LeetCode-51-N-Queens

算法描述：

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.

Example:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

解题思路：要求所有可能性，用回溯法求解。注意皇后合法性判断的三个条件，水平，45度斜线，135度斜线的计算方法。

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> results;
        vector<string> temp(n,string(n,'.'));
        backtracking(n, results, temp, 0);
        return results;
    }
    
    void backtracking(int n, vector<vector<string>>& results, vector<string>& temp, int row){
        if(row == n){
            results.push_back(temp);
            return;
        }
        
        for(int col=0; col< n; col++){
            temp[row][col] = 'Q';
            if(isValid(temp, row, col, n)){
                backtracking(n,results,temp, row+1);
            }
            temp[row][col] ='.';
        }
    }
    
    bool isValid(vector<string>& temp, int row, int col, int n){
        for(int i=0; i != row; i++){
            if(temp[i][col] == 'Q') return false;
        }
        
        for(int i=row-1, j=col-1; i >=0 && j >=0; i--,j--){
            if(temp[i][j]=='Q') return false;
        }
        for(int i=row-1,j=col+1; i>=0 && j < n; i--,j++){
            if(temp[i][j]=='Q') return false;
        }
        return true;
    }