LeetCode-52-N-Queens II

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 the number of distinct solutions to the n-queens puzzle.

Example:

Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

解题思路：回溯法求解。注意判断皇后合法条件。

    int totalNQueens(int n) {
        vector<string> temp(n,string(n,'.'));
        int res = 0;
        backtracking(res, temp,0, n);
        return res;
    }
    void backtracking(int &res, vector<string>& temp, int row, int n){
        if(row == n){
            res++;
            return;
        } 
        for(int col =0; col < n; col++){
            temp[row][col] = 'Q';
            if(isValid(temp, row, col, n)){
                backtracking(res, temp, row+1, n);
            }
            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;
    }