【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)

 

 class Solution {
 public:
     vector<vector<string> > solveNQueens(int n) {

         vector<int> q(n,-);
         vector<vector<string> > result;
         getQueens(,n,result,q);
         return result;
     }

     void PrintQueens(vector<int> &q,vector<vector<string> > &result)
     {
         int n=q.size();
         vector<string> tmp;
         string str;
         for(int i=;i<n;i++)
         {
             str="";
             for(int j=;j<n;j++)
             {
                 if(q[i]==j)str+='Q';
                 else str+='.';
             }
             tmp.push_back(str);
         }

         result.push_back(tmp);
     }

     void getQueens(int level,int &n,vector<vector<string> > &result,vector<int> &q)
     {
         if(level==n)
         {
             PrintQueens(q,result);
             return;
         }
         bool flag=false;
         for(int i=;i<n;i++)
         {
             q[level]=i;
             if(isValid(q,level))
             {
                 getQueens(level+,n,result,q);
             }
             q[level]=-;
         }
     }  

     bool isValid(vector<int> &q,int &level)
     {

         for(int i=;i<level;i++)
         {
             if(q[i]==q[level]||abs(q[level]-q[i])==abs(level-i)) return false;
         }

         return true;
     }
 };