[leetcode]N-Queens

最新推荐文章于 2020-07-10 00:48:29 发布

原创最新推荐文章于 2020-07-10 00:48:29 发布 · 514 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#N-Queens

leetcode 专栏收录该内容

78 篇文章

订阅专栏

本文介绍了一种使用回溯法解决N皇后问题的方法，并提供了一个C++实现示例。通过递归地放置皇后并检查冲突，该算法可以找出所有可能的解决方案。

N-Queens

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.."]
]

解题思路：回溯法

class Solution {
public:
    bool place(vector<int> &board, int t){
		for(int i = 0; i < t; i++){
			if(abs(t - i) == abs(board[t] - board[i]) 
			|| board[t] == board[i]) return false;
		}
		return true;        
    }
	void backTrace(vector<int> &board, int t, vector<string> &vs, vector<vector<string> > &vvs){
	    int n = board.size();
		if(t >= n){
		    vvs.push_back(vs);
			return;
		}
		for(int i = 0; i < n; i++){
			board[t] = i;
			string str(n, '.');
			str[i] = 'Q';
			vs.push_back(str);
			if(place(board, t)){
				backTrace(board, t + 1,vs, vvs);
			}
			vs.pop_back();
		}
	}
    vector<vector<string> > solveNQueens(int n) {
        vector<int> board(n, 0);
        vector<vector<string> > vvs;
        vector<string> vs;
        for(int i = 0; i < n; i++) board[i] = i;
        backTrace(board, 0, vs, vvs);
        
        return vvs;
    }
};