leetcode -- Sudoku Solver -- 经典重点

https://leetcode.com/problems/sudoku-solver/

思路就是dfs，这里可以把candidates子节点看做所有的点，然后判断if == ‘.’，也可以只scan 一遍9*9的board。

方法一

参考
http://www.cnblogs.com/zuoyuan/p/3770271.html

    def solveSudoku(self, board):
        def isValid(x,y):
            tmp=board[x][y]; board[x][y]='D'
            for i in range(9):
                if board[i][y]==tmp: return False
            for i in range(9):
                if board[x][i]==tmp: return False
            for i in range(3):
                for j in range(3):
                    if board[(x/3)*3+i][(y/3)*3+j]==tmp: return False
            board[x][y]=tmp
            return True
        def dfs(board):
            for i in range(9):
                for j in range(9):
                    if board[i][j]=='.':
                        for k in '123456789':
                            board[i][j]=k
                            if isValid(i,j) and dfs(board):
                                return True
                            board[i][j]='.'
                        return False#当一个pos，1-9所有的digit都不满足要求的时候，就要return False，回溯到上一个candidates。
            return True#如果所有的pos，所有的candidates都valid，那么return True
        dfs(board)

方法二

http://jelices.blogspot.hk/2014/06/leetcode-python-sudoku-solver.html

还可以子节点只是下一个节点。 但是这个程序更慢，不知道为什么？

class Solution:
    # @param board, a 9x9 2D array
    # Solve the Sudoku by modifying the input board in-place.
    # Do not return any value.
    def solveSudoku(self, board):
        self.solveSudokuRec(board,0,0)

    def solveSudokuRec(self, board,row,col):
        if row == 9:
            return True
        if col == 8:
            nextRow = row +1
            nextCol = 0
        else:
            nextRow = row
            nextCol = col+1
        if board[row][col]!='.':
            return self.solveSudokuRec(board,nextRow,nextCol)
        for c in range(1,10):
            if self.canPut(board,str(c),row,col):
                board[row][col] = str(c)
                if self.solveSudokuRec(board,nextRow,nextCol):
                    return True
                board[row][col] = '.'
        return False

    def canPut(self, board, char, row, col):
        for i in range(0,9):
            if board[row][i] == char:
                return False
            if board[i][col] == char:
                return False
        rowGroup = (row//3) * 3
        colGroup = (col//3) * 3 
        for i in range(rowGroup, rowGroup+3):
            for j in range(colGroup, colGroup+3):
                if board[i][j] == char:
                    return False
        return True