A*（A-Star)算法是一种静态路网中求解最短路最有效的直接搜索方法。
注意是最有效的直接搜索算法。之后涌现了很多预处理算法（ALT，CH，HL等等），在线查询效率是A*算法的数千甚至上万倍。
公式表示为：f(n)=g(n)+h(n)
其中f(n)是从初始点经由节点n到目标点的估价函数，
g(n)是在状态空间中从初始节点到n节点的实际代价，
h(n)是从n到目标节点最佳路径的估计代价。
保证找到最短路径（最优解的）条件，关键在于估价函数f(n)的选取：
估价值h(n)<= n到目标节点的距离实际值，这种情况下，搜索的点数多，搜索范围大，效率低。但能得到最优解。并且如果h(n)=d(n)，即距离估计h(n)等于最短距离，那么搜索将严格沿着最短路径进行，此时的搜索效率是最高的。
如果估价值>实际值,搜索的点数少，搜索范围小，效率高，但不能保证得到最优解。
using System;
usingSystem.Collections;
using System.Collections.Generic;
usingUnityEngine;
public enumGridType
{
Normal,//正常
Obstacle,//障碍物
Start,//起点
End//终点
}
//为了格子排序需要继承IComparable接口实现排序
public class
MapGrid : IComparable//排序接口
{
public int x;//记录坐标
public int y;
public int f;//总消耗
public int g;//当前点到起点的消耗
public int h;//当前点到终点的消耗
public GridType type;//格子类型
public MapGrid fatherNode;//父节点
//排序
public int CompareTo(object obj)//排序比较方法ICloneable的方法
{
//升序排序
MapGrid grid = (MapGrid)obj;
if (this.f < grid.f)
{
return -1;//升序
}
if (this.f > grid.f)
{
return 1;//降序
}
return 0;
}
}
public classAStar : MonoBehaviour
{
//格子大小
public int row = 5;
public int col = 10;
public int size = 70;//格子大小
public MapGrid[,] grids;//格子数组
public ArrayList openList;//开启列表
public ArrayList closeList;//结束列表
//开始,结束点位置
private int xStart = 2;
private int yStart = 1;
private int xEnd = 2;
private int yEnd = 5;
private StackfatherNodeLocation;
void Init()
{
grids = new MapGrid[row, col];//初始化数组
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col;j++)
{
grids[i, j] = newMapGrid();
grids[i, j].x = i;
grids[i, j].y = j;//初始化格子,记录格子坐标
}
}
grids[xStart, yStart].type =GridType.Start;
grids[xStart, yStart].h =Manhattan(xStart, yStart);//起点的h值
grids[xEnd, yEnd].type =GridType.End;//结束点
fatherNodeLocation = newStack();
//生成障碍物
for (int i = 1; i <= 3; i++)
{
grids[i, 3].type =GridType.Obstacle;
}
openList = new ArrayList();
openList.Add(grids[xStart,yStart]);
closeList = new ArrayList();
}
int Manhattan(int x, int y)//计算算法中的h
{
return (int)(Mathf.Abs(xEnd - x) +Mathf.Abs(yEnd - y)) * 10;
}
// Use this for initialization
void Start()
{
Init();
}
void DrawGrid()
{
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col;j++)
{
Color color =Color.yellow;
if (grids[i, j].type== GridType.Start)
{
color =Color.green;
}
else if (grids[i, j].type== GridType.End)
{
color =Color.red;
}
else if (grids[i,j].type == GridType.Obstacle)//障碍颜色
{
color =Color.blue;
}
else if(closeList.Contains(grids[i, j]))//关闭列表颜色如果当前点包含在closList里
{
color = Color.yellow;
}
else { color =Color.gray; }
GUI.backgroundColor= color;
GUI.Button(newRect(j * size, i * size, size, size), FGH(grids[i, j]));
}
}
}
//每个格子显示的内容
string FGH(MapGrid grid)
{
string str = "F" +grid.f + "\n";
str += "G" + grid.g +"\n";
str += "H" + grid.h +"\n";
str += "(" + grid.x +"," + grid.y + ")";
return str;
}
void OnGUI()
{
DrawGrid();
for (int i = 0; i
{
//生成一个空行,存放开启数组
GUI.Button(new Rect(i *size, (row + 1) * size, size, size), FGH((MapGrid)openList[i]));
}
//生成一个空行,存放关闭数组
for (int j = 0; j
{
GUI.Button(new Rect(j *size, (row + 2) * size, size, size), FGH((MapGrid)closeList[j]));
}
if (GUI.Button(new Rect(col *size, size, size, size), "next"))
{
NextStep();//点击到下一步
}
}
void NextStep()
{
if (openList.Count == 0)//没有可走的点
{
print("Over !");
return;
}
MapGrid grid =(MapGrid)openList[0];//取出openList数组中的第一个点
if (grid.type == GridType.End)//找到终点
{
print("Find");
ShowFatherNode(grid);//找节点//打印路线
return;
}
for (int i = -1; i <= 1; i++)
{
for (int j = -1; j <= 1;j++)
{
if (!(i == 0&& j == 0))
{
int x =grid.x + i;
int y =grid.y + j;
//x,y不超过边界,不是障碍物,不在closList里面
if (x >= 0&& x < row && y >= 0 && y < col &&grids[x, y].type != GridType.Obstacle && !closeList.Contains(grids[x,y]))
{
//到起点的消耗
int g= grid.g + (int)(Mathf.Sqrt((Mathf.Abs(i) + Mathf.Abs(j))) * 10);
if (grids[x, y].g == 0 || grids[x, y].g > g)
{
grids[x,y].g = g;
grids[x,y].fatherNode = grid;//更新父节点
}
//到终点的消耗
grids[x,y].h = Manhattan(x, y);
grids[x,y].f = grids[x, y].g + grids[x, y].h;
if (!openList.Contains(grids[x,y]))
{
openList.Add(grids[x,y]);//如果没有则加入到openlist
}
openList.Sort();//排序
}
}
}
}
//添加到关闭数组
closeList.Add(grid);
//从open数组删除
openList.Remove(grid);
}
//回溯法递归父节点
void ShowFatherNode(MapGrid grid)
{
if (grid.fatherNode != null)
{
//print(grid.fatherNode.x +"," + grid.fatherNode.y);
string str =grid.fatherNode.x + "," + grid.fatherNode.y;
fatherNodeLocation.Push(str);
ShowFatherNode(grid.fatherNode);
}
if (fatherNodeLocation.Count!=0)
{
print(fatherNodeLocation.Pop());
}
}
}
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