#Leetcode# 52. N-Queens II

https://leetcode.com/problems/n-queens-ii/

 

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.."]
]

题解：还是深搜 如果和之前的皇后不在同行列和对角线的时候可以放置 

　　　$n = 8$ 的时候有 $92$ 种放置方法

代码：

class Solution {
public:
    int totalNQueens(int n) {
        int ans = 0;
        vector<int> pos(n, -1);
        
        dfs(pos, 0, ans);
        return ans;
    }
    void dfs(vector<int>& pos, int step, int &ans) {
        int n = pos.size();
        if(step == n) ans ++;
        else {
            for(int i = 0; i < n; i ++) {
                if(ishere(pos, step, i)) {
                    pos[step] = i;
                    dfs(pos, step + 1, ans);
                    pos[step] = -1;
                }
            }
        }
    }
    bool ishere(vector<int>& pos, int line, int row) {
        for(int i = 0; i < line; i ++) {
            if(row == pos[i] || abs(line - i) == abs(row - pos[i]))
                return false;
        }
        return true;
    }
};