【leetcode】N-Queens

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 };