递归和回溯_leetcode51

#coding=utf-8

class Solution(object):
    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """


        self.col = [False for i in range(n)]
        self.diaS = [False for i in range(2*n - 1)]
        self.diaN = [False for i in range(2*n - 1)]



        ans = []
        self.res = []


        self.putQueen(n,0,ans)

        print self.res



    # 尝试在一个n皇后的问题中，摆放第index行皇后的位置
    def putQueen(self,n,index,ans):
        if index == n:
            self.res.append(self.generateBoard(n,ans[0:]))
            # self.res.append(ans[0:])

            return

        # 尝试将第index行的皇后摆放在第i列
        for i in range(n):
            if not self.col[i] and not self.diaS[index+i] and not self.diaN[index-i+n-1]:

                ans.append(i)

                self.col[i] = True
                self.diaS[index+i] = True
                self.diaN[index-i+n-1] = True

                self.putQueen(n,index+1,ans)

                ans.pop()
                self.col[i] = False
                self.diaS[index + i] = False
                self.diaN[index - i + n - 1] = False

        return


    def generateBoard(self,n,ans):


        board = [["." for i in range(n)] for i in range(n)]

        for i in range(n):
            board[i][ans[i]] = "Q"

        return map("".join,board)
        # return board


s = Solution()
s.solveNQueens(4)