Leetcode51 N-Queens

Posted 2022-12-13 xuweimdm

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.."]
]

Solution1

• 典型的回溯问题。

public class Solution 
    public List<List<String>> solveNQueens(int n) 
        List<List<String>> result = new ArrayList<List<String>>();
        if(n<=0) return result;
        help(n,0,new ArrayList<String>(),result);
        return result;        
    

    public void help(int n,int row,ArrayList<String> temp,List<List<String>> result)
        if(row>=n)
            result.add(temp);
            return;
        
        for(int col=0;col<n;col++)
            boolean flag = false;
            for(int i=0;i<temp.size();i++)//遍历已有的所有行
                int usedCol = Integer.MIN_VALUE;
                String s = temp.get(i);
                for(int j=0;j<s.length();j++)//找到该行的皇后所在列
                    if(s.charAt(j)=='Q')
                        usedCol = j;
                        break;
                    
                
                if(col==usedCol||Math.abs(row-i)==Math.abs(col-usedCol))
                    flag = true;
                    break;
                   
            
            if(flag) continue;
            ArrayList<String> temp1 = new ArrayList<String>(temp);
            char[] line = new char[n];
            for(int i=0;i<n;i++) line[i]='.';
            line[col] = 'Q';
            String current = new String(line);
            temp1.add(current);
            help(n,row+1,temp1,result);
        
        

Solution2

• 用一个数组巧妙的记录每行的皇后所在行和列，可以有更简洁的代码：

public class Solution 
    public List<List<String>> solveNQueens(int n) 
        List<List<String>> res = new ArrayList<List<String>>();
        help(n, 0, new int[n], res);
        return res;
    
    public void help(int n, int row, int[] used, List<List<String>> res)
        if(row>=n)
            ArrayList<String> temp = new ArrayList<String>();
            for(int col:used)
                char[] s = new char[n];
                Arrays.fill(s,'.');
                s[col] = 'Q';
                temp.add(new String(s));
            
            res.add(temp);
            return;
        
        for(int j=0,i=0;j<n;j++)
            for(i=0;i<row;i++) if(j==used[i]||Math.abs(i-row)==Math.abs(j-used[i])) break;
            if(i!=row) continue;
            used[row] = j;
            help(n,row+1,used,res);