[TODO]LeetCode 37. Sudoku Solver

Problem Statement

(Source) 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.

Tags: Backtracking, Hash Table.

Solution

class Solution(object):
    def solveSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: void Do not return anything, modify board in-place instead.
        """
        self.bt(board, 0, 0)


    def bt(self, board, i, j):
        m, n = len(board), len(board[0])
        if i == m - 1 and j == n - 1:
            return True
        for x in xrange(i, m):
            for y in xrange(n):
                if x == i and y < j:
                    continue
                if board[x][y] == '.':
                    for v in xrange(1, 10):
                        board[x][y] = str(v)
                        if self.check(board, x, y) and self.bt(board, x, y):
                            return True
                    board[x][y] == '.'
        return False


    def check(self, board, i, j):
        """Check whether the newly setted value at (i, j) satisfy all
        constraints.

        :type board: List[List[str]]
        """
        m, n = len(board), len(board[0])
        for y in xrange(n):
            if y != j and board[i][y] == board[i][j]:
                return False
        for x in xrange(m):
            if x != i and board[x][j] == board[i][j]:
                return False
        a, b = (i // 3) * 3, (j // 3) * 3
        for x in xrange(a, a + 3):
            for y in xrange(b, b + 3):
                if (x != i or y != j) and board[x][y] == board[i][j]:
                    return False
        return True