51. 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.."]
]
解题思路：经典N皇后问题，代码主要参照晴神宝典103页，P[index]=x表示第index行皇后的位置为x，hashTable[x]=True表示第x行已经有皇后放置了，对角线判断用了绝对值 简化了本来的算法

class Solution {
public:
    vector<vector<string> >ans;
    bool hashTable[100]={false};
    int P[100]={0};
    void generateP(int index,int n){
        if(index==n+1){
            string temp="";
            vector<string>tempAns;
            for(int i=1;i<=n;i++){
                temp="";
                for(int j=1;j<=n;j++)
                    temp+='.';
                temp[P[i]-1]='Q';
             //   cout<<temp<<endl;
               tempAns.push_back(temp);
            }
            ans.push_back(tempAns);
            return ;
        }
        for(int x=1;x<=n;x++){
            if(hashTable[x]==false){
                bool flag=true;
                for(int pre=1;pre<index;pre++){
                    if(abs(index-pre)==abs(x-P[pre])){
                        flag=false;
                        break;
                    }
                }
                if(flag){
                    P[index]=x;
                    hashTable[x]=true;
                    generateP(index+1,n);
                    hashTable[x]=false;
                }
            }
        }
        
    }
    vector<vector<string>> solveNQueens(int n) {
        generateP(1,n);
        return ans;
    }
};