LeetCode 51 N-Queens

转载：递归算法学习系列之八皇后问题

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.."]
]

java解法如下所示：

public class Solution {
    public void dfs(List<List<String>> res, List<String> list, Set<Integer> col, Set<Integer> diag1, Set<Integer> diag2, int row, int n){
        if(row==n){
            res.add(new ArrayList<String>(list));
            return;
        }
        //遍历该行的所有列
        for(int i=0;i<n;i++){
            if(col.contains(i)||diag1.contains(row+i)||diag2.contains(row-i))
                continue;
            col.add(i);
            diag1.add(row+i);
            diag2.add(row-i);
            char[] rowChar = new char[n];
            Arrays.fill(rowChar, '.');
            rowChar[i] = 'Q';
            String rowString = new String(rowChar);
            list.add(rowString);
            //继续搜索下一行
            dfs(res, list, col, diag1, diag2, row+1, n);
            //搜索完成后释放所用资源
            list.remove(list.size()-1);
            col.remove(i);
            diag1.remove(row+i);
            diag2.remove(row-i);
        }
    }
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> res = new ArrayList<List<String>>();
        if(n==0)
            return res;
        Set<Integer> col = new HashSet<Integer>(); //列集
        Set<Integer> diag1 = new HashSet<Integer>(); //正对角线集
        Set<Integer> diag2 = new HashSet<Integer>(); //副对角线集
        List<String> list = new ArrayList<String>(); //用于存放每一种情况
        dfs(res, list, col, diag1, diag2, 0, n);
        return res;
    }
}