【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 · 95 阅读

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CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/reachteam/p/4213979.html

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能的解决方案。使用了一个一维数组q来记录每行皇后的位置，并定义了判断是否冲突的函数isValid，最后实现了打印解决方案的函数。

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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.."]
]

采用q[i]表示第i行的Queen放置的位置

不合法的条件：q[i]==q[level]||abs(q[level]-q[i])==abs(level-i)

 1 class Solution {
 2 public:
 3     vector<vector<string> > solveNQueens(int n) {
 4        
 5         vector<int> q(n,-1);
 6         vector<vector<string> > result;
 7         getQueens(0,n,result,q);
 8         return result;
 9     }
10    
11     void PrintQueens(vector<int> &q,vector<vector<string> > &result)
12     {
13         int n=q.size();
14         vector<string> tmp;
15         string str;
16         for(int i=0;i<n;i++)
17         {
18             str="";
19             for(int j=0;j<n;j++)
20             {
21                 if(q[i]==j)str+='Q';
22                 else str+='.';
23             }
24             tmp.push_back(str);
25         }
26        
27         result.push_back(tmp);
28     }
29    
30     void getQueens(int level,int &n,vector<vector<string> > &result,vector<int> &q)
31     {
32         if(level==n)
33         {
34             PrintQueens(q,result);
35             return;
36         }
37         bool flag=false;
38         for(int i=0;i<n;i++)
39         {
40             q[level]=i;
41             if(isValid(q,level))
42             {
43                 getQueens(level+1,n,result,q);
44             }
45             q[level]=-1;
46         }
47     }  
48    
49     bool isValid(vector<int> &q,int &level)
50     {
51  
52         for(int i=0;i<level;i++)
53         {
54             if(q[i]==q[level]||abs(q[level]-q[i])==abs(level-i)) return false;
55         }
56        
57         return true;
58     }
59 };

转载于:https://www.cnblogs.com/reachteam/p/4213979.html