leetcode：N-Queens 【Java】

一、问题描述

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.."]]

二、问题分析

1、采用回溯算法；

2、找到一个可行解之后，还需要继续搜索。

三、算法代码

public class Solution {    public List<List<String>> solveNQueens(int n) {        List<List<String>> result = new ArrayList<>();        if (n <= 0) return result;        char[][] board = new char[n][n];        for (char[] row : board) {            Arrays.fill(row, '.');        }        boolean[] col_occupied = new boolean[n];        placeQueen(result, board, col_occupied, 0, n);        return result;    }    private void placeQueen(List<List<String>> result, char[][] board, boolean[] col_occupied, int rowNum, int n) {        if (rowNum == n) {            List<String> list = new ArrayList<String>();            for (char[] row : board) {                list.add(new String(row));            }            result.add(list);            return;        }        for (int colNum=0; colNum<n; colNum++) {            if (isValid(board, col_occupied, rowNum, colNum, n)){                board[rowNum][colNum] = 'Q';                col_occupied[colNum] = true;                placeQueen(result, board, col_occupied, rowNum+1, n);                board[rowNum][colNum] = '.'; //回溯，尝试皇后rowNum的下一个位置                col_occupied[colNum] = false;            }        }    }    private boolean isValid(char[][]board, boolean[] col_occupied, int row, int col, int n) {        if (col_occupied[col]) return false;        for (int i=1; row-i>=0 && col-i>=0; i++) {            if (board[row-i][col-i] == 'Q') return false;//反对角斜线        }        for (int i=1; row-i>=0 && col+i<n; i++) {            if (board[row-i][col+i] == 'Q') return false;//正对角斜线        }        return true;    }}