Leetcode 51. N-Queens

Leetcode

51. N-Queens

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..”]
]
原题可以查看
https://leetcode.com/problems/n-queens/?tab=Description

解题思路：
深度优先搜索，进行遍历，若当前位置可以放“皇后”，则对下一行的位置进行遍历。下面给出代码：

public class Solution {    public List<List<String>> solveNQueens(int n) {        List<List<String>> result = new ArrayList<>();        int[] recorder = new int[n+1];        dfs(1,n,recorder,result);        return result;    }//通过recorder 的记录给出其中一个可能的棋盘摆放结果    private List<String> generateBlock(int []recorder,int n){        List<String> block = new ArrayList<String>();        for(int i=1;i<=n;i++){            StringBuilder strBuilder = new StringBuilder();            for(int j=1;j<=n;j++){                if(recorder[i]==j){                    strBuilder.append("Q");                }else{                    strBuilder.append(".");                }            }            block.add(strBuilder.toString());        }        return block;    }//检查第x行，第y列能否放“皇后”    private boolean put(int x,int y,int[]recorder){        for(int i=1;i<x;i++){            int dx = Math.abs(x-i);            int dy = Math.abs(y-recorder[i]);            if(dx==dy||dy==0)                return false;        }        return true;    }//深度搜索    private void dfs(int row,int n,int[]recorder,List<List<String>> result){        if(row>n){            result.add(generateBlock(recorder,n));            return;        }        for(int i=1;i<=n;i++){            if(put(row,i,recorder)){                recorder[row]=i;                dfs(row+1,n,recorder,result);            }        }    }}

欢迎大家提出宝贵意见。