【LeetCode】51.N-Queens(hard)解题报告

【LeetCode】51.N-Queens(hard)解题报告

题目地址：https://leetcode.com/problems/n-queens/description/
题目描述：

  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.
  For example,There exist two distinct solutions to the 4-queens puzzle:
[
[“.Q..”, // Solution 1
“…Q”,
“Q…”,
“..Q.”],
[“..Q.”, // Solution 2
“Q…”,
“…Q”,
“.Q..”]
]

Solution:

//time:O(n*n)
//space:O(n)
class Solution {
    public List> solveNQueens(int n) {
        List> res = new ArrayList<>();
        if(n<=0) return res;
        helper(res,new int[n],0);
        return res;
    }
    public void helper(List> res,int[] queens,int pos){ //queen代表放的这一行的元素在哪一列上queens:[1,3,0,2];pos指行
        if(pos == queens.length){
            addSolution(res,queens);
            return; 
        }
        for(int i=0 ; iif(isValid(queens,pos)){
                helper(res,queens,pos+1);
            }
        }
    }
    public boolean isValid(int[] queens,int pos){
        for(int i=0;iif(queens[pos] == queens[i]){    //同一列
                return false;
            }else if(Math.abs(queens[pos] - queens[i]) == Math.abs(pos - i)){ //对角线
                return false;
            }
        }
        return true;
    }
    public void addSolution(List> res,int[] queens){
        List list = new ArrayList<>();
        for(int i=0 ; inew StringBuilder();
            for(int j=0 ; jif(queens[i] == j){
                    sb.append('Q');
                }else{
                    sb.append('.');
                }
            }
            list.add(sb.toString());
        }
        res.add(list);
    }
}

Date：2018年1月13日