偶然看到最短路勁問題,在遊戲、導航等領域都有所應用,覺着挺有意思的,便打算自己也實現一版 。最後選擇了高效簡潔的A*算法。
A*確實是一個非常優秀的實現,比起迪杰特斯拉、best-first等算法,這裏省去1萬字的讚美……
A*算法簡紹可以看該文:
http://blog.csdn.net/pi9nc/article/details/8779503
A*的實現卻並不複雜,關鍵第一點:判斷當前每一步後,下一步怎麼走,一般用一個開集和一個閉集分別來存儲下一步待走的格子 和已經走過的格子;第二點:如何判斷下一步走哪一個格子,這也是A*的優秀之處,它考慮了走過的距離(成本)和預期將要走的距離(期望),擁有快速有效的尋路能力;此處再省略1萬字的讚美……
本文稍加改進,用最小堆來存儲下一步可以走的格子,並用倒樹(指結點中僅有指向父結點的指針的樹,姑且讓我這麼說吧)來記錄路勁。
最小堆參看:http://blog.csdn.net/abcd_d_/article/details/40379125
總共四各類:
1、MyCompare.java 是一個接口
2、MinHeap.java 泛型最小堆 , 實現參照了java API中的ArrayList ,代碼可重用
3、Grid.java格子類,用於記錄格子信息和簡單操作
4、AStar.javaA* 算法主要邏輯類
上代碼:
package com.study.algorithm;
/**
* 比較大小的函數接口
* @author zhangshaoliang
* 2015-5-7下午12:28:12
*/
public interface MyCompare {
public boolean isLarger(MyCompare m2);
public boolean isSmaller(MyCompare m2);
public boolean isEqual(MyCompare m2);
}
package com.study.algorithm;
/**
* pojo ,格子
* <pre> F = G + H
* G 表示從起點 A 移動到網格上指定方格的移動耗費 (可沿斜方向移動,斜方向的代價爲對角線長度)
* H 表示從指定的方格移動到終點 B 的預計耗費 (H 有很多計算方法, 這裏我們設定只可以上下左右移動).</pre>
* @author zhangshaoliang
* 2015-5-7下午1:00:09
*/
public class Grid implements MyCompare{
private double F;
private double H;
private double G;
private int i ;
private int j;
private Grid parent; ///該格子的父格子
/**
* pojo ,格子
* @param F F = G + H
* @param G 表示從起點 A 移動到網格上指定方格的移動耗費 (可沿斜方向移動,斜方向的代價爲對角線長度)
* @param H 表示從指定的方格移動到終點 B 的預計耗費 (H 有很多計算方法, 這裏我們設定只可以上下左右移動).
* @param i 縱座標i
* @param j 橫座標j
* @param parent 父結點
*/
public Grid(double F,double G,double H,int i,int j,Grid parent){
this.F = F;
this.G = G;
this.H = H;
this.i = i;
this.j = j;
this.parent = parent;
}
public Grid(){}
public Grid getParent() {
return parent;
}
public void setParent(Grid parent) {
this.parent = parent;
}
public int getI() {
return i;
}
public int getJ() {
return j;
}
public void setI(int i) {
this.i = i;
}
public void setJ(int j) {
this.j = j;
}
/**
* 經過當前點到終點B的總耗費 期望值
* @return
*/
public double getF() {
return F;
}
/**
* H 表示從指定的方格移動到終點 B 的預計耗費 (H 有很多計算方法, 這裏我們設定只可以上下左右移動)
* @return
*/
public double getH() {
return H;
}
/**
* 表示從起點 A 移動到當前網格上的移動耗費 (可沿斜方向移動,斜方向的代價爲對角線長度)
* @return
*/
public double getG() {
return G;
}
public void setF(double f) {
F = f;
}
public void setH(double h) {
H = h;
}
public void setG(double g) {
G = g;
}
@Override
public boolean isLarger(MyCompare m2) {
// TODO Auto-generated method stub
return this.F>((Grid)m2).getF();
}
@Override
public boolean isSmaller(MyCompare m2) {
// TODO Auto-generated method stub
return this.F<((Grid)m2).getF();
}
@Override
public boolean isEqual(MyCompare m2) {
// TODO Auto-generated method stub
return this.F==((Grid)m2).getF();
}
}
package com.study.algorithm;
/**
* 最小堆
* @author zhangshaoliang
* 2015-5-7上午11:08:20
*/
public class MinHeap<E extends MyCompare> {
private int size;
private Object[] element;
public MinHeap(int maxSize){
size = 0;
element = new Object[maxSize];
}
public MinHeap(){
this(10);
}
/**
* 元素入堆
* @param e
*/
public void append(E e){
ensureCapacity(size+1);
element[size++] = e;///put the element to the end of the heap
adjustUp(); //adjust the heap to minHeap
}
/**
* 取出堆頂元素(最小元素)
* @return
*/
@SuppressWarnings("unchecked")
public E poll(){
if(isEmpty()){
return null;
}
E min = (E) element[0];
element[0] = element[size-1];///replace the min element with the last element
element[size-1] = null ;///let gc do its work
size--;
adjustDown();///adjust the heap to minHeap
return min;
}
/**
* 查看堆頂元素(最小元素)
* @return
*/
@SuppressWarnings("unchecked")
public E peek(){
if(isEmpty()){
return null;
}
return (E) element[0];
}
/**
* 是否爲空堆
* @return
*/
public boolean isEmpty(){
return size == 0 ;
}
/**
* 確保容量空間足夠
* @param minCapacity
*/
private void ensureCapacity(int minCapacity){
int oldCapacity = element.length;
if(minCapacity > oldCapacity){
int newCapacity = (oldCapacity*3)/2+1;///每次擴容至1.5倍
Object[] copy = new Object[newCapacity];
///調用本地C方法進行數組複製
System.arraycopy(element, 0, copy, 0, element.length);
element = copy;
}
}
/**
* 向上調整爲堆,將小值往上調
*/
@SuppressWarnings("unchecked")
private void adjustUp(){
E temp = (E) element[size-1]; ///get the last element
int parent = size - 1;
while(parent>0&&((E)element[(size - 1)/2]).isLarger(temp)){
///if smaller than it parent
element[parent] = element[(parent - 1)/2];
parent = (parent - 1)/2;
}
element[parent] = temp;
}
/**
* 向下調整爲堆
*/
@SuppressWarnings("unchecked")
private void adjustDown(){
E temp = (E) element[0]; ///get the first element
int child = 1;
while(child<size){
E left = (E) element[child];
E right = (E) element[child+1];///這裏的child+1不會越界(想想爲什麼)
if(right!=null&&left.isLarger(right)){
child++;
}
if(temp.isSmaller((E)element[child])){
break; ////如果比兩個孩子中較小者都還小,則結束
}
element[(child-1)/2] = element[child]; ///assign the smaller to its parent
child = child*2 + 1;
}
element[(child-1)/2] = temp;
}
}
package com.study.algorithm;
/**
* A*尋路算法
* <pre>
* 思路: 每次取期望值最小的位置作爲下一步要走的位置,F = G + H
* G 表示從起點 A 移動到網格上指定方格的移動耗費 (可沿斜方向移動,斜方向的代價爲對角線長度).
* H 表示從指定的方格移動到終點 B 的預計耗費 (H 有很多計算方法, 這裏我們設定只可以上下左右移動).
*
* 此處用一個最小堆來記錄開啓列表中的格子,每個格子有一個指向父格子的指針,以此記錄路勁 </pre>
* @author zhangshaoliang
* 2015-5-7上午10:58:54
*/
public class AStar {
private static MinHeap<Grid> open ;//= new MinHeap<Grid>();
// private static MTree close ;//= new MTree();
private Grid last; //記錄最後一個格子
private final String obstacle = "1";//障礙物標記值
private String end = "e"; ////目標標記值
private String start = "s";////開始標記值
//目標座標
private int end_i = -1;
private int end_j = -1;
//開始目標
private int start_i = -1;
private int start_j = -1;
/**
* 初始化操作
* @param boxs
*/
public void init(String[][] boxs){
for(int i=0;i<boxs.length;i++){
for(int j=0;j<boxs[0].length;j++){
if(boxs[i][j].equals(start)){
start_i = i;
start_j = j;
}
if(boxs[i][j].equals(end)){
end_i = i;
end_j = j;
}
}
}
Grid sGrid = new Grid(0, 0, 0, start_i, start_j, null);
open = new MinHeap<Grid>();
open.append(sGrid);///、將開始位置加入開集
}
/**
* 開始搜索
*/
public void search(String[][] boxs){
int height = boxs.length;
int width = boxs[0].length;
while(open.peek()!=null){//對開集進行遍歷,直到找到目標或者找不到通路
Grid g = open.poll();
int i = g.getI();
int j = g.getJ();
double pre_G = g.getG();///已耗費
for(int h=-1;h<=1;h++){
for(int w=-1;w<=1;w++){
int next_i = i + h; ///下一個將加入open 集的格子的i
int next_j = j + w;///下一個將加入open 集的格子的j
if(next_i>=0 && next_i<=height-1 && next_j>=0 && next_j<=width-1){
////數組不越界,則進行計算
if(boxs[next_i][next_j].equals(obstacle) || boxs[next_i][next_j].equals("-1") ||(h==0&&w==0)){
//如果該格子是障礙,或者格子本身,跳過
continue;
}
////計算該點到終點的最短路勁
double H = Math.abs(end_i - next_i) + Math.abs(end_j - next_j) ;
if(H<1){
///找到目標,記錄並結束
last = new Grid(0, pre_G, 0, next_i, next_j,g); ;
return ;
}
////如果是對角線則加1.4,否則加1
double G = Math.sqrt((next_i-i)*(next_i-i)+(next_j-j)*(next_j-j))>1 ? pre_G+1.4 : pre_G+1;
//生成新格子
Grid temp = new Grid(H+G, G, H, next_i, next_j,g);
////加入open集
open.append(temp);
boxs[i][j] = "-1";///表示此處已經計算過了
}
}
}
last = g;
}
}
/**
* 打印路勁
*/
public void printPath(){
if(end_i!=last.getI()||end_j!=last.getJ()){
System.out.println("無法到達終點!");
return ;
}
System.out.println("路勁逆序爲:");
while(true){
System.out.print("("+last.getI()+","+last.getJ()+")");
last = last.getParent();
if(last==null){
break;
}
System.out.print(" <———");
}
}
/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
/*Grid g1 = new Grid(2, 1, 2, 0, 0,null);
Grid g2 = new Grid(5, 1, 2, 0, 0,g1);
Grid g3 = new Grid(1, 1, 2, 0, 0,g1);
Grid g4 = new Grid(6, 1, 2, 0, 0,g2);
Grid g5 = new Grid(3, 1, 2, 0, 0,g3);
open = new MinHeap<Grid>();
open.append(g1);
open.append(g2);
open.append(g3);
open.append(g4);
open.append(g5);
//、測試最小堆
while(null!=open.peek()){
System.out.println(open.poll().getF());
}
*/
String[][] boxs = {//{"0","g"},{"s","0"}};
{"0","0","1","0","0"},
{"0","0","1","e","0"},
{"0","0","1","1","0"},
{"0","0","0","1","0"},
{"s","0","1","0","0"},
};
AStar star = new AStar();
star.init(boxs);
star.search(boxs);
star.printPath();
}
}
輸出結果:
<span style="font-size:18px;">路勁逆序爲:
(1,3) <———(2,4) <———(3,4) <———(4,3) <———(3,2) <———(3,1) <———(4,0)</span>