[LeetCode] 51. N-Queens - N皇后问题的解法-回溯法

秒速五厘米 2023-06-23 09:56 44阅读 0赞

# [\[LeetCode\] 51. N-Queens][LeetCode_ 51. N-Queens] #

## Problem ##

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.

Example:

Input: 4
    Output: [
     [".Q..",  // Solution 1
      "...Q",
      "Q...",
      "..Q."],
    
     ["..Q.",  // Solution 2
      "Q...",
      "...Q",
      ".Q.."]
    ]
    Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

## Solution ##

class Solution {
        public List<List<String>> solveNQueens(int n) {
            char[][] board = new char[n][n];
            for (int i = 0; i < n; i++) {
                Arrays.fill(board[i], '.');
            }
            List<List<String>> res = new ArrayList<>();
            dfs(board, 0, res);
            return res;
        }
        
        private void dfs(char[][] board, int col, List<List<String>> res) {
            if (col == board.length) {
                res.add(construct(board));
                return;
            }
            
            for (int row = 0; row < board.length; row++) {
                if (validate(board, row, col)) {
                    board[row][col] = 'Q';
                    dfs(board, col+1, res);
                    board[row][col] = '.';
                }
            }
        }
        
        private boolean validate(char[][] board, int row, int col) {
            for (int i = 0; i < board.length; i++) {
                for (int j = 0; j < col; j++) {
                    if (board[i][j] == 'Q' && (
                        i+j == row+col || row+j == col+i || row == i
                    )) return false;
                }
            }
            
            return true;
        }
        
        private List<String> construct(char[][] board) {
            List<String> res = new ArrayList<>();
            for (int i = 0; i < board.length; i++) {
                String str = new String(board[i]);
                res.add(str);
            }
            return res;
        }
    }

[LeetCode_ 51. N-Queens]: https://segmentfault.com/a/1190000017570535