以前空闲的时候用C#实现的路径规划算法，今日贴它出来，看大家有没有更好的实现方案。关于路径规划（最短路径）算法的背景知识，大家可以参考《C++算法－－图算法》一书。
该图算法描述的是这样的场景：图由节点和带有方向的边构成，每条边都有相应的权值，路径规划（最短路径）算法就是要找出从节点A到节点B的累积权值最小的路径。
首先，我们可以将“有向边”抽象为Edge类：
public class Edge
{
public string StartNodeID ;
public string EndNodeID ;
public double Weight ; //权值，代价
}
{
public string StartNodeID ;
public string EndNodeID ;
public double Weight ; //权值，代价
}
节点则抽象成Node类，一个节点上挂着以此节点作为起点的“出边”表。
public class Node
{
private string iD ;
private ArrayList edgeList ;//Edge的集合－－出边表
public Node(string id )
{
this.iD = id ;
this.edgeList = new ArrayList() ;
}
property
}
{
private string iD ;
private ArrayList edgeList ;//Edge的集合－－出边表
public Node(string id )
{
this.iD = id ;
this.edgeList = new ArrayList() ;
}
property
}
在计算的过程中，我们需要记录到达每一个节点权值最小的路径，这个抽象可以用PassedPath类来表示：
/// <summary>
/// PassedPath 用于缓存计算过程中的到达某个节点的权值最小的路径
/// </summary>
public class PassedPath
{
private string curNodeID ;
private bool beProcessed ; //是否已被处理
private double weight ; //累积的权值
private ArrayList passedIDList ; //路径
public PassedPath(string ID)
{
this.curNodeID = ID ;
this.weight = double.MaxValue ;
this.passedIDList = new ArrayList() ;
this.beProcessed = false ;
}
#region property
public bool BeProcessed
{
get
{
return this.beProcessed ;
}
set
{
this.beProcessed = value ;
}
}
public string CurNodeID
{
get
{
return this.curNodeID ;
}
}
public double Weight
{
get
{
return this.weight ;
}
set
{
this.weight = value ;
}
}
public ArrayList PassedIDList
{
get
{
return this.passedIDList ;
}
}
#endregion
}
/// PassedPath 用于缓存计算过程中的到达某个节点的权值最小的路径
/// </summary>
public class PassedPath
{
private string curNodeID ;
private bool beProcessed ; //是否已被处理
private double weight ; //累积的权值
private ArrayList passedIDList ; //路径
public PassedPath(string ID)
{
this.curNodeID = ID ;
this.weight = double.MaxValue ;
this.passedIDList = new ArrayList() ;
this.beProcessed = false ;
}
#region property
public bool BeProcessed
{
get
{
return this.beProcessed ;
}
set
{
this.beProcessed = value ;
}
}
public string CurNodeID
{
get
{
return this.curNodeID ;
}
}
public double Weight
{
get
{
return this.weight ;
}
set
{
this.weight = value ;
}
}
public ArrayList PassedIDList
{
get
{
return this.passedIDList ;
}
}
#endregion
}
另外，还需要一个表PlanCourse来记录规划的中间结果，即它管理了每一个节点的PassedPath。
/// <summary>
/// PlanCourse 缓存从源节点到其它任一节点的最小权值路径＝》路径表
/// </summary>
public class PlanCourse
{
private Hashtable htPassedPath ;
#region ctor
public PlanCourse(ArrayList nodeList ,string originID)
{
this.htPassedPath = new Hashtable() ;
Node originNode = null ;
foreach(Node node in nodeList)
{
if(node.ID == originID)
{
originNode = node ;
}
else
{
PassedPath pPath = new PassedPath(node.ID) ;
this.htPassedPath.Add(node.ID ,pPath) ;
}
}
if(originNode == null)
{
throw new Exception("The origin node is not exist !") ;
}
this.InitializeWeight(originNode) ;
}
private void InitializeWeight(Node originNode)
{
if((originNode.EdgeList == null) ||(originNode.EdgeList.Count == 0))
{
return ;
}
foreach(Edge edge in originNode.EdgeList)
{
PassedPath pPath = this[edge.EndNodeID] ;
if(pPath == null)
{
continue ;
}
pPath.PassedIDList.Add(originNode.ID) ;
pPath.Weight = edge.Weight ;
}
}
#endregion
public PassedPath this[string nodeID]
{
get
{
return (PassedPath)this.htPassedPath[nodeID] ;
}
}
}
在所有的基础构建好后，路径规划算法就很容易实施了，该算法主要步骤如下：
(1)用一张表(PlanCourse)记录源点到任何其它一节点的最小权值，初始化这张表时，如果源点能直通某节点，则权值设为对应的边的权，否则设为double.MaxValue。
(2)选取没有被处理并且当前累积权值最小的节点TargetNode，用其边的可达性来更新到达其它节点的路径和权值（如果其它节点 经此节点后权值变小则更新，否则不更新），然后标记TargetNode为已处理。
(3)重复(2)，直至所有的可达节点都被处理一遍。
(4)从PlanCourse表中获取目的点的PassedPath，即为结果。
下面就来看上述步骤的实现，该实现被封装在RoutePlanner类中：
/// <summary>
/// RoutePlanner 提供图算法中常用的路径规划功能。
/// 2005.09.06
/// </summary>
public class RoutePlanner
{
public RoutePlanner()
{
}
#region Paln
//获取权值最小的路径
public RoutePlanResult Paln(ArrayList nodeList ,string originID ,string destID)
{
PlanCourse planCourse = new PlanCourse(nodeList ,originID) ;
Node curNode = this.GetMinWeightRudeNode(planCourse ,nodeList ,originID) ;
#region 计算过程
while(curNode != null)
{
PassedPath curPath = planCourse[curNode.ID] ;
foreach(Edge edge in curNode.EdgeList)
{
PassedPath targetPath = planCourse[edge.EndNodeID] ;
double tempWeight = curPath.Weight + edge.Weight ;
if(tempWeight < targetPath.Weight)
{
targetPath.Weight = tempWeight ;
targetPath.PassedIDList.Clear() ;
for(int i=0 ;i<curPath.PassedIDList.Count ;i++)
{
targetPath.PassedIDList.Add(curPath.PassedIDList[i].ToString()) ;
}
targetPath.PassedIDList.Add(curNode.ID) ;
}
}
//标志为已处理
planCourse[curNode.ID].BeProcessed = true ;
//获取下一个未处理节点
curNode = this.GetMinWeightRudeNode(planCourse ,nodeList ,originID) ;
}
#endregion
//表示规划结束
return this.GetResult(planCourse ,destID) ;
}
#endregion
#region private method
#region GetResult
//从PlanCourse表中取出目标节点的PassedPath，这个PassedPath即是规划结果
private RoutePlanResult GetResult(PlanCourse planCourse ,string destID)
{
PassedPath pPath = planCourse[destID] ;
if(pPath.Weight == int.MaxValue)
{
RoutePlanResult result1 = new RoutePlanResult(null ,int.MaxValue) ;
return result1 ;
}
string[] passedNodeIDs = new string[pPath.PassedIDList.Count] ;
for(int i=0 ;i<passedNodeIDs.Length ;i++)
{
passedNodeIDs[i] = pPath.PassedIDList[i].ToString() ;
}
RoutePlanResult result = new RoutePlanResult(passedNodeIDs ,pPath.Weight) ;
return result ;
}
#endregion
#region GetMinWeightRudeNode
//从PlanCourse取出一个当前累积权值最小，并且没有被处理过的节点
private Node GetMinWeightRudeNode(PlanCourse planCourse ,ArrayList nodeList ,string originID)
{
double weight = double.MaxValue ;
Node destNode = null ;
foreach(Node node in nodeList)
{
if(node.ID == originID)
{
continue ;
}
PassedPath pPath = planCourse[node.ID] ;
if(pPath.BeProcessed)
{
continue ;
}
if(pPath.Weight < weight)
{
weight = pPath.Weight ;
destNode = node ;
}
}
return destNode ;
}
#endregion
#endregion
}
/// RoutePlanner 提供图算法中常用的路径规划功能。
/// 2005.09.06
/// </summary>
public class RoutePlanner
{
public RoutePlanner()
{
}
#region Paln
//获取权值最小的路径
public RoutePlanResult Paln(ArrayList nodeList ,string originID ,string destID)
{
PlanCourse planCourse = new PlanCourse(nodeList ,originID) ;
Node curNode = this.GetMinWeightRudeNode(planCourse ,nodeList ,originID) ;
#region 计算过程
while(curNode != null)
{
PassedPath curPath = planCourse[curNode.ID] ;
foreach(Edge edge in curNode.EdgeList)
{
PassedPath targetPath = planCourse[edge.EndNodeID] ;
double tempWeight = curPath.Weight + edge.Weight ;
if(tempWeight < targetPath.Weight)
{
targetPath.Weight = tempWeight ;
targetPath.PassedIDList.Clear() ;
for(int i=0 ;i<curPath.PassedIDList.Count ;i++)
{
targetPath.PassedIDList.Add(curPath.PassedIDList[i].ToString()) ;
}
targetPath.PassedIDList.Add(curNode.ID) ;
}
}
//标志为已处理
planCourse[curNode.ID].BeProcessed = true ;
//获取下一个未处理节点
curNode = this.GetMinWeightRudeNode(planCourse ,nodeList ,originID) ;
}
#endregion
//表示规划结束
return this.GetResult(planCourse ,destID) ;
}
#endregion
#region private method
#region GetResult
//从PlanCourse表中取出目标节点的PassedPath，这个PassedPath即是规划结果
private RoutePlanResult GetResult(PlanCourse planCourse ,string destID)
{
PassedPath pPath = planCourse[destID] ;
if(pPath.Weight == int.MaxValue)
{
RoutePlanResult result1 = new RoutePlanResult(null ,int.MaxValue) ;
return result1 ;
}
string[] passedNodeIDs = new string[pPath.PassedIDList.Count] ;
for(int i=0 ;i<passedNodeIDs.Length ;i++)
{
passedNodeIDs[i] = pPath.PassedIDList[i].ToString() ;
}
RoutePlanResult result = new RoutePlanResult(passedNodeIDs ,pPath.Weight) ;
return result ;
}
#endregion
#region GetMinWeightRudeNode
//从PlanCourse取出一个当前累积权值最小，并且没有被处理过的节点
private Node GetMinWeightRudeNode(PlanCourse planCourse ,ArrayList nodeList ,string originID)
{
double weight = double.MaxValue ;
Node destNode = null ;
foreach(Node node in nodeList)
{
if(node.ID == originID)
{
continue ;
}
PassedPath pPath = planCourse[node.ID] ;
if(pPath.BeProcessed)
{
continue ;
}
if(pPath.Weight < weight)
{
weight = pPath.Weight ;
destNode = node ;
}
}
return destNode ;
}
#endregion
#endregion
}
2006.05.22 应众多朋友要求，下面给出一个简单示例：
RoutePlanner.Plan 过程详解：
(1)用一张表(PlanCourse)记录源点到任何其它一节点的最小权值，初始化这张表时，如果源点能直通某节点，则权值设为对应的
边的权，否则设为double.MaxValue
(2)选取没有被处理并且当前累积权值最小的节点TargetNode，用其边的可达性来更新到达其它节点的路径和权值（如果其它节点
经此节点后权值变小则更新，否则不更新），然后标记TargetNode为已处理
(3)重复(2)，直至所有的可达节点都被处理一遍。
(4)从PlanCourse表中获取目的点的PassedPath，即为结果。
[STAThread]
static void Main(string[] args)
{
ArrayList nodeList = new ArrayList() ;
//***************** B Node *******************
Node aNode = new Node("A") ;
nodeList.Add(aNode) ;
//A -> B
Edge aEdge1 = new Edge() ;
aEdge1.StartNodeID = aNode.ID ;
aEdge1.EndNodeID = "B" ;
aEdge1.Weight = 10 ;
aNode.EdgeList.Add(aEdge1) ;
//A -> C
Edge aEdge2 = new Edge() ;
aEdge2.StartNodeID = aNode.ID ;
aEdge2.EndNodeID = "C" ;
aEdge2.Weight = 20 ;
aNode.EdgeList.Add(aEdge2) ;
//A -> E
Edge aEdge3 = new Edge() ;
aEdge3.StartNodeID = aNode.ID ;
aEdge3.EndNodeID = "E" ;
aEdge3.Weight = 30 ;
aNode.EdgeList.Add(aEdge3) ;
//***************** B Node *******************
Node bNode = new Node("B") ;
nodeList.Add(bNode) ;
//B -> C
Edge bEdge1 = new Edge() ;
bEdge1.StartNodeID = bNode.ID ;
bEdge1.EndNodeID = "C" ;
bEdge1.Weight = 5 ;
bNode.EdgeList.Add(bEdge1) ;
//B -> E
Edge bEdge2 = new Edge() ;
bEdge2.StartNodeID = bNode.ID ;
bEdge2.EndNodeID = "E" ;
bEdge2.Weight = 10 ;
bNode.EdgeList.Add(bEdge2) ;
//***************** C Node *******************
Node cNode = new Node("C") ;
&n
static void Main(string[] args)
{
ArrayList nodeList = new ArrayList() ;
//***************** B Node *******************
Node aNode = new Node("A") ;
nodeList.Add(aNode) ;
//A -> B
Edge aEdge1 = new Edge() ;
aEdge1.StartNodeID = aNode.ID ;
aEdge1.EndNodeID = "B" ;
aEdge1.Weight = 10 ;
aNode.EdgeList.Add(aEdge1) ;
//A -> C
Edge aEdge2 = new Edge() ;
aEdge2.StartNodeID = aNode.ID ;
aEdge2.EndNodeID = "C" ;
aEdge2.Weight = 20 ;
aNode.EdgeList.Add(aEdge2) ;
//A -> E
Edge aEdge3 = new Edge() ;
aEdge3.StartNodeID = aNode.ID ;
aEdge3.EndNodeID = "E" ;
aEdge3.Weight = 30 ;
aNode.EdgeList.Add(aEdge3) ;
//***************** B Node *******************
Node bNode = new Node("B") ;
nodeList.Add(bNode) ;
//B -> C
Edge bEdge1 = new Edge() ;
bEdge1.StartNodeID = bNode.ID ;
bEdge1.EndNodeID = "C" ;
bEdge1.Weight = 5 ;
bNode.EdgeList.Add(bEdge1) ;
//B -> E
Edge bEdge2 = new Edge() ;
bEdge2.StartNodeID = bNode.ID ;
bEdge2.EndNodeID = "E" ;
bEdge2.Weight = 10 ;
bNode.EdgeList.Add(bEdge2) ;
//***************** C Node *******************
Node cNode = new Node("C") ;
&n
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