A*演算法的C#實現
目錄
1,概述
本文的主要內容是講述A *尋路演算法的基本原理,實現步驟以及對應的C#程式碼,適合讀者用於學習A *演算法或
使用此程式碼提供的介面完成遊戲中的尋路功能。
2,A *演算法的基本原理
A *演算法是一種經典的啟發式演算法,演算法的核心是將節點n到目標點的代價定義為f(n)= g(n)+ h(n),其中 g(n)表示出發點到節點ñ的距離,h(n)是一種啟發式函式,表示節點ñ到目標點的評估代價,通常為了簡化我們採用曼哈頓距離來模擬。知道 f(n)如何計算後,A *演算法還有兩個重要的集合——open列表和closed列表,
3,A *演算法的實現步驟
①將出發點加入到open列表中。
②從open列表中選擇 f(n)最小的節點k,將節點k從open列表中移除,並將其加入到closed列表中。
③對於節點ķ周圍距離為1的每個可達節點t,執行以下操作:
a.如果t在closed列表中,丟棄這個節點;
b.如果t不在open列表中,將其加入open列表中;
c.如果t在open列表中,計算其f(n)並和open列表中該節點的f(n)的對比,如果它的f(n)更小,則更新open列表中該節點的資訊。
④重複②③直到目標點在closed列表中(表明求得最短路徑)或open列表為空(表明終點不可達)。
4,A *演算法的C#實現
檔名:
AStar.cs
演算法執行介面:
AStar.Instance.Execute(int [,] map,int srcX,int srcY,int distX,int distY,int reachableVal = 0,bool allowDiagonal = false);
輸出路徑介面:
AStar.Instance.DisplayPath(ANode aNode);
完整程式碼:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
/********************************************************************************
** auth: FengLinyi
** date: 2018/09/01
** desc: A*演算法的實現
** Ver.: V1.0.0
*********************************************************************************/
namespace DeepCSharp
{
class AStar
{
/// <summary>
/// 二維座標點
/// </summary>
public struct Point
{
public int x, y;
public Point(int _x, int _y)
{
x = _x;
y = _y;
}
}
/// <summary>
/// A*的每個節點
/// </summary>
public class ANode
{
public Point point;
public ANode parent;
public int fn, gn, hn;
}
private AStar() { }
public static AStar Instance { get; } = new AStar();
private int[,] map = null;
private Dictionary<Point, ANode> openList = null;
private HashSet<Point> closedList = null;
private Point dist;
private int reachableVal;
/// <summary>
/// 執行演算法
/// </summary>
/// <param name="map">二維網格地圖,邊緣需要用不可達的值填充</param>
/// <param name="srcX">當前點X座標</param>
/// <param name="srcY">當前點Y座標</param>
/// <param name="distX">目標點X座標</param>
/// <param name="distY">目標點Y座標</param>
public ANode Execute(int[,] map, int srcX, int srcY, int distX, int distY, int reachableVal = 0, bool allowDiagonal = false)
{
openList = new Dictionary<Point, ANode>();
closedList = new HashSet<Point>();
this.map = map;
this.dist = new Point(distX, distY);
this.reachableVal = reachableVal;
//將初始節點加入到open列表中
ANode aNode = new ANode();
aNode.point = new Point(srcX, srcY);
aNode.parent = null;
aNode.gn = 0;
aNode.hn = ManHattan(aNode.point, dist);
aNode.fn = aNode.gn + aNode.hn;
openList.Add(aNode.point, aNode);
while (openList.Count > 0)
{
//從open列表中找到f(n)最小的結點
ANode minFn = FindMinFn(openList);
Point point = minFn.point;
//判斷是否到達終點
if (point.x == dist.x && point.y == dist.y) return minFn;
//去除minFn,加入到closed列表中
openList.Remove(minFn.point);
closedList.Add(minFn.point);
//將minFn周圍的節點加入到open列表中
AddToOpenList(new Point(point.x - 1, point.y), minFn); //左
AddToOpenList(new Point(point.x + 1, point.y), minFn); //右
AddToOpenList(new Point(point.x, point.y - 1), minFn); //上
AddToOpenList(new Point(point.x, point.y + 1), minFn); //下
if(allowDiagonal)
{
AddToOpenList(new Point(point.x - 1, point.y - 1), minFn); //左上
AddToOpenList(new Point(point.x + 1, point.y - 1), minFn); //右上
AddToOpenList(new Point(point.x - 1, point.y + 1), minFn); //左下
AddToOpenList(new Point(point.x + 1, point.y + 1), minFn); //右下
}
}
return null;
}
/// <summary>
/// 輸出最短路徑
/// </summary>
/// <param name="aNode"></param>
public void DisplayPath(ANode aNode)
{
while(aNode != null)
{
Console.WriteLine(aNode.point.x + "," + aNode.point.y);
aNode = aNode.parent;
}
}
/// <summary>
/// 判斷節點是否可達,可達則將節點加入到open列表中
/// </summary>
/// <param name="a"></param>
/// <param name="parent"></param>
private void AddToOpenList(Point point, ANode parent)
{
if(IsReachable(point) && !closedList.Contains(point))
{
ANode aNode = new ANode();
aNode.point = point;
aNode.parent = parent;
aNode.gn = parent.gn + 1;
aNode.hn = ManHattan(point, dist);
aNode.fn = aNode.gn + aNode.hn;
if (openList.ContainsKey(aNode.point))
{
if (aNode.fn < openList[aNode.point].fn)
{
openList[aNode.point] = aNode;
}
}
else
openList.Add(aNode.point, aNode);
}
}
/// <summary>
/// 判定該點是否可達
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
private bool IsReachable(Point a)
{
return map[a.y, a.x] == this.reachableVal;
}
/// <summary>
/// 計算兩個點之間的曼哈頓距離
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
private int ManHattan(Point a, Point b)
{
return Math.Abs(a.x - b.x) + Math.Abs(a.y - b.y);
}
/// <summary>
/// 從open列表中獲取最小f(n)的節點
/// </summary>
/// <param name="aNodes"></param>
/// <returns></returns>
private ANode FindMinFn(Dictionary<Point, ANode> aNodes)
{
ANode minANode = null;
foreach(var e in aNodes)
{
if(minANode == null || e.Value.fn < minANode.fn)
{
minANode = e.Value;
}
}
return minANode;
}
}
}
5,測試
主函式中的程式碼:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace DeepCSharp
{
class Program
{
static void Main(string[] args)
{
int[,] map =
{
{1,1,1,1,1,1,1,1 },
{1,0,0,0,1,1,1,1 },
{1,1,1,0,1,1,1,1 },
{1,1,0,0,1,0,0,1 },
{1,1,0,0,0,0,0,1 },
{1,1,1,1,1,1,1,1 },
};
var node = AStar.Instance.Execute(map, 1, 1, 6, 4);
AStar.Instance.DisplayPath(node);
}
}
}
測試結果: