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;
}
}
/// <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 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;
}
}
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;
}
/// <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);
}
}
}
}
/// <summary>
/// MST
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="graph"></param>
/// <param name="weightFunc"></param>
/// <returns></returns>
public static IEnumerable <AdjacencyEdge <T> > GetMininumSpanningTreeKruskal <T>(
this AdjacencyListGraph <T> graph,
Func <AdjacencyEdge <T>, int> weightFunc
) where T : IEquatable <T>
{
var vertexs = graph.GetVertexs();
var edges = graph.GetEdges().ToList();
var sets = new Dictionary <AdjacencyVertex <T>, DisjointSet <AdjacencyVertex <T> > >();
var result = new List <AdjacencyEdge <T> >();
foreach (var vertex in vertexs)
{
sets[vertex] = (new DisjointSet <AdjacencyVertex <T> >(vertex));
}
foreach (var edge in edges)
{
edge.Weight = weightFunc(edge);
}
//吃自己写的狗粮,这狗粮不好吃啊
var sort = new QuickSort();
var sortEdges = sort.Sort(edges, (f, s) => f.Weight.CompareTo(s.Weight) > 0);
foreach (var sortEdge in sortEdges)
{
var startDisjointSet = sets[sortEdge.Start];
var endDisjointSet = sets[sortEdge.End];
DisjointSet <AdjacencyVertex <T> > newSet;
if (startDisjointSet.Find(startDisjointSet.GetNode(sortEdge.Start))
!= endDisjointSet.Find(endDisjointSet.GetNode(sortEdge.End)))
{
newSet = startDisjointSet.Union(endDisjointSet);
result.Add(sortEdge);
sets[sortEdge.Start] = newSet;
sets[sortEdge.End] = newSet;
}
}
return(result);
}
public int GenericPushRelabel(
AdjacencyListGraph <T> graph
, AdjacencyVertex <T> source
, AdjacencyVertex <T> target
)
{
var maxFolw = 0;
InitializePreflow(graph, source);
while (true)
{
}
return(maxFolw);
}
/// <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);
}
/// <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>
/// 获取连通图的算法是我有信心感觉我自己想的结构是对的，之后继续再验证。
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public static IEnumerable <DisjointSet <AdjacencyVertex <T> > > GetConnectedComponenets <T>
(
this AdjacencyListGraph <T> graph
) where T : IEquatable <T>
{
var vertexs = graph.GetVertexs();
var edges = graph.GetEdges();
var sets = new Dictionary <AdjacencyVertex <T>, DisjointSet <AdjacencyVertex <T> > >();
var result = new List <DisjointSet <AdjacencyVertex <T> > >();
foreach (var vertex in vertexs)
{
sets[vertex] = (new DisjointSet <AdjacencyVertex <T> >(vertex));
}
foreach (var edge in edges)
{
var startDisjointSet = sets[edge.Start];
var endDisjointSet = sets[edge.End];
DisjointSet <AdjacencyVertex <T> > newSet;
if (startDisjointSet.Find(startDisjointSet.GetNode(edge.Start))
!= endDisjointSet.Find(endDisjointSet.GetNode(edge.End)))
{
newSet = startDisjointSet.Union(endDisjointSet);
sets[edge.Start] = newSet;
sets[edge.End] = newSet;
if (!result.Contains(newSet))
{
result.Add(newSet);
}
}
}
return(result);
}
/// <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);
}
}
}
/// <summary>
/// 创建转置图
/// </summary>
/// <param name="copyAction">创建新结点复制属性</param>
/// <returns></returns>
public AdjacencyListGraph <T> CreateTransposeGraph(
Func <AdjacencyVertex <T>, AdjacencyVertex <T> > copyAction = null)
{
if (!HasDirection)
{
throw new InvalidOperationException("must hasdirection graph");
}
if (copyAction == null)
{
copyAction = (oldVertex) => new AdjacencyVertex <T>()
{
Key = oldVertex.Key, Identifier = oldVertex.Identifier
};
}
var graph = new AdjacencyListGraph <T>(true);
var vertexs = new Dictionary <int, AdjacencyVertex <T> >();
var edges = new List <AdjacencyEdge <T> >();
foreach (var item in _adjacencyDictionary.Values)
{
var newVertex = copyAction(item);
vertexs.Add(newVertex.Identifier, newVertex);
}
foreach (var item in _adjacencyDictionary.Values)
{
edges.AddRange(GetVertexEdge(item)
.Select
(o => new AdjacencyEdge <T>(vertexs[o.End.Identifier], vertexs[o.Start.Identifier]))
);
}
graph.CreatGraph(vertexs.Values, edges);
return(graph);
}
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;
}
//这个用改造通用版本有点勉强吧！应该没错
private IList <AdjacencyListGraph <T> > DepthFirstSearchStronglyConnected()
{
var stronglyConnectedGraphs = new List <AdjacencyListGraph <T> >();
foreach (var item in _adjacencyDictionary.Values)
{
item.Color = Color.White;
item.Predecessor = null;
}
_time = 0;
foreach (var item in _adjacencyDictionary.Values)
{
if (item.Color == Color.White)
{
var graph = new AdjacencyListGraph <T>(true);
DepthFirstSearchVisitStronglyConnected(item, graph);
stronglyConnectedGraphs.Add(graph);
}
}
return(stronglyConnectedGraphs);
}
private void Relabel(AdjacencyListGraph <T> graph, AdjacencyVertex <T> vertex)
{
}