[Leetcode] N Queens I,II

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 · 303 阅读

0 ·

CC 4.0 BY-SA版权

Leetcode 专栏收录该内容

67 篇文章

订阅专栏

本文介绍了一种解决N皇后问题的有效方法，通过回溯算法找到所有可行的棋盘配置，使得N个皇后彼此不受攻击。文章详细展示了如何利用递归进行状态搜索，并检查每一步是否符合规则。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

http://leetcode.com/onlinejudge#question_51

The n-queens puzzle is the problem of placing n queens on an nÃ—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.."]
]

class Solution {
public:
bool check(int row, int* place)   
    {
        for(int i=0;i<row;i++)
        {
            int diff = abs(place[row]-place[i]);
            if(diff == 0 || diff == row - i) return false;
        }
        return true;
    }
    
    void placeQueens(int row, int n, int &count, int* place,  
                     vector<vector<string> > &result)   
    {        
        if(row==n)
        //indicates success
        {
            vector<string> tmp;
            count++;
            for(int i=0;i<n;i++)
            {
                string str(n,'.');
                str[place[i]] = 'Q';
                tmp.push_back(str);
            } 
            result.push_back(tmp);
            return;
        }        
        for(int i=0;i<n;i++)
        {
            place[row] = i;
            if(check(row,place))
            {
                placeQueens(row+1,n,count,place,result);
            }
        }                         
    }    
    
    int totalNQueens(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<vector<string> > result;
        int count = 0;
        int* place = new int[n]; 
        placeQueens(0,n,count,place,result);
        return count;
    }
};