Leetcode-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.."]
]

Have you met this question in a real interview?

 

Analysis:

How to determine whether the current position at jth row is valid? Suppose jth row position is place[j] and ith row position is place[i]. Then we found that place[i] leads three positions at jth row invalid. They are place[i], place[i]+j-i, place[i]-(j-i).

 

Solution:

public class Solution {
    public List<String[]> solveNQueens(int n) {
        List<String[]> res = new ArrayList<String[]>();
        int[] place = new int[n];
        Arrays.fill(place,-1);
        int level = 0;
  
        while (level!=-1){
            if (level>=n){
                constructRes(place,res,n);
                level--;
                continue;
            }

            int val = place[level];
            val++;
            while (val<n){
                boolean valid = true;
                for (int i=0;i<level;i++)
                    if (val==place[i] || val==place[i]+level-i || val==place[i]-(level-i)){
                        valid = false;
                        break;
                    }
                if (valid) break;
                else val++;
            }

            if (val<n){
                place[level]=val;
                level++;
            } else {
                place[level]=-1;
                level--;
            }
        }

        return res;
        
    }

    public void constructRes(int[] place, List<String[]> res, int n){
        char[] line = new char[n];
        Arrays.fill(line,'.');
        String[] oneRes = new String[n];
        for (int i=0;i<n;i++){
            int val = place[i];
            line[val]='Q';
            String lineStr = new String(line);
            line[val]='.';
            oneRes[i]=lineStr;
        }
        res.add(oneRes);
    }       
}