The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example,
There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]

]

这题的解法和前面一题N queen II 一样，规则是两个queen不能再同一个行，列或者diagnal 所以每个循环里面有 board[i]!=j abs(k-i)!=abs[board[i]-j]

其他的是常规的dfs解法

代码如下：

class Solution:
    # @return a list of lists of string
    def solveNQueens(self, n):
        def check(k,j,board):
            for i in range(k):
                if board[i]==j or abs(k-i)==abs(board[i]-j):
                    return False
            return True
        def dfs(depth,board,valuelist,solution):
            #for i in range(len(board)):
            if depth==len(board):
                solution.append(valuelist)
            for row in range(len(board)):
                if check(depth,row,board):
                    s='.'*len(board)
                    board[depth]=row
                    dfs(depth+1,board,valuelist+[s[:row]+'Q'+s[row+1:]],solution)
        board=[-1 for i in range(n)]
        solution=[]
        dfs(0,board,[],solution)
        return solution