public static void BFS(DrawingSurface ds, int start)
{
var adjList = ds.GetAdjList();
var que = new Queue <int>();
bool[] visited = new bool[ds.Vertices.Count];
que.Enqueue(start - 1);
visited[start - 1] = true;
while (que.Count > 0)
{
start = que.Dequeue();
ReDrawCircle(ds, start, activeVertex, 700);
foreach (var vertex in adjList[start])
{
if (!visited[vertex])
{
ReDrawCircle(ds, vertex, processedVertex, 700);
que.Enqueue(vertex);
visited[vertex] = true;
}
}
ReDrawCircle(ds, start, processedVertex, 700);
}
ClearVertices(ds);
}
public void UpLoad(DrawingSurface ds)
{
XmlDocument xml = new XmlDocument();
xml.Load(filename);
XmlElement xroot = xml.DocumentElement;
ds.Edges.Clear();
Circle.number = 0;
ds.Vertices.Clear();
foreach (XmlElement xnode in xroot)
{
foreach (XmlElement xNode in xnode)
{
if (xNode.Name == "node")
{
var c = new Circle(0, 0);
c.uniqueNumber = Convert.ToInt32(xNode.GetAttribute("id")) + 1;
ds.Vertices.Add(c);
}
if (xNode.Name == "edge")
{
var isDirected = xNode.GetAttribute("directed") == "true" ? true : false;
Console.WriteLine(xNode.GetAttribute("source"));
var startVertex = ds.Vertices[Convert.ToInt32(xNode.GetAttribute("source"))];
var endVertex = ds.Vertices[Convert.ToInt32(xNode.GetAttribute("target"))];
var weight = (float)Convert.ToDouble(xNode.FirstChild.InnerText);
var edge = new Edge(startVertex, endVertex, weight, isDirected);
ds.Edges.Add(edge);
}
}
}
}
private static int[] TopologicalSort(DrawingSurface ds)
{
var visited = new HashSet <int>();
var answer = new int[ds.Vertices.Count];
Dictionary <int, List <int> > adjList = ds.GetAdjList();
var currentPlace = ds.Vertices.Count;
for (var vertex = 0; vertex < ds.Vertices.Count; ++vertex)
{
if (!visited.Contains(vertex))
{
DFS(vertex);
}
}
void DFS(int start)
{
visited.Add(start);
foreach (var vertex in adjList[start])
{
if (!visited.Contains(vertex))
{
DFS(vertex);
}
}
answer[--currentPlace] = start;
}
return(answer);
}
public void Save(DrawingSurface ds)
{
FileStream fs = File.Create(filename);
fs.Close();
StreamWriter sr = new StreamWriter(filename);
sr.WriteLine("<?xml version='1.0' encoding='utf-8'?>");
sr.WriteLine("<graphml xmlns='http://graphml.graphdrawing.org/xmlns'\n xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' \n xsi:schemaLocation='http://graphml.graphdrawing.org/x \n http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd'>");
sr.WriteLine(" <key id='d1' for='edge' attr.name='weight' attr.type='float'/>");
sr.WriteLine(" <graph id='G'>");
foreach (Circle vertex in ds.Vertices)
{
sr.WriteLine($" <node id ='{vertex.uniqueNumber - 1}'/>");
}
foreach (Edge edge in ds.Edges)
{
sr.WriteLine($" <edge directed='{edge.isDirected.ToString().ToLower()}' source='{edge.start}' target='{edge.end}'>");
sr.WriteLine($" <data key='d1'>{edge.w},0</data>");
sr.WriteLine($" </edge>");
}
sr.WriteLine(" </graph>");
sr.WriteLine("</graphml>");
sr.Close();
}
public void Build(DrawingSurface ds, bool visualize)
{
(width, height) = (ds.Width - 2 * Circle.radious, ds.Height - 2 * Circle.radious);
var adjM = GetNotDirectedAdjMatrix(ds.Edges);
isReady = false;
int sleepTime = 25;
ds.TurnMoving(false);
FillArrays();
for (var i = 0; i < 10000 && !isReady; ++i)
{
Move(adjM);
sleepTime = (i > 1500) ? 10 : (i > 2500) ? 0 : sleepTime;
if (visualize && i > 20)
{
Visualize(ds, sleepTime);
}
}
Visualize(ds, 0);
if (visualize)
{
ds.FillGraph(Color.Lime, Color.Lime);
Thread.Sleep(1000);
ds.FillGraph(Color.White, Color.Gray);
}
ds.TurnMoving(true);
}
private static void AlgorithmDone(DrawingSurface ds)
{
ds.FillGraph(Color.Lime, Color.Lime);
Thread.Sleep(500);
ds.FillGraph(Color.White, Color.Gray);
Thread.Sleep(500);
}
public static void KruskalSpanningTree(DrawingSurface ds)
{
if (!ds.IsFullyConnected() || ds.IsDirected())
{
ErrorBox err = new ErrorBox("Graph has to be undirected and fully connected");
err.ShowDialog();
return;
}
var spanningTreeColor = Color.Green;
var edgesNum = ds.Edges.Count;
var adjMatrix = ds.GetDistMatrix();
var cost = .0;
var result = new List <Tuple <int, int> > {
};
var treeId = new List <int> {
};
ds.Edges.OrderBy(x => adjMatrix[x.start, x.end]);
for (var i = 0; i < ds.Vertices.Count; ++i)
{
treeId.Add(i);
}
for (var i = 0; i < edgesNum; ++i)
{
(var start, var end) = (ds.Edges[i].start, ds.Edges[i].end);
var weight = adjMatrix[start, end];
if (treeId[start] != treeId[end])
{
cost += weight;
for (var k = 0; k < ds.Edges.Count; ++k)
{
if (((ds.Edges[k].start == start && ds.Edges[k].end == end) ||
(ds.Edges[k].start == end && ds.Edges[k].end == start)))
{
ds.Edges[k].fillColor = spanningTreeColor;
ds.Vertices[ds.Edges[k].start].fillColor = spanningTreeColor;
ds.Vertices[ds.Edges[k].end].fillColor = spanningTreeColor;
ds.Invalidate();
Thread.Sleep(2000);
}
}
int oldId = treeId[end], newId = treeId[start];
for (var j = 0; j < ds.Vertices.Count; ++j)
{
if (treeId[j] == oldId)
{
treeId[j] = newId;
}
}
}
}
Thread.Sleep(5000);
ClearEdges(ds);
ClearVertices(ds);
}
private static void ClearVertices(DrawingSurface ds)
{
for (var i = 0; i < ds.Vertices.Count; ++i)
{
ds.Vertices[i].label = "";
ds.Vertices[i].fillColor = Color.White;
}
ds.Invalidate();
}
public static void Colouring(DrawingSurface ds)
{
if (!ds.IsUndirected())
{
var err = new ErrorBox("Graph has to be unoriented");
err.ShowDialog();
return;
}
var rnd = new Random {
};
var adjList = ds.GetAdjList();
List <int> nodePowers = ds.GetNodePowers();
List <int> vertices = Enumerable.Range(0, ds.Vertices.Count).OrderByDescending(u => nodePowers[u]).ToList();
List <int> colors_list = Enumerable.Repeat(-1, ds.Vertices.Count).ToList();
int colors_used = 1;
colors = colors.OrderBy(x => rnd.Next()).ToArray();
colors_list[vertices[0]] = 0;
foreach (var vertex in vertices)
{
if (vertex == vertices[0])
{
continue;
}
var adjacentColors = new HashSet <int> {
};
foreach (var adjvertices in adjList[vertex])
{
if (colors_list[adjvertices] != -1)
{
adjacentColors.Add(colors_list[adjvertices]);
}
}
HashSet <int> possibleColors = colors_list.Where(u => u != -1).Except(adjacentColors).ToHashSet();
if (possibleColors.Count == 0)
{
colors_used += 1;
colors_list[vertex] = colors_used - 1;
}
else
{
if (colors_list[vertex] == -1)
{
colors_list[vertex] = possibleColors.Min();
}
}
}
foreach (var vertex in vertices)
{
ReDrawCircle(ds, vertex, colors[colors_list[vertex]]);
}
Thread.Sleep(5000);
ClearVertices(ds);
}
private void Visualize(DrawingSurface ds, int sleepTime)
{
(double max, double min) = GetMaxMin();
for (var i = 0; i < vertexNum; ++i)
{
MoveCircle(ds, i, max, min);
}
ds.Invalidate();
Thread.Sleep(sleepTime);
}
public static void KuhnMatching(DrawingSurface ds)
{
Dictionary <int, List <int> > adjMatrix = ds.GetAdjList();
var maxMatchingColor = Color.Yellow;
var used = new List <bool>();
List <int> matching = Enumerable.Repeat(-1, ds.Vertices.Count).ToList();
bool dfs(int vertex)
{
if (used[vertex])
{
return(false);
}
used[vertex] = true;
foreach (var to in adjMatrix[vertex])
{
if (matching[to] == -1 || (dfs(matching[to])))
{
matching[to] = vertex;
return(true);
}
}
return(false);
}
for (var i = 0; i < ds.Vertices.Count; ++i)
{
for (var j = 0; j < ds.Vertices.Count; ++j)
{
used.Add(false);
}
dfs(i);
}
for (var i = 0; i < ds.Vertices.Count; ++i)
{
if (matching[i] != 1)
{
for (var k = 0; k < ds.Edges.Count; ++k)
{
if (((ds.Edges[k].start == i && ds.Edges[k].end == matching[i]) ||
(ds.Edges[k].start == matching[i] && ds.Edges[k].end == i)))
{
ds.Edges[k].fillColor = maxMatchingColor;
ds.Vertices[ds.Edges[k].start].fillColor = maxMatchingColor;
ds.Vertices[ds.Edges[k].end].fillColor = maxMatchingColor;
ds.Invalidate();
Thread.Sleep(2000);
}
}
}
}
Thread.Sleep(5000);
ClearEdges(ds, false);
ClearVertices(ds);
}
private void MoveCircle(DrawingSurface ds, int i, double max, double min)
{
x[i].dx /= max; x[i].dy /= max;
double Xvalue = (Math.Abs(width * min / max) + Circle.radious * 2);
double Yvalue = (Math.Abs(height * min / max) + Circle.radious * 2);
double Xscaler = (width + Xvalue) / width;
double Yscaler = (height + Yvalue) / height;
int newX = (int)((x[i].dx * (width) + Xvalue) / Xscaler);
int newY = (int)((x[i].dy * (height) + Yvalue) / Yscaler);
ds.Vertices[i].center = new Point(newX, newY);
}
private static void ClearEdges(DrawingSurface ds, bool labelsToo = false)
{
for (var i = 0; i < ds.Edges.Count; i++)
{
ds.Edges[i].fillColor = Color.Gray;
if (labelsToo)
{
ds.Edges[i].SetLabel("");
}
}
ds.Invalidate();
}
public static void DFS(DrawingSurface ds, int start)
{
Stack <int> stack = new Stack <int>();
stack.Push(start - 1);
var adjList = ds.GetAdjList();
bool[] visited = new bool[ds.Vertices.Count];
while (stack.Count > 0)
{
var vertex = stack.Peek();
ReDrawCircle(ds, vertex, activeVertex, 700);
if (!visited[vertex])
{
visited[vertex] = true;
ReDrawCircle(ds, vertex, processedVertex, 700);
}
bool remove = true;
foreach (int adjvertex in adjList[vertex])
{
if (!visited[adjvertex])
{
stack.Push(adjvertex);
remove = false;
ReDrawCircle(ds, vertex, processedVertex, 700);
break;
}
}
if (remove)
{
int v = stack.Pop();
ReDrawCircle(ds, v, processedVertex, 700);
}
}
ClearVertices(ds);
}
public static void Dijkstra(DrawingSurface ds, int start)
{
if (ds.ContainsNegativeEdge())
{
var err = new ErrorBox("Graph contains negative edges");
err.ShowDialog();
return;
}
Dictionary <int, List <Edge> > adjList = ds.GetDestAdjList();
var que = new C5.IntervalHeap <Edge>(new EdgeCompare());
double[] dist = Enumerable.Repeat((double)int.MaxValue, adjList.Count).ToArray();
int[] parent = Enumerable.Repeat(-1, adjList.Count).ToArray();
var visitedColor = Color.Green;
var processedColor = Color.Yellow;
var currentEdgeColor = Color.Red;
que.Add(new Edge(ds.Vertices[start], ds.Vertices[start], 0, true));
dist[start] = 0;
for (var i = 0; i < ds.Vertices.Count; ++i)
{
ds.Vertices[i].label = "INF";
}
ds.Vertices[start].label = "0";
while (que.Count != 0)
{
var currEdge = que.FindMin(); que.DeleteMin();
var startVertex = (ds.Vertices[currEdge.end].fillColor == visitedColor) ? currEdge.start : currEdge.end;
ReDrawCircle(ds, startVertex, visitedColor);
foreach (var edge in adjList[startVertex])
{
var currVertex = (edge.end != startVertex) ? edge.end : edge.start;
ReDrawEdge(ds, edge, currentEdgeColor, 300);
if (ds.Vertices[currVertex].fillColor != visitedColor)
{
ReDrawCircle(ds, currVertex, processedColor, 0);
}
Thread.Sleep(1000);
if (dist[currVertex] > dist[startVertex] + edge.w)
{
dist[currVertex] = dist[startVertex] + edge.w;
parent[currVertex] = startVertex;
ds.Vertices[currVertex].label = $"{Math.Round(dist[currEdge.end], 3)}+{Math.Round(edge.w, 3)}";
ds.Invalidate();
Thread.Sleep(1000);
que.Add(edge);
}
ds.Vertices[currVertex].label = (dist[currVertex] == int.MaxValue) ? "INF" : $"{dist[currVertex]}";
ReDrawEdge(ds, edge, Color.Gray, 0);
}
}
msg.SetTitle("Dijkstra algorithm result:");
msg.MoveToCorner(ds.FindForm() as Form1);
msg.StartMenu();
for (var target = 0; target < adjList.Count; ++target)
{
if (start != target)
{
var currWay = GetWay(start, target, parent);
PrintWay(currWay, dist[target]);
Thread.Sleep(1000);
}
}
msg.WaitOne();
ClearEdges(ds);
ClearVertices(ds);
}
private static void ReDrawEdge(DrawingSurface ds, Edge edge, Color color, int delay = 1000)
{
edge.fillColor = color;
ds.Invalidate();
Thread.Sleep(delay);
}
private static void ReDrawCircle(DrawingSurface ds, int i, Color color, int delay = 1000)
{
ds.Vertices[i].fillColor = color;
ds.Invalidate();
Thread.Sleep(delay);
}
public static void BackTrackingColouring(DrawingSurface ds, int colorAmount)
{
bool isSafe(int[,] adjmat, int[] color)
{
for (var i = 0; i < ds.Vertices.Count; ++i)
{
for (var j = i + 1; j < ds.Vertices.Count; ++j)
{
if (adjmat[i, j] == 1 && color[j] == color[i])
{
return(false);
}
}
}
return(true);
}
bool GraphColouring(int[,] adjmat, int bound, int index, int[] color)
{
if (index == ds.Vertices.Count)
{
if (isSafe(adjmat, color))
{
for (var k = 0; k < ds.Vertices.Count; ++k)
{
ReDrawCircle(ds, k, colors[color[k]]);
}
return(true);
}
return(false);
}
for (var j = 1; j <= bound; ++j)
{
color[index] = j;
if (GraphColouring(adjmat, bound, index + 1, color))
{
return(true);
}
color[index] = 0;
}
return(false);
}
var adjMatrix = ds.GetAdjMatrix();
var colorsList = new List <int> {
};
if (!ds.IsUndirected())
{
var err = new ErrorBox("Graph has to be unoriented");
err.ShowDialog();
return;
}
for (var i = 0; i < ds.Vertices.Count; ++i)
{
colorsList.Add(0);
}
if (!GraphColouring(adjMatrix, colorAmount, 0, colorsList.ToArray()))
{
var err = new ErrorBox($"Graph cannot be coloured into {colorAmount} colours");
err.ShowDialog();
return;
}
Thread.Sleep(5000);
ClearVertices(ds);
}
public static void ConnectedComponents(DrawingSurface ds)
{
int[] sortedVertices = TopologicalSort(ds);
var oldGraphEdges = new List <Edge>(ds.Edges);
Dictionary <int, List <int> > adjList = ds.GetAdjList();
var visited = new HashSet <int>();
var component = new List <int>();
var componentsList = new List <List <int> >();
var rnd = new Random(Guid.NewGuid().GetHashCode());
foreach (var edge in ds.Edges)
{
var tmp = edge.start;
edge.setStart(ds.Vertices[edge.end]);
edge.setEnd(ds.Vertices[tmp]);
}
foreach (var vertex in sortedVertices)
{
if (!visited.Contains(vertex))
{
DFS(vertex);
}
if (component.Count != 0)
{
componentsList.Add(new List <int>(component));
component.Clear();
}
}
void DFS(int start)
{
visited.Add(start);
component.Add(start);
foreach (var vertex in adjList[start])
{
if (!visited.Contains(vertex))
{
DFS(vertex);
}
}
}
foreach (var edge in ds.Edges)
{
var tmp = edge.start;
edge.setStart(ds.Vertices[edge.end]);
edge.setEnd(ds.Vertices[tmp]);
}
foreach (var comp in componentsList)
{
var colorForCurrentComponent = Color.FromArgb(255, rnd.Next(255), rnd.Next(255), rnd.Next(255));
foreach (var el in comp)
{
ds.Vertices[el].fillColor = colorForCurrentComponent;
}
for (var i = 0; i < ds.Vertices.Count; ++i)
{
for (var j = 0; j < ds.Vertices.Count; ++j)
{
if (i != j)
{
for (var k = 0; k < ds.Edges.Count; ++k)
{
if (((ds.Edges[k].start == i && ds.Edges[k].end == j) ||
(ds.Edges[k].start == j && ds.Edges[k].end == i)) &&
comp.Contains(i) && comp.Contains(j))
{
ds.Edges[k].fillColor = colorForCurrentComponent;
}
}
}
}
}
ds.Invalidate();
}
Thread.Sleep(5000);
ClearEdges(ds);
ClearVertices(ds);
ds.Invalidate();
}
public static void PrimSpanningTree(DrawingSurface ds)
{
if (!ds.IsFullyConnected() || ds.IsDirected())
{
ErrorBox err = new ErrorBox("Graph has to be undirected and fully connected");
err.ShowDialog();
return;
}
const int INF = int.MaxValue;
var vertexNum = ds.Vertices.Count;
var spanningTreeColor = Color.Red;
var adjMatrix = ds.GetDistMatrix();
var used = new bool[vertexNum];
double[] minEdge = Enumerable.Repeat((double)INF, vertexNum).ToArray();
int[] selectedEdge = Enumerable.Repeat(-1, vertexNum).ToArray();
minEdge[0] = 0;
for (var i = 0; i < vertexNum; ++i)
{
var vertex = -1;
for (var j = 0; j < vertexNum; ++j)
{
if (!used[j] && (vertex == -1 || minEdge[j] < minEdge[vertex]))
{
vertex = j;
}
}
if (minEdge[vertex] == INF)
{
ErrorBox err = new ErrorBox("Minimum spanning tree cannot be found");
err.ShowDialog();
return;
}
used[vertex] = true;
if (selectedEdge[vertex] != -1)
{
for (var k = 0; k < ds.Edges.Count; ++k)
{
if (((ds.Edges[k].start == vertex && ds.Edges[k].end == selectedEdge[vertex]) ||
(ds.Edges[k].start == selectedEdge[vertex] && ds.Edges[k].end == vertex)))
{
ds.Edges[k].fillColor = spanningTreeColor;
ds.Invalidate();
ds.Vertices[ds.Edges[k].start].fillColor = spanningTreeColor;
ds.Vertices[ds.Edges[k].end].fillColor = spanningTreeColor;
ds.Invalidate();
Thread.Sleep(2000);
}
}
}
for (var toVertex = 0; toVertex < vertexNum; ++toVertex)
{
if (adjMatrix[vertex, toVertex] < minEdge[toVertex])
{
minEdge[toVertex] = adjMatrix[vertex, toVertex];
selectedEdge[toVertex] = vertex;
}
}
}
Thread.Sleep(5000);
ClearEdges(ds);
ClearVertices(ds);
ds.Invalidate();
}
public static void FordFulkerson(DrawingSurface ds)
{
if (ds.IsUndirected())
{
var err = new ErrorBox("Graph have to be directed!");
err.ShowDialog();
return;
}
if (ds.ContainsNegativeEdge())
{
var err = new ErrorBox("Graph can not contain negative edges!");
err.ShowDialog();
return;
}
Dictionary <int, List <Edge> > adjList = ds.GetDestAdjList();
(var source, var sink) = GetSourceAndSink(adjList);
if (source == -1 || sink == -1)
{
var err = new ErrorBox("Graph have to contain source and sink!");
err.ShowDialog();
return;
}
;
var fulkersonItems = new FulkersonItem[adjList.Count, adjList.Count];
var minimalFlow = .0;
var flows = new List <double>();
msg.MoveToCorner(ds.FindForm() as Form1);
msg.SetTitle("Ford-Fulkerson algorithm result:\n");
msg.StartMenu();
for (var i = 0; i < adjList.Count; ++i)
{
for (var j = 0; j < adjList.Count; ++j)
{
fulkersonItems[i, j] = new FulkersonItem();
}
}
for (var start = 0; start < adjList.Count; ++start)
{
foreach (var edge in adjList[start])
{
fulkersonItems[start, edge.end].toFlow = edge.w;
edge.SetLabel($"{edge.w}/{0}");
}
}
while (minimalFlow != -1)
{
ds.Vertices[source].fillColor = Color.Green;
ds.Vertices[sink].fillColor = Color.Red;
ds.Invalidate();
minimalFlow = ProcessFulkerson(source, sink, adjList, ref fulkersonItems, ds);
if (minimalFlow != -1)
{
flows.Add(minimalFlow);
}
ClearVertices(ds);
ClearEdges(ds, false);
}
AlgorithmDone(ds);
msg.AddText($"Total maximal flow:\n");
msg.AddText("f(G) = ");
for (var i = 0; i < flows.Count; ++i)
{
msg.AddText($"{flows[i]} ");
if (i != flows.Count - 1)
{
msg.AddText("+ ");
}
Thread.Sleep(700);
}
msg.AddText($"= {flows.Sum()}");
msg.WaitOne();
ClearVertices(ds);
ClearEdges(ds, true);
}
private static double ProcessFulkerson(int source, int sink, Dictionary <int, List <Edge> > adjL,
ref FulkersonItem[,] items, DrawingSurface ds)
{
var stack = new Stack <int>();
var currentVertex = source;
bool[] visited = Enumerable.Repeat(false, adjL.Count).ToArray();
var minimalFlow = 1e6;
int[] pred = Enumerable.Repeat(-1, adjL.Count).ToArray();
var inFlowColor = Color.Blue;
var targeColor = Color.Green;
stack.Push(source);
while (currentVertex != sink && stack.Count > 0)
{
currentVertex = stack.Peek();
visited[currentVertex] = true;
if (currentVertex == source)
{
Thread.Sleep(1000);
}
ReDrawCircle(ds, currentVertex, inFlowColor);
if (currentVertex == sink)
{
ReDrawCircle(ds, sink, targeColor);
break;
}
var waysFrom = WaysFrom(currentVertex, adjL, items, visited);
if (waysFrom.Count == 0)
{
ReDrawCircle(ds, currentVertex, Color.White, 0);
if (currentVertex == source)
{
Thread.Sleep(1000);
break;
}
stack.Pop();
continue;
}
var maxIndex = waysFrom[0];
foreach (var vertex in waysFrom)
{
if (!visited[vertex] &&
items[currentVertex, vertex].toFlow > items[currentVertex, maxIndex].toFlow)
{
maxIndex = vertex;
}
}
minimalFlow = Math.Min(minimalFlow, items[currentVertex, maxIndex].toFlow);
pred[maxIndex] = currentVertex;
stack.Push(maxIndex);
foreach (var edge in adjL[currentVertex])
{
if (edge.end == maxIndex)
{
ReDrawEdge(ds, edge, Color.Red);
edge.fillColor = Color.Gray;
break;
}
}
}
if (pred[sink] == -1)
{
return(-1);
}
currentVertex = sink;
msg.AddText($"Flow at current step: f(v) = {minimalFlow}\n");
Thread.Sleep(1000);
while (pred[currentVertex] != -1)
{
var parent = pred[currentVertex];
items[parent, currentVertex].toFlow -= minimalFlow;
items[parent, currentVertex].backFlow += minimalFlow;
foreach (var edge in adjL[parent])
{
if (edge.end == currentVertex)
{
edge.SetLabel($"{items[parent, currentVertex].toFlow}/{items[parent, currentVertex].backFlow}");
edge.fillColor = Color.Red;
ReDrawCircle(ds, currentVertex, Color.White);
ReDrawEdge(ds, edge, Color.Gray, 0);
break;
}
}
currentVertex = pred[currentVertex];
if (pred[currentVertex] == -1)
{
ReDrawCircle(ds, currentVertex, Color.White);
}
}
return(minimalFlow);
}
