【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,-1);
        vector<vector<string> > result;
        getQueens(0,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=0;i<n;i++)
        {
            str="";
            for(int j=0;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=0;i<n;i++)
        {
            q[level]=i;
            if(isValid(q,level))
            {
                getQueens(level+1,n,result,q);
            }
            q[level]=-1;
        }
    }  
   
    bool isValid(vector<int> &q,int &level)
    {
 
        for(int i=0;i<level;i++)
        {
            if(q[i]==q[level]||abs(q[level]-q[i])==abs(level-i)) return false;
        }
       
        return true;
    }
};