常用十大算法（十）— 踏棋盘算法

归子莫

发布于：2020年9月9日

常用十大算法（十）— 踏棋盘算法

博客说明

文章所涉及的资料来自互联网整理和个人总结，意在于个人学习和经验汇总，如有什么地方侵权，请联系本人删除，谢谢！

介绍

马踏棋盘算法也被称为骑士周游问题
将马随机放在国际象棋的8×8棋盘Board0～7]的某个方格中，马按走棋规则(马走日字)进行移动。要求每个方格只进入一次，走遍棋盘上全部64个方格

思路

马踏棋盘问题(骑士周游问题)实际上是图的深度优先搜索(DFS)的应用。
如果使用回溯（就是深度优先搜索）来解决，假如马儿踏了53个点，如图：走到了第53个，坐标（1,0），发现已经走到尽头，没办法，那就只能回退了，查看其他的路径，就在棋盘上不停的回溯…… ，

代码实现

package com.atguigu.horse;

import java.awt.Point;
import java.util.ArrayList;
import java.util.Comparator;

public class HorseChessboard {

	private static int X; // 列
	private static int Y; // 行
	
	private static boolean visited[];
	private static boolean finished; 
	
	public static void main(String[] args) {
		X = 8;
		Y = 8;
		int row = 1; 
		int column = 1; 
		int[][] chessboard = new int[X][Y];
		visited = new boolean[X * Y];
		long start = System.currentTimeMillis();
		traversalChessboard(chessboard, row - 1, column - 1, 1);
		long end = System.currentTimeMillis();
		System.out.println("时间: " + (end - start));
		for(int[] rows : chessboard) {
			for(int step: rows) {
				System.out.print(step + "\t");
			}
			System.out.println();
		}
	}
	
	public static void traversalChessboard(int[][] chessboard, int row, int column, int step) {
		chessboard[row][column] = step;
		visited[row * X + column] = true; 
		ArrayList<Point> ps = next(new Point(column, row));
		sort(ps);
		while(!ps.isEmpty()) {
			Point p = ps.remove(0);
			if(!visited[p.y * X + p.x]) {
				traversalChessboard(chessboard, p.y, p.x, step + 1);
			}
		}
		if(step < X * Y && !finished ) {
			chessboard[row][column] = 0;
			visited[row * X + column] = false;
		} else {
			finished = true;
		}
	}
	

	public static ArrayList<Point> next(Point curPoint) {
		ArrayList<Point> ps = new ArrayList<Point>();
		Point p1 = new Point();
		if((p1.x = curPoint.x - 2) >= 0 && (p1.y = curPoint.y -1) >= 0) {
			ps.add(new Point(p1));
		}
		if((p1.x = curPoint.x - 1) >=0 && (p1.y=curPoint.y-2)>=0) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x + 1) < X && (p1.y = curPoint.y - 2) >= 0) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x + 2) < X && (p1.y = curPoint.y - 1) >= 0) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x + 2) < X && (p1.y = curPoint.y + 1) < Y) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x + 1) < X && (p1.y = curPoint.y + 2) < Y) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x - 1) >= 0 && (p1.y = curPoint.y + 2) < Y) {
			ps.add(new Point(p1));
		}
		if ((p1.x = curPoint.x - 2) >= 0 && (p1.y = curPoint.y + 1) < Y) {
			ps.add(new Point(p1));
		}
		return ps;
	}

	//排序
	public static void sort(ArrayList<Point> ps) {
		ps.sort(new Comparator<Point>() {
			@Override
			public int compare(Point o1, Point o2) {
				int count1 = next(o1).size();
				int count2 = next(o2).size();
				if(count1 < count2) {
					return -1;
				} else if (count1 == count2) {
					return 0;
				} else {
					return 1;
				}
			}
		});
	}
}