public void BronKerbosh_MIS(List <VertexGraph> R, List <VertexGraph> P, List <VertexGraph> X, Graph graph, List <List <VertexGraph> > MaxIS)
{
if (!P.Any() && !X.Any())
{
MaxIS.Add(R);
return;
}
else
{
while (P.Any())
{
VertexGraph v = P.First();
List <VertexGraph> P1 = new List <VertexGraph>(P);
List <VertexGraph> X1 = new List <VertexGraph>(X);
List <VertexGraph> R1 = new List <VertexGraph>(R);
R1.Add(v);
foreach (var u in graph.GetVertexLists(v))
{
P1.Remove(u);
X1.Remove(u);
}
P1.Remove(v);
BronKerbosh_MIS(R1, P1, X1, graph, MaxIS);
P.Remove(v);
X.Add(v);
}
}
}
public int EdmondsKarp(VertexGraph I, VertexGraph S, Graph graph, int[,] capacity, out int[,] legalFlows)
{
int flow = 0;
legalFlows = new int[graph.VertexCount, graph.VertexCount];
while (true)
{
int[] parent;
int new_flow = bfs(I, S, out parent, graph, capacity, legalFlows);
if (new_flow == 0)
{
break;
}
flow += new_flow;
int v = S.Number;
while (v != I.Number)
{
int prev = parent[v];
legalFlows[prev, v] += new_flow;
legalFlows[v, prev] -= new_flow;
v = prev;
}
}
return(flow);
}
public List <VertexGraph> Dfs(VertexGraph start, VertexGraph finish, List <VertexGraph> result, Graph graph)
{
result.Add(start);
foreach (var v in graph.GetVertexLists(start))
{
if (!result.Contains(v) && !result.Contains(finish))
{
Dfs(v, finish, result, graph);
}
}
return(result);
}
public List <VertexGraph> GetVertexLists(VertexGraph vertex)
{
var result = new List <VertexGraph>();
foreach (var edge in Edges)
{
if (edge.From == vertex)
{
result.Add(edge.To);
}
}
return(result);
}
public void Path(VertexGraph u, VertexGraph v, int[,] next, List <VertexGraph> path)
{
if (next[u.Number, v.Number] == 0)
{
return;
}
path.Add(u);
while (u != v)
{
VertexGraph n1 = new VertexGraph(next[u.Number, v.Number]);
u = n1;
path.Add(u);
}
}
public void BronKerbosh(List <VertexGraph> R, List <VertexGraph> P, List <VertexGraph> X, Graph graph, List <List <VertexGraph> > MaxCliques)
{
if (!P.Any() && !X.Any())
{
//if (R.Count >= 3)
MaxCliques.Add(R);
return;
}
else
{
while (P.Any())
{
VertexGraph v = P.First();
List <VertexGraph> intersectionP = new List <VertexGraph>();
List <VertexGraph> intersectionX = new List <VertexGraph>();
// Пересечение с P
foreach (var u in graph.GetVertexLists(v))
{
for (int j = 0; j < P.Count; j++)
{
VertexGraph w = P[j];
if (u == w)
{
intersectionP.Add(u);
}
}
// Пересечение с Х
for (int k = 0; k < X.Count; k++)
{
VertexGraph l = X[k];
if (u == l)
{
intersectionX.Add(u);
}
}
}
List <VertexGraph> R_new = new List <VertexGraph>(R);
R_new.Add(v);
BronKerbosh(R_new, intersectionP, intersectionX, graph, MaxCliques);
P.Remove(v);
X.Add(v);
}
}
}
public List <VertexGraph> Wave(VertexGraph start, VertexGraph finish, Graph graph)
{
var list = new List <VertexGraph>();
list.Add(start);
for (int i = 0; i < list.Count; i++)
{
var vertex = list[i];
foreach (var v in graph.GetVertexLists(vertex))
{
if (!list.Contains(v) && !list.Contains(finish))
{
list.Add(v);
}
}
}
return(list);
}
public Graph(string InputText)
{
Vertices = new List <VertexGraph>();
Edges = new List <EdgeGraph>();
if (InputText != String.Empty)
{
InputText = InputText.Replace(" ", "");
InputText = InputText.Replace("\r", "");
int k = 0; string[] col;
string[] text = InputText.Split('\n');
foreach (var row in text)
{
col = row.Split(',');
VertexGraph from = new VertexGraph(k);
Vertices.Add(from);
for (int i = 0; i < col.Length; i++)
{
if (col[i] != "0" && col[i] != "")
{
VertexGraph to = new VertexGraph(i);
EdgeGraph edge;
if (col[i] != "1")
{
int weight = int.Parse(col[i]);
edge = new EdgeGraph(from, to, weight);
}
else
{
edge = new EdgeGraph(from, to);
}
Edges.Add(edge);
}
}
k++;
}
}
}
int bfs(VertexGraph I, VertexGraph S, out int[] parent, Graph graph, int[,] capacity, int[,] legalFlows)
{
parent = new int [graph.VertexCount];
for (int i = 0; i < graph.VertexCount; i++)
{
parent[i] = -1;
}
parent[I.Number] = -2;
int[] m = new int[graph.VertexCount];
m[I.Number] = int.MaxValue;
Queue <VertexGraph> q = new Queue <VertexGraph>();
q.Enqueue(I);
while (q.Any())
{
VertexGraph cur = q.Dequeue();
foreach (var next in graph.GetVertexLists(cur))
{
if (capacity[cur.Number, next.Number] - legalFlows[cur.Number, next.Number] > 0 && parent[next.Number] == -1)
{
parent[next.Number] = cur.Number;
m[next.Number] = Math.Min(m[cur.Number], capacity[cur.Number, next.Number] - legalFlows[cur.Number, next.Number]);
if (next != S)
{
q.Enqueue(next);
}
else
{
return(m[S.Number]);
}
}
}
}
return(0);
}
public EdgeGraph(VertexGraph from, VertexGraph to, int weight = 1)
{
From = from;
To = to;
Weight = weight;
}
public void AddEdge(VertexGraph from, VertexGraph to, int weight)
{
var edge = new EdgeGraph(from, to, weight);
Edges.Add(edge);
}
public void AddEdge(VertexGraph from, VertexGraph to)
{
var edge = new EdgeGraph(from, to);
Edges.Add(edge);
}
public void AddVertex(VertexGraph vertex)
{
Vertices.Add(vertex);
}
private void Run1_Click_1(object sender, EventArgs e)
{
int index = Tasks.SelectedIndex;
Algorithms algorithms = new Algorithms();
switch (index)
{
case 0:
{
output.Clear();
List <int> res = new List <int>();
bool answer = algorithms.FindEulerPath(graph, out res);
if (answer)
{
output.AppendText("Нет эйлерова пути!\n");
}
else
{
if (res.First() == res.Last())
{
output.AppendText("Граф НЕ полуэйлеровый, а эйлеровый!");
}
else
{
output.AppendText("Граф полуэйлеровый!\nЭйлеров путь:\n");
foreach (var v in res)
{
output.AppendText(v.ToString() + " ");
}
}
}
break;
}
case 1:
{
output.Clear();
List <VertexGraph> combsub = new List <VertexGraph>();
List <VertexGraph> not = new List <VertexGraph>();
List <List <VertexGraph> > MaxCliques = new List <List <VertexGraph> >();
List <VertexGraph> candidates = graph.GetVertices();
List <VertexGraph> max = new List <VertexGraph>();
algorithms.BronKerbosh(combsub, candidates, not, graph, MaxCliques);
if (MaxCliques.Count > 1)
{
output.AppendText("Наибольшая клика:\n");
max = MaxCliques[0];
for (int i = 1; i < MaxCliques.Count; i++)
{
if (MaxCliques[i].Count > max.Count)
{
max = MaxCliques[i];
}
}
foreach (var item in max)
{
output.AppendText(item.ToString() + " ");
}
}
else
{
output.AppendText("Наибольших клик нет!\n");
}
break;
}
case 2:
{
output.Clear();
VertexGraph S = new VertexGraph(graph.VertexCount - 1);
VertexGraph I = new VertexGraph(0);
int [,] capacity = graph.GetMatrix();
int[,] legalFlows = new int[graph.VertexCount, graph.VertexCount];
int max_flow = algorithms.EdmondsKarp(I, S, graph, capacity, out legalFlows);
output.AppendText($"Максимальный поток = {max_flow}\n");
int rows = legalFlows.GetUpperBound(0) + 1;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < rows; j++)
{
output.AppendText(legalFlows[i, j].ToString() + " ");
}
output.AppendText("\n");
}
break;
}
case 3:
{
output.Clear();
List <VertexGraph> combsub = new List <VertexGraph>();
List <VertexGraph> not = new List <VertexGraph>();
List <List <VertexGraph> > MaxIS = new List <List <VertexGraph> >();
List <VertexGraph> candidates = graph.GetVertices();
List <VertexGraph> max = new List <VertexGraph>();
algorithms.BronKerbosh_MIS(combsub, candidates, not, graph, MaxIS);
if (MaxIS.Count > 1)
{
output.AppendText("Наибольшее независимое множество:\n");
max = MaxIS[0];
for (int i = 1; i < MaxIS.Count; i++)
{
if (MaxIS[i].Count > max.Count)
{
max = MaxIS[i];
}
}
foreach (var item in max)
{
output.AppendText(item.ToString() + " ");
}
}
else
{
output.AppendText("Наибольшее независимого множества нет!\n");
}
break;
}
case 4:
{
output.Clear();
int[,] next = new int[graph.VertexCount, graph.VertexCount];
int[,] distanse = algorithms.Floyd_Warshall(graph, next);
VertexGraph start = new VertexGraph(0);
VertexGraph finish = new VertexGraph(graph.VertexCount - 1);
List <VertexGraph> path = new List <VertexGraph>();
algorithms.Path(start, finish, next, path);
output.AppendText("Матрица кратчайших расстояний:\n");
int rows = distanse.GetUpperBound(0) + 1;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < rows; j++)
{
output.AppendText(distanse[i, j].ToString() + " ");
}
output.AppendText("\n");
}
output.AppendText($"\nКратчайший путь от вершины " + start.ToString() + " до " + finish.ToString() + ":\n");
foreach (var item in path)
{
output.AppendText(item.ToString() + " ");
}
break;
}
}
}