常用十大算法（十）— 踏棋盘算法
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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 + " ");
}
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;
}
}
});
}
}
感谢
尚硅谷
