/// <summary>
/// Отрисовка ориентированного графа с выделенным маршрутом
/// </summary>
/// <param name="graph">орг. граф</param>
/// <param name="path">маршрут</param>
/// <returns>битовое изображение</returns>
public static Bitmap Drawing(Digraph graph, Digraph.Path path)
{
if (graph == null || graph.CountVertex() == 0)
throw new Exception("Невозможно отрисовать граф. Граф пуст.");
if (path == null || !path.IsExists())
return Drawing(graph);
string script = "digraph G { nrankdir=LR node [style=\"filled\", fillcolor=\"skyblue\"]";
for (int i = 0; i < graph.CountVertex(); i++)
script += (i + 1) + " ";
for (int i = 0; i < graph.CountVertex(); i++)
for (int j = 0; j < graph.CountVertex(); j++)
if (!float.IsInfinity(graph[i, j]))
{
script += (i + 1) + " -> " + (j + 1) + " [label=\"" + graph[i, j] + "\"";
if (path.IsContain(new Digraph.Edge(i, j, graph[i, j])))
script += ", fontcolor=\"firebrick\", color=\"firebrick2\", penwidth=3, weight=1";
script += "] ";
}
script += "}";
return RenderingOnGraphviz(script);
}
/// <summary>
/// Создание пошагового метода ветвей и границ
/// </summary>
/// <param name="graph">орг. граф</param>
public BranchAndBound(Digraph graph)
{
// метод ветвей и границ для указанного графа
Graph = graph;
// переход в следующее состояние
next = IterationState.Start;
// создание пустого маршрута коммивояжера
TsPath = new Digraph.Path(Graph);
if (Graph.CountVertex() == 0)
{
// пустой маршрут
// окончание метода
next = IterationState.Stop;
}
else if (Graph.CountVertex() == 1)
{
// маршрут из одной вершины
TsPath.Append(new Digraph.Edge(0, 0, 0));
// окончание метода
next = IterationState.Stop;
}
else if (Graph.CountVertex() == 2)
{
// маршрут из двух вершин
TsPath.Append(new Digraph.Edge(0, 1, Graph[0, 1]));
TsPath.Append(new Digraph.Edge(1, 0, Graph[1, 0]));
// окончание метода
next = IterationState.Stop;
}
}
public static Digraph<char> Build(string s)
{
string[] edges = s.Split(',');
Digraph<char> ret = new Digraph<char>();
foreach (var e in edges)
{
var trimed_e = e.Trim();
ret.AddEdge(trimed_e[0], trimed_e[1], double.Parse(trimed_e.Substring(2)));
}
return ret;
}
/// <summary>
/// does the id[] array contain the strongly connected components?
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public bool Check(Digraph g)
{
var tc = new TransitiveClosure(g);
for (var v = 0; v < g.V; v++)
{
for (var w = 0; w < g.V; w++)
{
if (StronglyConnected(v, w) != (tc.Reachable(v, w) && tc.Reachable(w, v)))
return false;
}
}
return true;
}
// установка значений всех виджетов и полей значениями по-умолчанию
public void Default()
{
imageTsPath = imageGraph = null;
iterator = null;
tspImg.Source = null;
graph = new Digraph();
tsPath = new Digraph.Path(graph);
tspPathTxtBox.Text = "";
ExitTraceTsp();
traceTspBttn.IsEnabled = false;
}
public KosarajuCC(Digraph G)
{
mark = new bool[G.v()];
id = new int[G.v()];
DepthFirstOrder order = new DepthFirstOrder(G.reverse());
foreach (int s in order.getReversePost())
{
if (!mark[s])
{
dfs(G, s);
count++;
}
}
}
/**
* Returns a random simple digraph containing {@code V} vertices and {@code E} edges.
* @param V the number of vertices
* @param E the number of vertices
* @return a random simple digraph on {@code V} vertices, containing a total
* of {@code E} edges
* @throws IllegalArgumentException if no such simple digraph exists
*/
public static Digraph simple(int V, int E) {
if (E > (long) V*(V-1)) throw new IllegalArgumentException("Too many edges");
if (E < 0) throw new IllegalArgumentException("Too few edges");
Digraph G = new Digraph(V);
SET<Edge> set = new SET<Edge>();
while (G.E() < E) {
int v = StdRandom.uniform(V);
int w = StdRandom.uniform(V);
Edge e = new Edge(v, w);
if ((v != w) && !set.contains(e)) {
set.add(e);
G.addEdge(v, w);
}
}
return G;
}
/// <summary>
/// does the id[] array contain the strongly connected components?
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public bool Check(Digraph g)
{
var tc = new TransitiveClosure(g);
for (var v = 0; v < g.V; v++)
{
for (var w = 0; w < g.V; w++)
{
if (StronglyConnected(v, w) != (tc.Reachable(v, w) && tc.Reachable(w, v)))
{
return(false);
}
}
}
return(true);
}
public void Digraph_RemoveEdge()
{
var digraph = new Digraph();
digraph.AddVertex(0);
digraph.AddVertex(1);
digraph.AddVertex(2);
digraph.AddEdge(0, 1);
digraph.AddEdge(0, 2);
digraph.RemoveEdge(0, 1);
Assert.That(digraph.V, Is.EqualTo(3));
Assert.That(digraph.E, Is.EqualTo(1));
Assert.That(digraph.GetAdjList(0).Count(), Is.EqualTo(1));
}
private bool check(Digraph G)
{
TransitiveClosure tc = new TransitiveClosure(G);
for (int v = 0; v < G.V(); v++)
{
for (int w = 0; w < G.V(); w++)
{
if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v)))
{
return(false);
}
}
}
return(true);
}
/**
* Computes the strong components of the digraph {@code G}.
* @param G the digraph
*/
public GabowSCC(Digraph G) {
marked = new boolean[G.V()];
stack1 = new Stack<Integer>();
stack2 = new Stack<Integer>();
id = new int[G.V()];
preorder = new int[G.V()];
for (int v = 0; v < G.V(); v++)
id[v] = -1;
for (int v = 0; v < G.V(); v++) {
if (!marked[v]) dfs(G, v);
}
// check that id[] gives strong components
assert check(G);
}
private void DFS(Digraph g, int v)
{
marked[v] = true;
ListBag <int> list = g.Adj(v);
BagNode <int> node = list.first;
while (node != null)
{
if (!marked[node.t])
{
DFS(g, node.t);
}
node = node.next;
}
}
private int[] rank; // rank[v] = position of vertex v in topological order
public Topological(Digraph G)
{
DirectedCycle finder = new DirectedCycle(G);
if (!finder.hasCycle())
{
DepthFirstOrder dfs = new DepthFirstOrder(G);
order = dfs.reversePost();
rank = new int[G.V()];
int i = 0;
foreach (int v in order)
{
rank[v] = i++;
}
}
}
public Widget GetWidget(AssemblyDefinition assembly)
{
this.assembly = assembly;
Digraph digraph = GetDotData(assembly);
image = new Image(DotHelper.BuildDotImage(digraph));
AddinScrolledWindow sw = new AddinScrolledWindow();
sw.AddWithViewport(image);
sw.ShowAll();
sw.OnRefresh += delegate {
Refresh();
};
return(sw);
}
public CircleNodeScene()
{
this.mGraph = new Digraph <CircleNode, ArrowEdge>();
this.mLayoutTimer = new Timer();
this.mLayoutTimer.Interval = 1000 / 25;
this.mLayoutTimer.Tick += new EventHandler(OnLayoutTimerTick);
this.mLayout = null;
this.mMouseUpHistory = new int[3];
for (int i = 0; i < this.mMouseUpHistory.Length; i++)
{
this.mMouseUpHistory[i] = -1;
}
}
public void UpdateEdges()
{
Digraph <StateNode, StateEdge> .GEdge edge;
Digraph <StateNode, StateEdge> graph = this.mScene.StateGraph;
int index = graph.IndexOfNode(this);
for (int i = graph.EdgeCount - 1; i >= 0; i--)
{
edge = graph.InternalEdgeAt(i);
if (edge.SrcNode.Index == index ||
edge.DstNode.Index == index)
{
edge.Data.Update();
}
}
}
/**
* Initializes a new digraph that is a deep copy of the specified digraph.
*
* @param G the digraph to copy
*/
public Digraph(Digraph G) {
this(G.V());
this.E = G.E();
for (int v = 0; v < V; v++)
this.indegree[v] = G.indegree(v);
for (int v = 0; v < G.V(); v++) {
// reverse so that adjacency list is in same order as original
Stack<Integer> reverse = new Stack<Integer>();
for (int w : G.adj[v]) {
reverse.push(w);
}
for (int w : reverse) {
adj[v].add(w);
}
}
}
private void Dfs(Digraph G, int vertex)
{
_marked.Add(vertex);
foreach (var neighborVertex in G.GetNeighbors(vertex))
{
if (_marked.Contains(neighborVertex))
{
continue;
}
Dfs(G, neighborVertex);
}
_reversePost.Push(vertex);
}
public KosarajuSCC(Digraph G)
: base(G)
{
_marked = new bool[G.V()];
_id = new int[G.V()];
DepthFirstOrder order = new DepthFirstOrder(G.Reverse());
foreach (var v in order.ReversePost())
{
if (!_marked[v])
{
Dfs(G, v);
_count++;
}
}
}
/// <summary>
/// Checks desktop
/// </summary>
/// <param name="desktop"></param>
static public void Check(this IDesktop desktop)
{
IDesktop d = desktop.Root;
CheckObject ch = new CheckObject(checkLink);
List <IObjectLabel> objects;
List <IArrowLabel> arrows;
PureDesktopPeer.GetFullList(d, out objects, out arrows);
Digraph graph = PureDesktop.CreateDigraph(objects, arrows, null, ch);
List <DigraphLoop> loops = graph.Loops;
foreach (DigraphLoop loop in loops)
{
Check(loop);
}
}
public KosarajuSCC(Digraph digraph)
{
marked = new bool[digraph.Vertices];
id = new int[digraph.Vertices];
var order = new DepthFirstOrder(digraph.Reverse());
foreach (var s in order.ReversePost())
{
if (!marked[s])
{
Dfs(digraph, s);
count++;
}
}
}
private bool check(Digraph digraph)
{
TransitiveClosure transitiveClosure = new TransitiveClosure(digraph);
for (int i = 0; i < digraph.V(); i++)
{
for (int j = 0; j < digraph.V(); j++)
{
if (this.stronglyConnected(i, j) != ((!transitiveClosure.reachable(i, j) || !transitiveClosure.reachable(j, i)) ? false : true))
{
return(false);
}
}
}
return(true);
}
static string Add_Edge_ThrowsExceptionWhenEitherVertexNotInGraph()
{
var expectedMessage1 = "Vertex Id 1 is not an element within V";
var expectedMessage2 = "Vertex Id 2 is not an element within V";
// Arrange preconditions
var graph = new Digraph<int, int, int>();
var vertex1 = new Vertex<int, int>(1);
var vertex2 = new Vertex<int, int>(2);
// Act
bool result;
try
{
graph.AddEdge(vertex1, vertex2, 1);
return Fail;
}
catch (Exception ex)
{
result = expectedMessage1 == ex.Message;
}
try
{
var graphPrime = graph.AddVertex(vertex2, vertex2.Identifier);
graphPrime.AddEdge(vertex1, vertex2, 1);
return Fail;
}
catch (Exception ex)
{
result = expectedMessage1 == ex.Message;
}
try
{
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
graphPrime.AddEdge(vertex1, vertex2, 1);
return Fail;
}
catch (Exception ex)
{
result = expectedMessage2 == ex.Message;
}
return result ? Pass : Fail;
}
private Digraph graph; // the underlying digraph
public SymbolDigraph(TextAsset txt, char sparator) //jobs.txt
{
st = new ST <string, int>();
// First pass builds the index by reading strings to associate
// distinct strings with an index
string[] lines = txt.text.Split(new char[1] {
'\n'
}, StringSplitOptions.RemoveEmptyEntries);
for (int i = 0; i < lines.Length; i++)
{
string[] lineStrs = lines[i].Split(new char[1] {
sparator
}, StringSplitOptions.RemoveEmptyEntries);
foreach (string str in lineStrs)
{
if (!st.contains(str))
{
st.put(str, st.size());
}
}
}
keys = new string[st.size()];
foreach (string name in st.keys())
{
keys[st.GetValue(name)] = name;
}
// second pass builds the digraph by connecting first vertex on each
// line to all others
graph = new Digraph(st.size());
foreach (string line in lines)
{
string[] lineStrs = line.Split(new char[1] {
sparator
}, StringSplitOptions.RemoveEmptyEntries);
int v = st.GetValue(lineStrs[0]);
for (int i = 1; i < lineStrs.Length; i++)
{
int w = st.GetValue(lineStrs[i]);
graph.AddEdge(v, w);
}
}
}
/**
* Unit tests the {@code DirectedEulerianCycle} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
int V = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
// Eulerian cycle
Digraph G1 = DigraphGenerator.eulerianCycle(V, E);
unitTest(G1, "Eulerian cycle");
// Eulerian path
Digraph G2 = DigraphGenerator.eulerianPath(V, E);
unitTest(G2, "Eulerian path");
// empty digraph
Digraph G3 = new Digraph(V);
unitTest(G3, "empty digraph");
// self loop
Digraph G4 = new Digraph(V);
int v4 = StdRandom.uniform(V);
G4.addEdge(v4, v4);
unitTest(G4, "single self loop");
// union of two disjoint cycles
Digraph H1 = DigraphGenerator.eulerianCycle(V/2, E/2);
Digraph H2 = DigraphGenerator.eulerianCycle(V - V/2, E - E/2);
int[] perm = new int[V];
for (int i = 0; i < V; i++)
perm[i] = i;
StdRandom.shuffle(perm);
Digraph G5 = new Digraph(V);
for (int v = 0; v < H1.V(); v++)
for (int w : H1.adj(v))
G5.addEdge(perm[v], perm[w]);
for (int v = 0; v < H2.V(); v++)
for (int w : H2.adj(v))
G5.addEdge(perm[V/2 + v], perm[V/2 + w]);
unitTest(G5, "Union of two disjoint cycles");
// random digraph
Digraph G6 = DigraphGenerator.simple(V, E);
unitTest(G6, "simple digraph");
// 4-vertex digraph
Digraph G7 = new Digraph(new In("eulerianD.txt"));
unitTest(G7, "4-vertex Eulerian digraph");
}
// BFS from single source
private void bfs(Digraph G, int s) {
Queue<Integer> q = new Queue<Integer>();
marked[s] = true;
distTo[s] = 0;
q.enqueue(s);
while (!q.isEmpty()) {
int v = q.dequeue();
for (int w : G.adj(v)) {
if (!marked[w]) {
edgeTo[w] = v;
distTo[w] = distTo[v] + 1;
marked[w] = true;
q.enqueue(w);
}
}
}
}
private int count; // number of strongly-connected components
public KosarajuSharirSCC(Digraph G)
{
// compute reverse postorder of reverse graph
DepthFirstOrder dfs = new DepthFirstOrder(G.Reverse());
// run DFS on G, using reverse postorder to guide calculation
marked = new bool[G.V()];
id = new int[G.V()];
foreach (int v in dfs.reversePost())
{
if (!marked[v])
{
DFS(G, v);
count++;
}
}
}
private Digraph <ParsingResults> ConstructGraph(IEnumerable <ParsingResults> to_do)
{
Digraph <ParsingResults> g = new Digraph <ParsingResults>();
HashSet <ParsingResults> done = new HashSet <ParsingResults>();
Stack <ParsingResults> stack = new Stack <ParsingResults>();
foreach (ParsingResults f in to_do)
{
stack.Push(f);
}
while (stack.Count > 0)
{
ParsingResults f = stack.Pop();
var workspace = f.Item.Workspace;
g.AddVertex(f);
done.Add(f);
foreach (string d in f.PropagateChangesTo)
{
Document d_doc = workspace.FindDocument(d);
ParsingResults d_pd = ParsingResultsFactory.Create(d_doc);
if (done.Contains(d_pd))
{
continue;
}
stack.Push(d_pd);
}
}
foreach (ParsingResults v in g.Vertices)
{
HashSet <string> deps = v.PropagateChangesTo;
var workspace = v.Item.Workspace;
Document doc = workspace.FindDocument(v.FullFileName);
ParsingResults pd = ParsingResultsFactory.Create(doc);
foreach (string d in deps)
{
Document d_doc = workspace.FindDocument(d);
ParsingResults d_pd = ParsingResultsFactory.Create(d_doc);
g.AddEdge(new DirectedEdge <ParsingResults>(pd, d_pd));
}
}
return(g);
}
private readonly int height; //Drawing surface height (maximum height)
/// <summary>
/// Initializes a new instance of TriangularLatticeForm
/// </summary>
/// <param name="width">Drawing surface width (maximum width)</param>
/// <param name="height">Drawing surface height (maximum height)</param>
/// <exception cref="ArgumentOutOfRangeException"/>
public TriangularLatticeForm(int width, int height)
{
if (width <= 0)
{
throw new ArgumentOutOfRangeException(nameof(width));
}
if (height <= 0)
{
throw new ArgumentOutOfRangeException(nameof(height));
}
InitializeComponent();
TriangularLatticeDigraph = null;
this.width = width;
this.height = height;
}
private Stack<Integer> path = null; // Eulerian path; null if no suh path
/**
* Computes an Eulerian path in the specified digraph, if one exists.
*
* @param G the digraph
*/
public DirectedEulerianPath(Digraph G) {
// find vertex from which to start potential Eulerian path:
// a vertex v with outdegree(v) > indegree(v) if it exits;
// otherwise a vertex with outdegree(v) > 0
int deficit = 0;
int s = nonIsolatedVertex(G);
for (int v = 0; v < G.V(); v++) {
if (G.outdegree(v) > G.indegree(v)) {
deficit += (G.outdegree(v) - G.indegree(v));
s = v;
}
}
// digraph can't have an Eulerian path
// (this condition is needed)
if (deficit > 1) return;
// special case for digraph with zero edges (has a degenerate Eulerian path)
if (s == -1) s = 0;
// create local view of adjacency lists, to iterate one vertex at a time
Iterator<Integer>[] adj = (Iterator<Integer>[]) new Iterator[G.V()];
for (int v = 0; v < G.V(); v++)
adj[v] = G.adj(v).iterator();
// greedily add to cycle, depth-first search style
Stack<Integer> stack = new Stack<Integer>();
stack.push(s);
path = new Stack<Integer>();
while (!stack.isEmpty()) {
int v = stack.pop();
while (adj[v].hasNext()) {
stack.push(v);
v = adj[v].next();
}
// push vertex with no more available edges to path
path.push(v);
}
// check if all edges have been used
if (path.size() != G.E() + 1)
path = null;
assert check(G);
}
private readonly int height; //Drawing surface height (maximum height)
/// <summary>
/// Initializes a new instance of RandomDigraphGeneratorForm
/// </summary>
/// <param name="width">Drawing surface width (maximum width)</param>
/// <param name="height">Drawing surface height (maximum height)</param>
/// <exception cref="ArgumentOutOfRangeException"/>
public RandomDigraphGeneratorForm(int width, int height)
{
if (width <= 0)
{
throw new ArgumentOutOfRangeException(nameof(width));
}
if (height <= 0)
{
throw new ArgumentOutOfRangeException(nameof(height));
}
InitializeComponent();
Digraph = null;
this.width = width;
this.height = height;
}
public override bool Execute()
{
int i, j;
DGEdge edge;
List <DGEdge> edges;
Digraph <DGNode, DGEdge> dg
= this.mNode.mState.DecisionGraph;
StateNode fState = this.mNode.mScene.FocusedState;
if (fState != null && fState.Equals(this.mNode.mState))
{
for (i = this.mSelectedEdges.Count - 1; i >= 0; i--)
{
edge = this.mSelectedEdges[i];
this.mNode.mScene.SelectDGEdge(edge, false);
}
}
for (i = this.mAPs.Length - 1; i >= 0; i--)
{
edges = this.mAPs[i].Edges;
for (j = edges.Count - 1; j >= 0; j--)
{
edge = edges[j];
dg.RemoveEdge(edge.SrcNode, edge.DstNode);
edge.SetParent(null);
}
}
foreach (IEdgeAction action in this.mActions)
{
action.Redo();
}
this.mNode.mState.AddRootDGEdges();
this.mSliceList.Clear();
Array.Clear(this.mNode.mSliceAnchors, 0,
this.mNode.mSliceCount);
this.mNode.mSliceCount = 0;
for (i = this.mAPs.Length - 1; i >= 0; i--)
{
this.mAPs[i].SetParent(null);
}
this.mNode.UpdateVisualization();
return(true);
}
public override void Undo()
{
int i, j;
DGEdge edge;
List <DGEdge> edges;
Digraph <DGNode, DGEdge> dg
= this.mNode.mState.DecisionGraph;
this.mSliceList.AddRange(this.mSlices);
Array.Copy(this.mAPs, 0, this.mNode.mSliceAnchors, 0,
this.mAPs.Length);
this.mNode.mSliceCount = this.mAPs.Length;
for (i = this.mAPs.Length - 1; i >= 0; i--)
{
this.mAPs[i].SetParent(this.mNode);
}
this.mNode.UpdateVisualization();
foreach (IEdgeAction action in this.mActions)
{
action.Undo();
}
for (i = this.mAPs.Length - 1; i >= 0; i--)
{
edges = this.mAPs[i].Edges;
for (j = edges.Count - 1; j >= 0; j--)
{
edge = edges[j];
edge.SetParent(this.mNode.mState);
dg.AddEdge(edge);
}
}
this.mNode.mState.RemoveRootDGEdges();
StateNode fState = this.mNode.mScene.FocusedState;
if (fState != null && fState.Equals(this.mNode.mState))
{
for (i = this.mSelectedEdges.Count - 1; i >= 0; i--)
{
edge = this.mSelectedEdges[i];
this.mNode.mScene.SelectDGEdge(edge, false);
}
}
}
public void TestDigraph_AddEdge_FailsWithMissingNodes()
{
var g = new Digraph <int, Edge <int> >();
var sourceInside = 1;
var targetInside = 2;
g.AddNode(sourceInside);
g.AddNode(targetInside);
var sourceOutside = 3;
var targetOutside = 4;
foreach (var source in new[] { sourceInside, sourceOutside })
{
foreach (var target in new[] { targetInside, targetOutside })
{
var signature = "source=" + source + "; target=" + target;
var edge = new Edge <int>(source, target);
Assert.IsNotNull(edge);
var isValid = (source < 3) && (target < 3); // The edge is valid, if both nodes are in the graph.
try
{
Assert.AreEqual(isValid,
g.AddEdge(edge),
"Should be able to add edge only if edge is valid. @signature=" + signature);
if (!isValid)
{
Assert.Fail("Expect an exception if edge is invalid. @signature=" + signature);
}
}
catch (KeyNotFoundException)
{
Assert.IsTrue(!isValid,
"Expect this exception only if edge is invalid. @signature=" + signature);
}
catch (Exception ex)
{
Assert.Fail("Unexpected type '" + ex.GetType().ToString() + "' of exception. @signature=" + signature);
}
}
}
}
protected override void OnFinishNode(
Digraph <Node, Edge> .GNode n, uint depth)
{
int index = n.Index;
if (this.mDatas[index].LowLink == this.mDatas[index].Depth)
{
/*this.mRoots.Add(n.Data);
* int count = 0;
* Node[] comp = new Node[this.mStackCount];
* int i = -1;
* while (i != index)
* {
* i = this.mStack[--this.mStackCount];//this.mStack.Pop();
* comp[count++] = this.mDatas[i].Data;
* }
* Node[] newComp = new Node[count];
* Array.Copy(comp, 0, newComp, 0, count);
* this.mComponents.Add(newComp);/* */
if (this.mCompCount == this.mRoots.Length)
{
Digraph <Node, Edge> .GNode[] roots;
if (this.mCompCount == 0)
{
roots = new Digraph <Node, Edge> .GNode[4];
}
else
{
roots = new Digraph <Node, Edge> .GNode[2 * this.mCompCount];
Array.Copy(this.mRoots, 0, roots, 0, this.mCompCount);
}
this.mRoots = roots;
}
this.mRoots[this.mCompCount] = n;
int i = -1;
while (i != index)
{
i = this.mStack[--this.mStackCount];
this.mCompIds[i] = this.mCompCount;
}
this.mCompCount++;
}
}
/**/
public static void main(string[] strarr)
{
string str = strarr[0];
string str2 = strarr[1];
SymbolDigraph symbolDigraph = new SymbolDigraph(str, str2);
Digraph digraph = symbolDigraph.G();
while (!StdIn.IsEmpty)
{
string str3 = StdIn.readLine();
Iterator iterator = digraph.adj(symbolDigraph.index(str3)).iterator();
while (iterator.hasNext())
{
int i = ((Integer)iterator.next()).intValue();
StdOut.println(new StringBuilder().append(" ").append(symbolDigraph.name(i)).toString());
}
}
}
static string Add_Edge_InsertsEdgeFromV1ToV2AndReturnsGPrime()
{
// Arrange preconditions
var graph = new Digraph<int, int, int>();
var vertex1 = new Vertex<int, int>(1);
var vertex2 = new Vertex<int, int>(2);
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
var graphDoublePrime = graphPrime.AddVertex(vertex2, vertex2.Identifier);
var edgeLabel = 1;
// Act
var graphTriplePrime = graphDoublePrime.AddEdge(vertex1, vertex2, edgeLabel);
// Assert postconditions
if (graphTriplePrime == graphDoublePrime) return Fail;
if (!graphTriplePrime.FromEdges(vertex1).Any()) return Fail;
if (graphTriplePrime.FromEdges(vertex2).Any()) return Fail;
return graphTriplePrime.GetEdge(vertex1, vertex2) == edgeLabel ? Pass : Fail;
}
/// <summary>
/// Отрисовка ориентированного графа
/// </summary>
/// <param name="graph">орг. граф</param>
/// <returns>битовое изображение</returns>
public static Bitmap Drawing(Digraph graph)
{
if (graph == null || graph.CountVertex() == 0)
throw new Exception("Невозможно отрисовать граф. Граф не задан.");
string script = "digraph G { nrankdir=LR node [style=\"filled\", fillcolor=\"skyblue\"]";
for (int i = 0; i < graph.CountVertex(); i++)
script += (i + 1) + " ";
for (int i = 0; i < graph.CountVertex(); i++)
for (int j = 0; j < graph.CountVertex(); j++)
if (!float.IsInfinity(graph[i, j]))
script += (i + 1) + " -> " + (j + 1) + " [label=\"" + graph[i, j] + "\"] ";
script += "}";
return RenderingOnGraphviz(script);
}
private readonly bool[] _marked; // marked[v] = has vertex v been visited?
#endregion Fields
#region Constructors
/// <summary>
/// Computes the strong components of the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
public KosarajuSharirSCC(Digraph g)
{
// compute reverse postorder of reverse graph
var dfs = new DepthFirstOrder(g.Reverse());
// run DFS on G, using reverse postorder to guide calculation
_marked = new bool[g.V];
_id = new int[g.V];
foreach (int v in dfs.ReversePost())
{
if (!_marked[v])
{
Dfs(g, v);
_count++;
}
}
// check that id[] gives strong components
//assert check(G);
}
/// <summary>
/// DFS on graph G
/// </summary>
/// <param name="g"></param>
/// <param name="v"></param>
private void Dfs(Digraph g, int v)
{
_marked[v] = true;
_id[v] = _count;
foreach (int w in g.Adj(v))
{
if (!_marked[w]) Dfs(g, w);
}
}
static string Update_Vertex_ThowsExceptionWhenVertexIsNotInGraph()
{
var expectedMessage = "Vertex Id Id1 is not an element within V";
// Arrange preconditions
var graph = new Digraph<string, string, string>();
var vertex = new Vertex<string, string>("Id1");
var label = "Label1";
// Act
bool result;
try
{
graph.UpdateVertex(vertex, label);
return Fail;
}
catch (Exception ex)
{
result = expectedMessage == ex.Message;
}
return result ? Pass : Fail;
}
static string Add_Vertex_InsertsVertexWithLabelAndReturnsGPrime()
{
var expectedLabel = "Foo";
// Arrange Preconditions
var graph = new Digraph<decimal, string, int>();
var vertex = new Vertex<decimal, string>(1000m);
// Act
var graphPrime = graph.AddVertex(vertex, expectedLabel);
// Assert Postconditions
if (graphPrime == graph) return Fail;
if (graphPrime.IsEmpty) return Fail;
if (!graph.IsEmpty) return Fail;
if (!graphPrime.HasVertex(vertex)) return Fail;
return graphPrime.GetVertex(vertex).Equals(expectedLabel) ? Pass:Fail;
}
/// <summary>
/// Исключение подмаршрутов в графе
/// </summary>
/// <param name="matrix">редуцированная матрица</param>
/// <param name="dsu">непересекающиеся множества вершин</param>
/// <param name="edges">ребро ветвления, которое уже находяться в маршруте или не входит в него</param>
private static void ExcludeSubRoute(ReductionMatrix matrix, Dsu dsu, Digraph.Edge edge)
{
// если ребро не входит в ветвление
if (edge.Begin < 0 || edge.End < 0)
// исключение данного ребра из матрицы
matrix[Math.Abs(edge.Begin), Math.Abs(edge.End)] = float.PositiveInfinity;
// ребро входит в ветвление
else
{
// исключение строки и столбца из матрицы, соответсвующие началу и концу ребра
matrix.DeleteRowColumn(edge.Begin, edge.End);
// исключение оставщихся подмаршрутов
for (int i = 0; i < matrix.Size; i++)
for (int j = 0; j < matrix.Size; j++)
if (dsu.Find(edge.Begin) == dsu.Find(i) && dsu.Find(edge.End) == dsu.Find(j))
matrix[j, i] = float.PositiveInfinity;
// объединение двух вершин графа в одно множество
dsu.Union(edge.Begin, edge.End);
}
}
private EquationDecomposition(EquationSystem eqsys)
{
/** This algorithm decomposes a given equation system into smaller equation blocks
* which can be solved subsequently. The algorithm is sometimes referred to as
* Tarjan's sorting or Dulmage-Mendelson decomposition.
*
* The algorithm consists of several steps. The description below will use the
* following notions:
* Var: The set of variables of the whole equation system
* Eqn: The set of equations of the whole equation system
* Var u Eqn: The set unification of Var and Eqn
*
* Step (1): Maximum matching
* Define an undirected graph G = (V, E) with V = Var u Eqn.
* Whenever an equation eqn \in Eqn references a variable var \in Var
* add the edge (eqn, var) to E.
* Compute a maximum matching M between variables and equations.
* M will now contain a set of equation/variable pairs.
*
* Step (2): Finding strongly connected components
* Define a directed graph Gd = (V, Ed) with V = Var u Eqn.
* Whenever an equation eqn \in Eqn references a variable var \in Var
* add the edge (eqn, var) to Ed.
* For each equation/variable pair (eqn, var) in M add furthermore
* the edge (var, eqn) to Ed.
* Note: Matched equation/variable pairs will result in bi-directional edges in Ed.
* Compute the strongly connected components SCC of Gd.
* SCC is a set of subsets of V such that each subset represents one component.
*
* Step (3): Building the tree of equation blocks
* Defined a directed graph Dt = (SCC, Et).
* For each equation eqn \in Eqn which is assigned to component c1 and
* references a variable var \in Var which is assigned to component c2
* add an edge (c1, c2) to Et of c1 and c2 are different.
*
* The resulting graph will have a tree/forest sutrcture. Each node
* represents an equation block. An edge b1 -> b2 represents a dependency in the
* that b2 must be solved prior to b1. A schedule can be found by topological
* sorting the tree.
* */
if (eqsys == null ||
eqsys.Equations == null ||
eqsys.Variables == null)
throw new ArgumentException("null reference in equation system argument");
if (eqsys.Equations.Count != eqsys.Variables.Count)
throw new ArgumentException("equation system is not well-constrained!");
/** Assign each equation and each variable an index which will be a unique node
* ID within the graphs. Indices are assigned as follows:
* - Equations get indices from 0...count(equations)-1
* - Variables get indices from count(equations)...count(equations)+count(variables)
* Note: Assuming a well-constrained equation system, count(equations) = count(variables)
**/
int curidx = 0;
foreach (Expression eq in eqsys.Equations)
{
eq.Cookie = curidx++;
}
Dictionary<object, int> idx = new Dictionary<object, int>();
foreach (Variable v in eqsys.Variables)
{
idx[v] = curidx++;
}
// Steps 1 and 2: Construct G and Gd
Graph g = new Graph(curidx);
Digraph dg = new Digraph(curidx);
for (int i = 0; i < eqsys.Equations.Count; i++)
{
Expression eq = eqsys.Equations[i];
LiteralReference[] lrs = eq.ExtractLiteralReferences();
foreach (LiteralReference lr in lrs)
{
int j;
if (idx.TryGetValue(lr.ReferencedObject, out j))
{
g.AddEdge(i, j);
dg.AddEdge(i, j);
}
}
}
// Step 1: Maximum matching
GraphAlgorithms.Matching m = g.GetMaximumMatching();
bool success = m.IsMaximumCardinality;
for (int i = 0; i < eqsys.Equations.Count; i++)
{
int k = m[i];
if (k >= 0)
dg.AddEdge(k, i);
}
// Step 2: Strongly connected components
StrongComponents sc = dg.GetStrongComponents();
int numc = sc.NumComponents;
EquationBlock[] blocks = new EquationBlock[numc];
for (int i = 0; i < numc; i++)
{
blocks[i] = new EquationBlock();
}
// Step 3: Construct the tree
Digraph dg2 = new Digraph(numc);
for (int i = 0; i < eqsys.Equations.Count; i++)
{
int c = sc[i];
blocks[c].EqSys.Equations.Add(eqsys.Equations[i]);
int vi = m[i];
Variable v = eqsys.Variables[vi - eqsys.Equations.Count];
blocks[c].EqSys.Variables.Add(v);
List<int> outset = dg.GetOutSet(i);
foreach (int ovi in outset)
{
int oc = sc[ovi];
if (c != oc)
dg2.AddEdge(c, oc);
}
}
List<int> rootSet = new List<int>();
List<int> sinkSet = new List<int>();
for (int c = 0; c < numc; c++)
{
if (dg2.GetOutDegree(c) == 0)
rootSet.Add(c);
if (dg2.GetInDegree(c) == 0)
sinkSet.Add(c);
List<int> outset = dg2.GetOutSet(c);
foreach (int oc in outset)
blocks[c].Predecessors.Add(blocks[oc]);
List<int> inset = dg2.GetInSet(c);
foreach (int ic in inset)
blocks[c].Successors.Add(blocks[ic]);
}
RootSet = (from int c in rootSet
select blocks[c]).ToArray();
SinkSet = (from int c in sinkSet
select blocks[c]).ToArray();
AllBlocks = blocks;
}
private readonly DirectedDFS[] _tc; // tc[v] = reachable from v
#endregion Fields
#region Constructors
/// <summary>
/// Computes the transitive closure of the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
public TransitiveClosure(Digraph g)
{
_tc = new DirectedDFS[g.V];
for (var v = 0; v < g.V; v++)
_tc[v] = new DirectedDFS(g, v);
}
/// <summary>
/// Создание матрицы на основе матрциы смежности
/// </summary>
/// <param name="matrix">матрца смежности</param>
public ReductionMatrix(Digraph.AdjacencyMatrix matrix)
: base(matrix)
{
RealSize = Size;
}
public void Init()
{
g = DigraphBuilder.Build(g_s);
srn = new SimpleRouteNavigator<char>(g);
finder = new BellmanFordShotestPathFinder<char>(g);
}
public void Method()
{
Digraph<HV, HE>.Arc arc = new Digraph<HV, HE>.Arc(start, succ.First, succ.Second);
}
/// <summary>
/// Создания ветвления
/// </summary>
/// <param name="lowerBound">нижняя граница ветвления</param>
/// <param name="branchingEdge">ребро ветвления</param>
public Branch(float lowerBound, Digraph.Edge branchingEdge)
{
LowerBound = lowerBound;
BranchingEdge = branchingEdge;
}
/// <summary>
/// Нахождение маршрута коммивояжера
/// </summary>
/// <param name="graph">ограф. граф</param>
/// <returns>маршрут коммивояжера</returns>
public static Digraph.Path Tsp(Digraph graph)
{
// маршрут коммивояжера
var TsPath = new Digraph.Path(graph);
// если граф пуст
if (graph.CountVertex() == 0)
{
// пустой маршрут
return TsPath;
}
// если граф имеет одну вершину
else if (graph.CountVertex() == 1)
{
TsPath.Append(new Digraph.Edge(0, 0, 0));
// маршрут для одной вершины
return TsPath;
}
// если граф имеет две вершины
else if (graph.CountVertex() == 2)
{
TsPath.Append(new Digraph.Edge(0, 1, graph[0, 1]));
TsPath.Append(new Digraph.Edge(1, 0, graph[1, 0]));
// маршрут для двух вершин
return TsPath;
}
/// Создания неперекающихся множеств вершин в графе,
/// для определения и исключения подмаршрутов графа
var dsu = new Dsu(graph.CountVertex());
// минимальное ветвление
var minBranch = new Branch(float.PositiveInfinity, null);
/// Получение исходной матрицы смежности данного графа
var matrix = new ReductionMatrix(graph.Adjacency);
/// Создание корня и дерева ветвления
var parentBranch = new Branch(matrix.Reduce(), null);
var tree = new TreeBranch(graph, parentBranch);
for (; ; )
{
// ребра с нулевой стоимостью
var zeroEdges = new List<Digraph.Edge>();
// Получение всех ребер и соответсвующих штрафов
for (int i = 0; i < matrix.Size; i++)
for (int j = 0; j < matrix.Size; j++)
if (matrix[i, j] == 0)
zeroEdges.Add(new Digraph.Edge(i, j, matrix.MinInRow(i, j) + matrix.MinInColumn(j, i)));
// если нет ребер ветвления - нет маршрута коммивояжера
if (zeroEdges.Count == 0)
return new Digraph.Path(graph);
/// Определение ребра ветвления - ребра с максимальным штрафом
var branchingEdge = zeroEdges.OrderByDescending(e => e.Cost).ToList().First();
/// Процесс ветления - не включая данное ребро
var leftBranch = new Branch(parentBranch.LowerBound + branchingEdge.Cost,
new Digraph.Edge(-branchingEdge.Begin, -branchingEdge.End, float.PositiveInfinity));
// добавление ветвления в дерево
tree.Add(parentBranch, Branch.Direction.Left, leftBranch);
/// Процесс ветления - включая данное ребро
ExcludeSubRoute(matrix, dsu, branchingEdge);
var rightBranch = new Branch(parentBranch.LowerBound + matrix.Reduce(),
new Digraph.Edge(branchingEdge.Begin, branchingEdge.End, graph[branchingEdge.Begin, branchingEdge.End]));
// добавление ветвления в дерево
tree.Add(parentBranch, Branch.Direction.Right, rightBranch);
/// Проверка на достаточность размера матрцицы
if (matrix.RealSize == 2)
{
// новый родитель
parentBranch = rightBranch;
/// Добавление оставщихся ребер в дерево ветвлений
for (int i = 0; i < matrix.Size; i++)
for (int j = 0; j < matrix.Size; j++)
if (matrix[i, j] == 0)
{
// новый потомок
rightBranch = new Branch(parentBranch.LowerBound, new Digraph.Edge(i, j, graph[i, j]));
tree.Add(parentBranch, Branch.Direction.Right, rightBranch);
// потомок теперь родитель
parentBranch = rightBranch;
}
/// Определение нового минимального ветвления
if (parentBranch.LowerBound < minBranch.LowerBound)
minBranch = parentBranch;
}
/// Выбор новой родительской вершины из еще не подвергшихся ветвлению
parentBranch = tree.GetNotGoBranches().OrderBy(b => b.LowerBound).ToList().First();
/// Проверка на нахождения минимального ветвления и остановки
if (minBranch.LowerBound <= parentBranch.LowerBound)
break;
/// Корректировка матрицы для данного ветвления и редуцирование
if (parentBranch != rightBranch)
{
// новые непересекающиеся множества вершин
dsu = new Dsu(graph.CountVertex());
// исходная редуцированная матрица
matrix = new ReductionMatrix(graph.Adjacency);
// получение текущих вершин для данного ветвления
var currentPath = tree.GetEdgesBranching(parentBranch);
// исключение всех подмаршрутов
foreach (var e in currentPath)
ExcludeSubRoute(matrix, dsu, e);
// редуцирование матрицы
matrix.Reduce();
}
}
// формирование маршрута коммивояжера
TsPath = tree.CreatePathFromBranch(minBranch);
return TsPath;
}
static string Update_Edge_ThrowsExceptionWhenEdgeNotInGraph()
{
var expectedMessage = "Edge from vertex 1 to 2 is not an element within E";
// Arrange preconditions
var graph = new Digraph<int, int, int>();
var vertex1 = new Vertex<int, int>(1);
var vertex2 = new Vertex<int, int>(2);
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
var graphDoublePrime = graphPrime.AddVertex(vertex2, vertex2.Identifier);
// Act
bool result;
try
{
graphDoublePrime.UpdateEdge(vertex1, vertex2, 5);
return Fail;
}
catch (Exception ex)
{
result = expectedMessage == ex.Message;
}
return result ? Pass : Fail;
}
static void OutputGraphStringRepresentation()
{
var graph = new Digraph<int, int, int>();
var vertex1 = new Vertex<int, int>(1);
var vertex2 = new Vertex<int, int>(2);
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
var graphDoublePrime = graphPrime.AddVertex(vertex2, vertex2.Identifier);
var edgeLabel = 1;
var graphTriplePrime = graphDoublePrime.AddEdge(vertex1, vertex2, edgeLabel);
var vertex3 = new Vertex<int, int>(3);
var graphQuadruplePrime = graphTriplePrime.AddVertex(vertex3, vertex3.Identifier);
var graphQuintuplePrime = graphQuadruplePrime.AddEdge(vertex1, vertex3, edgeLabel + 1);
var graphSextuplePrime = graphQuintuplePrime.AddEdge(vertex3, vertex2, edgeLabel + 2);
Console.WriteLine(graphSextuplePrime.ToString());
}
/// <summary>
/// Создание дерева ветвления
/// </summary>
/// <param name="graph">орг. граф для которого строится дерево ветвлений</param>
/// <param name="root">корень дерева</param>
public TreeBranch(Digraph graph, Branch root)
{
Graph = graph;
Root = root;
}
private List<byte[]> GetPredecessorModelPositions(
Bitmap image, int tileSize, Digraph<TileGenerationRecord>.Vertex v, byte[] partialPos,
int nLeft, int nSkip, bool suppressSubpaths, bool suppressUngenerated)
{
List<byte[]> positions = new List<byte[]>();
if (nSkip != 0)
{
// skip this node and go to its predecessors
if (v.Predecessors.Length == 0)
{
positions.Add(partialPos);
}
foreach (Digraph<TileGenerationRecord>.Vertex pred in v.Predecessors)
{
if (pred.Label.IsGenerated || !suppressUngenerated)
{
positions.AddRange(GetPredecessorModelPositions(
image, tileSize, pred, partialPos, nLeft, nSkip - 1, suppressSubpaths, suppressUngenerated
));
}
else
{
Console.WriteLine("hit un-generated tile at {0}, {1}", pred.Label.Point.X, pred.Label.Point.Y);
}
}
}
else if (nLeft != 0)
{
// add this node's position to the partial and go to its predecessors
if (!suppressSubpaths || v.Predecessors.Length == 0)
{
positions.Add(partialPos);
}
Color c = image.GetPixel(v.Label.Point.X, v.Label.Point.Y);
byte[] thisPosition = new byte[] { c.R, c.G, c.B };
byte[] nextPartial = new byte[partialPos.Length + thisPosition.Length];
Array.Copy(partialPos, nextPartial, partialPos.Length);
Array.Copy(thisPosition, 0, nextPartial, partialPos.Length, thisPosition.Length);
foreach (Digraph<TileGenerationRecord>.Vertex pred in v.Predecessors)
{
if (pred.Label.IsGenerated || !suppressUngenerated)
{
positions.AddRange(GetPredecessorModelPositions(
image, tileSize, pred, nextPartial, nLeft - 1, nSkip, suppressSubpaths, suppressUngenerated
));
}
else
{
Console.WriteLine("hit un-generated tile at {0}, {1}", pred.Label.Point.X, pred.Label.Point.Y);
}
}
}
else
{
// done
positions.Add(partialPos);
}
return positions;
}
static string Update_Vertex_ChangesLabelOnVertexAndReturnsGPrime()
{
// Arrange preconditions
var graph = new Digraph<float, object, int>();
var f = .33333f;
var vertex = new Vertex<float, object>(f);
var object1 = new object();
var graphPrime = graph.AddVertex(vertex,object1);
// Act
var object2 = new object();
var graphDoublePrime = graphPrime.UpdateVertex(vertex, object2);
// Assert postconditions
if(graphDoublePrime == graphPrime) return Fail;
if(graphDoublePrime.GetVertex(vertex) == object1) return Fail;
return graphDoublePrime.GetVertex(vertex) == object2 ? Pass : Fail;
}
private Digraph<TileGenerationRecord> MakeDependencyGraph(int w, int h)
{
Digraph<TileGenerationRecord> depGraph = new Digraph<TileGenerationRecord>();
int wTile = w, hTile = h;
Digraph<TileGenerationRecord>.Vertex[,] vertices = new Digraph<TileGenerationRecord>.Vertex[wTile, hTile];
// build vertices
for (int y = 0; y < hTile; y++)
{
for (int x = 0; x < wTile; x++)
{
vertices[x, y] = new Digraph<TileGenerationRecord>.Vertex(new TileGenerationRecord(new Point(x, y), false));
depGraph.Add(vertices[x, y]);
}
}
// build edges
for (int y = 0; y < hTile; y++)
{
for (int x = 0; x < wTile; x++)
{
if (x != 0) depGraph.DrawEdge(vertices[x - 1, y], vertices[x, y]);
if (y != 0) depGraph.DrawEdge(vertices[x, y - 1], vertices[x, y]);
}
}
return depGraph;
}
static string Remove_Vertex_DeletesVertexAndReturnsGPrime()
{
// Arrange Preconditions
var date = DateTime.Now;
var graph = new Digraph<DateTime, string, int>();
var vertex = new Vertex<DateTime, string>(date);
var graphPrime = graph.AddVertex(vertex, "Foo");
// Act
var graphDoublePrime = graphPrime.RemoveVertex(vertex);
// Assert Postconditions
if (graphDoublePrime == graphPrime) return Fail;
if (!graphPrime.GetVertex(vertex).Equals("Foo")) return Fail;
if (!graphDoublePrime.IsEmpty) return Fail;
if (!graphPrime.HasVertex(vertex)) return Fail;
return !graphDoublePrime.HasVertex(vertex) ? Pass:Fail;
}
static string Remove_Vertex_ThrowsExceptionWhenVertexIsNotInGraph()
{
var expectedMessage = "Vertex Id 1 is not an element within V";
// Arrange Preconditions
var graph = new Digraph<int, string, int>();
var vertex = new Vertex<int, string>(1);
// Act
var result = false;
try
{
var graphPrime = graph.RemoveVertex(vertex);
return Fail;
}
catch (ArgumentException ae)
{
result = ae.Message == expectedMessage;
}
return result ? Pass : Fail;
}
static string Remove_Edge_DeletesEdgeFromGraphGAndReturnsGPrime()
{
// Arrange preconditons
var graph = new Digraph<int, int, int>();
var vertex1 = new Vertex<int, int>(1);
var vertex2 = new Vertex<int, int>(2);
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
var graphDoublePrime = graphPrime.AddVertex(vertex2, vertex2.Identifier);
var edgeLabel = 1;
var graphTriplePrime = graphDoublePrime.AddEdge(vertex1, vertex2, edgeLabel);
// Act
var graphQuadruplePrime = graphTriplePrime.RemoveEdge(vertex1, vertex2);
// Assert postconditions
if (graphQuadruplePrime == graphTriplePrime) return Fail;
return !graphQuadruplePrime.HasEdge(vertex1,vertex2) ? Pass : Fail;
}
static string Update_Edge_ChangesEdgeLabelAndReturnsGPrime()
{
// Arrange preconditons
var graph = new Digraph<char, int, int>();
var vertex1 = new Vertex<char, int>('a');
var vertex2 = new Vertex<char, int>('b');
var graphPrime = graph.AddVertex(vertex1, vertex1.Identifier);
var graphDoublePrime = graphPrime.AddVertex(vertex2, vertex2.Identifier);
var edgeLabel = 1;
var graphTriplePrime = graphDoublePrime.AddEdge(vertex1, vertex2, edgeLabel);
// Act
var updatedEdgeLabel = 2;
var graphQuadruplePrime = graphTriplePrime.UpdateEdge(vertex1, vertex2, updatedEdgeLabel);
// Assert
if (graphQuadruplePrime == graphTriplePrime) return Fail;
if (graphQuadruplePrime.GetEdge(vertex1, vertex2) == edgeLabel) return Fail;
return graphQuadruplePrime.GetEdge(vertex1, vertex2) == updatedEdgeLabel ? Pass : Fail;
}