37. Sudoku Solver 数独求解

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

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

...and its solution numbers marked in red.

class Solution:
    def validPos(self, board, row, col, c):
        x = 3 * int(row / 3)    # 3*3 start x index
        y = 3 * int(col / 3)    # 3*3 start y index
        for i in range(9):
            if board[row][i] == c:
                return False
            if board[i][col] == c:
                return False
            if board[x + int(i / 3)][y + i % 3] == c:
                return False
        return True
    def solve(self, board, solved):
        while solved != 81 and board[int(solved / 9)][solved % 9] != ".":
            solved += 1
        if solved is 81:
            return True
        i = int(solved / 9)
        j = solved % 9
        for c in "123456789":
            if self.validPos(board, i, j, c):
                board[i][j] = c
                if self.solve(board, solved):
                    return True
                else:
                    board[i][j] = "."
        return False;
    def solveSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: void Do not return anything, modify board in-place instead.
        """
        self.solve(board, 0)

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