N-Queens

题目地址：
https://leetcode.com/problems/n-queens/description/

题目：

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.."]
]

解题思路：
这题就是用传统的backtracking就可以。

代码：

public static void main(String[] args){
    NQueens nQueens = new NQueens();
    List<List<String>> rst = nQueens.solveNQueens(4);
    System.out.println(rst);
}

public List<List<String>> solveNQueens(int n) {
    List<List<String>> rst = new ArrayList<>();
    char[][] board = new char[n][n];
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            board[i][j] = '.';
        }
    }
    dfs(board, 0, rst);
    return rst;
}

private void dfs(char[][] board, int row, List<List<String>> rst) {
    if(row == board.length){
        rst.add(build(board));
        return;
    }
    for(int col = 0; col <= board[0].length - 1; col++){
        if(valid(row, col, board)){
            board[row][col] = 'Q';
            dfs(board, row + 1, rst);
            board[row][col] = '.';
        }
    }
}

private List<String> build(char[][] board) {
    List<String> rst = new ArrayList<>();
    for(int i = 0; i < board.length; i++){
        String s = new String(board[i]);
        rst.add(s);
    }
    return rst;
}

private boolean valid(int x, int y, char[][] board) {
    for(int i = 0; i <= x - 1; i++){
        for(int j = 0; j <= board.length - 1; j++){
            if(board[i][j] == 'Q' && (j == y || (x - i == y - j || x - i == j - y))){
                return false;
            }
        }
    }
    return true;
}