clear")

board = [
    [0, 0, 0, 0, 0, 0, 0, 0, 0],
    [1, 0, 0, 0, 7, 0, 9, 0, 0],
    [0, 3, 0, 0, 4, 0, 0, 0, 6],
    [2, 0, 0, 0, 0, 0, 0, 0, 5],
    [9, 0, 0, 0, 6, 0, 0, 0, 7],
    [0, 0, 1, 0, 5, 7, 0, 0, 3],
    [0, 0, 2, 4, 0, 0, 6, 0, 0],
    [4, 0, 0, 0, 1, 0, 8, 0, 0],
    [0, 0, 0, 5, 0, 2, 0, 0, 0],
]

print(board_to_string(solve(board)))