[LeetCode]N-Queens

最新推荐文章于 2020-07-10 00:48:29 发布

转载最新推荐文章于 2020-07-10 00:48:29 发布 · 40 阅读

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原文链接：http://www.cnblogs.com/Rosanna/p/3515865.html

本文介绍了一种使用回溯算法解决N皇后问题的方法，并提供了一个C++实现示例。该算法能够找出所有可能的放置方案，使得N个皇后在N×N的棋盘上互不攻击。

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.."]
]

思考:回溯。

class Solution {
public:
    bool check(vector<int> ans,int k,int i)
    {
        for(int j=0;j<k;j++)
        {
            if(ans[j]==i||(abs(i-ans[j])==abs(k-j))) return false;
        }
        return true;
    }
    void Queens(vector<vector<string> > &res,vector<int> &ans,int k,int n)
    {
        for(int i=0;i<n;i++)
        {
            if(check(ans,k,i))
            {
                ans[k]=i;
                if(k==n-1)
                {
                    vector<string> temp;
                    for(int j=0;j<n;j++)
                    {
                        string str(n,'.');
                        str[ans[j]]='Q';
                        temp.push_back(str);
                    }
                    res.push_back(temp);
                }
                else Queens(res,ans,k+1,n);
            }
        }
    }
    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string> > res;
        vector<int> ans(n,0);
        Queens(res,ans,0,n);
        return res;
    }
};

转载于:https://www.cnblogs.com/Rosanna/p/3515865.html