A*算法. Knight Moves

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为了说明A*算法，通过求解一个问题引入

Knight Moves

中国象棋里，马的走法是按照“日”字行走，如下图所示，最多有8个方向可以选择。

这是跳一步可以到达的8个格子。

对问题进行抽象，把每个格子看成一个点的坐标。目标：马从起点x1,y1到x2,y2，怎样走所需的步数最少，路线是怎样的。

每步的跳跃造成的马坐标的变化可能为{{-2,-1},{-2,1},{2,-1},{2,1},{-1,-2},{-1,2},{1,-2},{1,2}}

假设A1的坐标为(0,0)

代码（用STL的优先队列实现的取f值最小的元素）

import java.util.ArrayList;import java.util.Comparator;import java.util.PriorityQueue;public class Astar {static class Knight{int x,y;int step=0;int f,g,h;char row; int column;Knight parent = null;public Knight(char c, int n){this.x = c - 'A';this.y = n - 1;this.row = c;this.column = n;}public Knight(int x, int y){this.x = x;this.y = y;this.row = (char) (x + (int)'A');this.column = y + 1;}}static Knight k,end;//k is start point, end is end pointstatic int sum;public boolean in(Knight p){if(p.x<0 || p.y<0 || p.x>=8 || p.y>=8)return false;return true;}//manhattan估价函数public static int h(Knight p, Knight end){return (Math.abs(p.x-end.x)+Math.abs(p.y-end.y))*10;}int[][] dir={{-2,-1},{-2,1},{2,-1},{2,1},{-1,-2},{-1,2},{1,-2},{1,2}};boolean[][] visited = new boolean[8][8];//以f值为key排序static Comparator<Knight> OrderComparator = new Comparator<Knight>(){public int compare(Knight k1, Knight k2){int f1 = k1.f;int f2 = k2.f;if(f1>f2) return 1;else if(f2>f1) return -1;else return 0;}};static PriorityQueue<Knight> openSet = new PriorityQueue<Knight>(OrderComparator);static ArrayList<Knight> closedSet = new ArrayList<Knight>();public Astar(){Knight t;while(!openSet.isEmpty()){t = openSet.remove();visited[t.x][t.y] = true;closedSet.add(t);if(t.x == end.x && t.y == end.y){sum = t.step;end = t;break;}for(int i = 0; i<8;i++){Knight s = new Knight(t.x + dir[i][0],t.y + dir[i][1]);if(in(s) && !visited[s.x][s.y]){s.g = t.g + 23;s.h = h(s,end);s.f = s.g + s.h;s.step = t.step + 1;s.parent = t;//parent of s is topenSet.add(s);}}}}public static void main(String[] args){k = new Knight('A', 1);end = new Knight('A', 2);k.g = k.step = 0;k.h = Astar.h(k,end);k.f = k.g + k.h;k.parent = null;//start is root, without parentwhile(!openSet.isEmpty()) openSet.poll();openSet.add(k);//startnew Astar();System.out.println("step is " + sum);while(end!=null){System.out.println(end.row+","+end.column+","+end.f);end = end.parent;}}}

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