DFS-8 Queen

Title: 8 Queens

emample, when n = 4, the output is [[1, 3, 0, 2], [2, 0, 3, 1]], indicating that 4 queens have 2 swings. The first method is
[1,3,0,2], that is,
rowIndex = 0, and the corresponding Q is at column colIndex = 1, that is, the Q of the first row is in the second column

	Q
			Q
Q
		Q

package com.mjp.ai.dfs;

import com.google.common.collect.Lists;

import java.util.List;
import java.util.stream.Collectors;

/**
 * Author：m
 * Date： 2023/04/17 22:57
 */
public class Queen8 {
    
    
    public static void main(String[] args) {
    
    
        int n = 4;
        List<List<String>> result = searchQueen(n);
        System.out.println(result);
    }

    private static List<List<String>> searchQueen(int n) {
    
    
        if (n <= 3) {
    
    
            return Lists.newArrayList();
        }

        List<List<String>> result = Lists.newArrayList();
        List<Integer> colsCombine = Lists.newArrayList();
        recursion(result, colsCombine, n);
        return result;
    }

    private static void recursion(List<List<String>> result, List<Integer> colCombine, int n) {
    
    
        // 1.终止条件
        // 2.小集合添加至大集合（当n=4,colCombine为[1,3,0,2]时，说明找到了四皇后的一种摆法）
        if (n == colCombine.size()) {
    
    
            result.add(colCombine.stream().map(String::valueOf).collect(Collectors.toList()));
            return;
        }

        // 3.for循环
        for (int colIndex = 0; colIndex < n; colIndex++) {
    
    
            // 3.1去重或过滤（即欲放Q的当前行、当前列，同列、同递增斜线上、同递减斜线上均为Q时，才能在此处放Q）
            if (! allowQInThisRowIndexAndThisColIndex(colCombine, colCombine.size(), colIndex)) {
    
    
                continue;
            }
            // 3.2优化|剪枝
            // 3.3添加元素到小集合
            colCombine.add(colIndex);
            // 3.4递归
            recursion(result, colCombine, n);
            // 3.5回溯(小集合删除最后一个元素)
            colCombine.remove(colCombine.size() - 1);
        }
    }

    private static boolean allowQInThisRowIndexAndThisColIndex(List<Integer> colCombine, int thisRowIndex, int thisColIndex) {
    
    
        // 如果colCombine为[0]，则说明第rowIndex = 0行第colIndex = 0列有个Q
        // 我们判断Q是否能放在，thisRowIndex = 1行 thisColIndex = 列

        // 这里判断thisRowIndex行，thisColIndex列能否放Q，需要从rowIndex = 0一直判断到rowIndex = thisRowIndex- 1行，这些行上存放的Q是否和(thisRowIndex行，thisColIndex)存在以下三种冲突
        for (int rowIndex = 0; rowIndex < thisRowIndex; rowIndex++) {
    
    
            // rowIndex行对应的皇后所在列
            Integer getColIndexFromCombineByRowIndex = colCombine.get(rowIndex);

            // 1.判断冲突1：（thisRowIndex，thisColIndex）和已存在的皇后（rowIndex，getColIndexFromCombineByRowIndex）是否在同一列
            if (thisColIndex == getColIndexFromCombineByRowIndex) {
    
    
                return false;//如果存在冲突，则说明（thisRowIndex，thisColIndex）处不能放Q
            }

            // 2.判断冲突2：（thisRowIndex，thisColIndex）和已存在的皇后（rowIndex，getColIndexFromCombineByRowIndex）是否在同一条递减斜线上
            if (thisRowIndex - thisColIndex == rowIndex - getColIndexFromCombineByRowIndex) {
    
    
                return false;
            }

            // 3.判断冲突3：（thisRowIndex，thisColIndex）和已存在的皇后（rowIndex，getColIndexFromCombineByRowIndex）是否在同一条递增斜线上
            if (thisRowIndex + thisColIndex == rowIndex + getColIndexFromCombineByRowIndex) {
    
    
                return false;
            }
        }
        // 如果rowIndex = 0一直判断到rowIndex = thisRowIndex- 1行，这些行上存放的Q均不与(thisRowIndex行，thisColIndex)存在上述三种冲突，则说明此处可放Q
        return true;
    }
}