/// <summary>
/// 单源最短路径会把一个点到其它所有点的最短路径算出来
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="graph"></param>
/// <param name="source"></param>
/// <param name="weightFuc"></param>
/// <returns></returns>
public static bool BellmanFord <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> source,
Func <AdjacencyListGraph <T>, AdjacencyVertex <T>, AdjacencyVertex <T>, int> weightFuc
) where T : IEquatable <T>
{
graph.InitializeSingleSource(source);
for (int i = 1; i <= graph.VertexLenght; i++)
{
foreach (var edge in graph.GetEdges())
{
graph.Relax(edge.Start, edge.End, weightFuc);
}
}
foreach (var edge in graph.GetEdges())
{
if (edge.Start.WeightBound >
Add(edge.End.WeightBound, weightFuc(graph, edge.Start, edge.End)))
{
return(false);
}
}
return(true);
}
public AdjacencyVertex <T> CreateVertex(AdjacencyVertex <T> vertex)
{
return(new AdjacencyVertex <T>()
{
Key = vertex.Key, Identifier = vertex.Identifier
});
}
public AdjacencyEdge <T> CreateEdge(AdjacencyVertex <T> start, AdjacencyVertex <T> end, int weight)
{
var edge = new AdjacencyEdge <T>(start, end);
edge.Weight = weight;
return(edge);
}
private void DepthFirstSearchVisit(AdjacencyVertex <T> source, Action <AdjacencyVertex <T> > finalVisitAction)
{
source.Color = Color.Gray;
_time = _time + 1;
source.FisrtVisitTime = _time;
var edges = GetVertexEdge(source);
foreach (var item in edges)
{
var vertex = item.End;
if (vertex.Color == Color.White)
{
vertex.Predecessor = source;
DepthFirstSearchVisit(vertex, finalVisitAction);
}
}
source.Color = Color.Black;
_time = _time + 1;
source.FinalVisitTime = _time;
finalVisitAction?.Invoke(source);
}
private void InitializePreflow(AdjacencyListGraph <T> graph
, AdjacencyVertex <T> source)
{
var vertexs = graph.GetVertexs();
foreach (var vertex in vertexs)
{
vertex.Height = 0;
vertex.Preflow = 0;
}
var edges = graph.GetEdges();
foreach (FlowEdge <T> edge in edges)
{
edge.Flow = 0;
edge.Revolution.Flow = 0;
}
source.Height = vertexs.Count();
var sourceEdges = graph.GetVertexEdge(source);
foreach (FlowEdge <T> sourceEdge in sourceEdges)
{
sourceEdge.Flow = sourceEdge.Capacity;
sourceEdge.Revolution.Flow = -sourceEdge.Capacity;
sourceEdge.End.Preflow = sourceEdge.Capacity;
source.Preflow = source.Preflow - sourceEdge.Capacity;
}
}
public void AddEdge(AdjacencyVertex <T> first, AdjacencyVertex <T> second)
{
AddEdge(CreateEdge(first, second));
if (!HasDirection)
{
AddEdge(CreateEdge(second, first));
}
}
public void AddVertex(AdjacencyVertex <T> vertex)
{
if (!IsVertexExist(vertex))
{
_adjacencyDictionary[vertex.Identifier] = vertex;
}
else
{
}
}
public AdjacencyVertex <T> CreateVertex(T key)
{
var vertex = new AdjacencyVertex <T>()
{
Key = key
};
vertex.Identifier = GetCurrentIdentifier();
return(vertex);
}
public IEnumerable <AdjacencyEdge <T> > GetVertexEdge(AdjacencyVertex <T> vertex)
{
var edges = new List <AdjacencyEdge <T> >();
var edge = vertex.FirstEdge;
while (edge != null)
{
edges.Add(edge);
edge = edge.Next;
}
return(edges);
}
public AdjacencyEdge <T> GetEdge(AdjacencyVertex <T> first, AdjacencyVertex <T> second)
{
var edge = first.FirstEdge;
while (edge != null)
{
if (edge.End == second)
{
return(edge);
}
edge = edge.Next;
}
return(null);
}
public static void InitializeSingleSource <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> source
) where T : IEquatable <T>
{
var vertexs = graph.GetVertexs();
foreach (var vertex in vertexs)
{
vertex.WeightBound = int.MaxValue;
vertex.Predecessor = null;
}
source.WeightBound = 0;
}
public static void Relax <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> first,
AdjacencyVertex <T> second,
Func <AdjacencyListGraph <T>, AdjacencyVertex <T>, AdjacencyVertex <T>, int> weightFuc
) where T : IEquatable <T>
{
var newBound = Add(first.WeightBound, weightFuc(graph, first, second));
if (second.WeightBound > newBound)
{
second.WeightBound = newBound;
second.Predecessor = first;
}
}
/// <summary>
/// 单源最短路径会把一个点到其它所有点的最短路径算出来
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="graph"></param>
/// <param name="source"></param>
/// <param name="weightFuc"></param>
/// <returns></returns>
public static void Dijkstra <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> source,
Func <AdjacencyListGraph <T>, AdjacencyVertex <T>, AdjacencyVertex <T>, int> weightFuc
) where T : IEquatable <T>
{
graph.InitializeSingleSource(source);
var calcVertexs = new List <AdjacencyVertex <T> >();
var vertexs = graph.GetVertexs().ToList();
//不想再增加AdjacencyVertex对象的负担了
var queue = new ExtentionBinanyHeap <AdjacencyVertex <T> >
(
vertexs,
(first, second) =>
{
return(first.WeightBound < second.WeightBound);
}
);
// while (!queue.IsEmpty) 竟然把while写成if有才
while (!queue.IsEmpty)
{
var min = queue.Extract();
Console.WriteLine("calcVertex");
Console.WriteLine(min);
calcVertexs.Add(min);
var edges = graph.GetVertexEdge(min);
foreach (var edge in edges)
{
var oldWeight = edge.End.WeightBound;
Relax(graph, edge.Start, edge.End, weightFuc);
//没有索引位置一下让我傻逼了!网上找了一下也是有调整的。
if (oldWeight != edge.End.WeightBound)
{
queue.UpdateKey(edge.End, edge.End);
}
}
}
}
public int GenericPushRelabel(
AdjacencyListGraph <T> graph
, AdjacencyVertex <T> source
, AdjacencyVertex <T> target
)
{
var maxFolw = 0;
InitializePreflow(graph, source);
while (true)
{
}
return(maxFolw);
}
/// <summary>
/// 看不懂算法导论上的实现
/// </summary>
/// <param name="graph"></param>
/// <param name="source"></param>
/// <param name="target"></param>
public int EdmondsKarp(
AdjacencyListGraph <T> graph
, AdjacencyVertex <T> source
, AdjacencyVertex <T> target)
{
var maxflow = 0;
var edges = graph.GetEdges().Select(d => d as FlowEdge <T>);
foreach (var edge in edges)
{
edge.Flow = 0;
}
while (true)
{
var path = GetResidualPath(graph, source, target);
if (path == null || path.Count == 0)
{
break;
}
var tempFlow = int.MaxValue;
//感觉第一次写这样的for循环
for (var edge = path[target]; edge != null; edge = path[edge.Start])
{
tempFlow = Math.Min(tempFlow, edge.ResidualCapacity);
}
Console.WriteLine();
Console.WriteLine($"pathflow:{tempFlow}");
for (var edge = path[target]; edge != null; edge = path[edge.Start])
{
edge.Flow = edge.Flow + tempFlow;
edge.Revolution.Flow = edge.Revolution.Flow - tempFlow;
Console.WriteLine($"edge:{edge}");
}
maxflow = maxflow + tempFlow;
}
return(maxflow);
}
/// <summary>
/// 怎么输出最小生成树？
/// 很神奇的是这个贪心算法是对的
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="graph"></param>
/// <param name="root"></param>
/// <param name="weightFunc"></param>
public static IList <AdjacencyEdge <T> > GetMininumSpanningTreePrim <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> root,
Func <AdjacencyEdge <T>, int> weightFunc
) where T : IEquatable <T>
{
var vertexs = graph.GetVertexs().ToList();
//TempStorage顶点到到某一顶点相连的最小权值。
foreach (var vertex in vertexs)
{
vertex.TempStorage = int.MaxValue;
vertex.Predecessor = null;
}
root.TempStorage = 0;
var result = new List <AdjacencyEdge <T> >();
var queue = new ExtentionBinanyHeap <AdjacencyVertex <T> >(vertexs, (f, s) => f.TempStorage < s.TempStorage);
while (!queue.IsEmpty)
{
var min = queue.Extract();
if (min != root)
{
result.Add(graph.GetEdge(min.Predecessor, min));
}
var edges = graph.GetVertexEdge(min);
foreach (var edge in edges)
{
var weight = weightFunc(edge);
//TODO: 还有一个包含判断
if (edge.End.BelongedHeap == queue && weight < edge.End.TempStorage)
{
edge.End.Predecessor = min;
edge.End.TempStorage = weight;
queue.UpdateKey(edge.End, edge.End);
}
}
}
return(result);
}
public IDictionary <AdjacencyVertex <T>, FlowEdge <T> > GetResidualPath(
AdjacencyListGraph <T> graph
, AdjacencyVertex <T> source
, AdjacencyVertex <T> target)
{
var path = new Dictionary <AdjacencyVertex <T>, FlowEdge <T> >();
var vertexs = graph.GetVertexs();
foreach (var vertex in vertexs)
{
vertex.Predecessor = null;
}
path[source] = null;
var queue = new Queue <AdjacencyVertex <T> >();
queue.Enqueue(source);
while (!queue.IsEmpty)
{
var current = queue.Dequeue();
var currentEdges = graph.GetVertexEdge(current);
foreach (FlowEdge <T> currentEdge in currentEdges)
{
if (currentEdge.End != source &&
currentEdge.End.Predecessor == null &&
currentEdge.Capacity > currentEdge.Flow
)
{
path[currentEdge.End] = currentEdge;
currentEdge.End.Predecessor = current;
queue.Enqueue(currentEdge.End);
}
}
}
if (target.Predecessor == null)
{
return(null);
}
return(path);
}
public IEnumerable <AdjacencyEdge <T> > CreateNonDirectionEdge(AdjacencyVertex <T> start, AdjacencyVertex <T> end, int weight)
{
var edges = new List <AdjacencyEdge <T> >();
var edge = new AdjacencyEdge <T>(start, end);
edge.Weight = weight;
edges.Add(edge);
var secondedge = new AdjacencyEdge <T>(end, start);
secondedge.Weight = weight;
//加边加错了，bug就是这么神奇
//edges.Add(edge);
edges.Add(secondedge);
return(edges);
}
public IEnumerable <AdjacencyVertex <T> > GetPath(AdjacencyVertex <T> source, AdjacencyVertex <T> vertex)
{
var path = new List <AdjacencyVertex <T> >();
if (source == vertex)
{
path.Add(vertex);
return(path);
}
if (vertex.Predecessor == null)
{
return(null);
// Console.WriteLine("no path form source:{0} vertex:{1}", source, vertex);
}
else
{
path.AddRange(GetPath(source, vertex.Predecessor));
return(path);
}
}
/// <summary>
/// 有向无回路图
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="graph"></param>
/// <param name="source"></param>
/// <param name="weightFuc"></param>
/// <returns></returns>
public static void DAGShortestPath <T>(
this AdjacencyListGraph <T> graph,
AdjacencyVertex <T> source,
Func <AdjacencyListGraph <T>, AdjacencyVertex <T>, AdjacencyVertex <T>, int> weightFuc
) where T : IEquatable <T>
{
graph.TopologicalSort();
graph.InitializeSingleSource(source);
var vertexs = graph.GetVertexs();
foreach (var orderVertex in vertexs)
{
var edges = graph.GetVertexEdge(orderVertex);
foreach (var edge in edges)
{
graph.Relax(edge.Start, edge.End, weightFuc);
}
}
}
private void DepthFirstSearchVisitStronglyConnected
(AdjacencyVertex <T> source
, AdjacencyListGraph <T> graph
)
{
source.Color = Color.Gray;
_time = _time + 1;
source.FisrtVisitTime = _time;
var edges = GetVertexEdge(source);
//调整
var newSource = CreateVertex(source);
graph.AddVertex(newSource);
foreach (var item in edges)
{
var vertex = item.End;
if (vertex.Color == Color.White)
{
//调整
var newVertex = CreateVertex(vertex);
graph.AddVertex(newVertex);
graph.AddEdge(new AdjacencyEdge <T>(newVertex, newSource));
vertex.Predecessor = source;
DepthFirstSearchVisitStronglyConnected(vertex, graph);
}
}
source.Color = Color.Black;
_time = _time + 1;
source.FinalVisitTime = _time;
}
public void BreadthFirstSearch(AdjacencyVertex <T> source, Action <AdjacencyVertex <T> > finalVisitAction)
{
var grayQueue = new Queue <AdjacencyVertex <T> >();
foreach (var vertex in _adjacencyDictionary.Values)
{
if (vertex == source)
{
continue;
}
vertex.Distance = int.MaxValue;
vertex.Predecessor = null;
vertex.Color = Color.White;
}
source.Color = Color.Gray;
source.Predecessor = null;
source.Distance = 0;
grayQueue.Enqueue(source);
while (!grayQueue.IsEmpty)
{
var startVertex = grayQueue.Dequeue();
foreach (var edge in GetVertexEdge(startVertex))
{
var endVertex = edge.End;
if (endVertex.Color == Color.White)
{
endVertex.Color = Color.Gray;
endVertex.Distance = startVertex.Distance + 1;
endVertex.Predecessor = startVertex;
grayQueue.Enqueue(endVertex);
}
}
startVertex.Color = Color.Black;
finalVisitAction(startVertex);
}
}
public bool Equals(AdjacencyVertex <T> other)
{
return(Key.Equals(other.Key));
}
private void Relabel(AdjacencyListGraph <T> graph, AdjacencyVertex <T> vertex)
{
}
public AdjacencyEdge(AdjacencyVertex <T> start, AdjacencyVertex <T> end)
{
Start = start;
End = end;
}
public FlowEdge(AdjacencyVertex <T> start, AdjacencyVertex <T> end, int capacity)
: base(start, end)
{
Capacity = capacity;
}
public AdjacencyEdge <T> CreateEdge(AdjacencyVertex <T> start, AdjacencyVertex <T> end)
{
return(new AdjacencyEdge <T>(start, end));
}
public bool IsVertexExist(AdjacencyVertex <T> vertex)
{
return(_adjacencyDictionary.ContainsKey(vertex.Identifier));
}