题解 | #N皇后问题#

总结：
1.解决n皇后问题需要使用dfs解决，由于棋子不能同行同列，同一条斜线，需要先判断是否满足这一条件。左斜线的满足行列序号和相同，右斜线的点满足行列值序号差相同。为了保证查询条件时间复杂度为O1,故将该条件值保存在HashSet，使得查询速度为O1。

import java.util.*;


public class Solution {
    /**
     * 
     * @param n int整型 the n
     * @return int整型
     */
    private List<int[]> result = new ArrayList<>();
    int num = 0;
    public int Nqueen (int n) {
        // write code here
        int[] path = new int[n];

        Set<Integer> column = new HashSet<>();
        Set<Integer> dignoal1 = new HashSet<>();
        Set<Integer> dignoal2 = new HashSet<>();
        Arrays.fill(path,-1);
        dfs(path,n,0,column,dignoal1,dignoal2);
        return num;
    }
    public void dfs(int[] path,int n,int row,Set<Integer> column,Set<Integer> dignoal1,Set<Integer> dignoal2){
        if(row==n){
            result.add(path);
            num++;
            return;
        }
        for(int i=0;i<n;i++){
            if(column.contains(i))
                continue;
            int left = row+i;
            if(dignoal1.contains(left))
                continue;
            int right = row-i;
            if(dignoal2.contains(right))
                continue;
            path[row]=i;
            column.add(i);
            dignoal1.add(left);
            dignoal2.add(right);
            dfs(path,n,row+1,column,dignoal1,dignoal2);
            path[row] = -1;
            column.remove(i);
            dignoal1.remove(left);
            dignoal2.remove(right);

        }
    }
}