Skip to content

37. Sudoku Solver

Difficulty Topics

Description

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

 

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

 

Constraints:

  • board.length == 9
  • board[i].length == 9
  • board[i][j] is a digit or '.'.
  • It is guaranteed that the input board has only one solution.

Solution

sudoku-solver.py
class Solution:
    def solveSudoku(self, board: List[List[str]]) -> None:
        """
        Do not return anything, modify board in-place instead.
        """

        def backtrack(board):
            for row in range(9):
                for col in range(9):
                    if board[row][col] == '.':
                        for x in map(str, range(1, 10)):
                            if isValid(board, row, col, x):
                                board[row][col] = x

                                if backtrack(board): 
                                    return True
                                else:
                                    board[row][col] = '.'

                        return False

            return True

        def isValid(board, row, col, x):
            for k in range(9):
                if board[k][col] == x: return False
                if board[row][k] == x: return False
                if board[(row // 3 * 3) + k // 3][(col // 3 * 3) + k % 3] == x: return False

            return True

        backtrack(board)
        return board