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leetcode笔记：51. n

admin 11月 14, 2020 0

#	Title	Difficulty	Topic
51	N-Queens	Hard	Backtracking

Description

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.

Backtracking

LeetCode 51. N-Queens - 花花酱刷题找工作 EP41视频里讲的很清晰。

class  {
    public List<List<String>> solveNQueens(int n) {
        char[][] board = new char[n][n];
        for(int i=0; i<n; i++) {
            for(int j=0; j<n; j++) {
                board[i][j] = '.';
            }
        }
        List<List<String>> res = new ArrayList<>();
        dfs(board, 0, res);
        return res;
    }
    
    public void dfs(char[][] board, int row, List<List<String>> res) {
        int n = board.length;
        if(row == n) {
            List<String> tmp = new ArrayList<>();
            for(int i=0; i<n; i++) {
                tmp.add(new String(board[i]));
            }
            res.add(tmp);
            return;
        }
        
        for(int j=0; j<n; j++) {
            if(isValid(board, row, j)) {
                board[row][j] = 'Q';
                dfs(board, row+1, res);
                board[row][j] = '.';
            }
        }
    }
    
    public boolean isValid(char[][] board, int row, int col) {
        int n = board.length;
        for(int j=0; j<n; j++) {
            if(board[j][col] != '.') return false;
            if(row+col-j >= 0 && row+col-j < n && board[row+col-j][j] != '.') return false;
            if(row-col+j >= 0 && row-col+j < n && board[row-col+j][j] != '.') return false;
        }
        return true;
    }
}