private void ConnectTwoNodes(int node1, int node2)
{
if (Graph.GetConnection(node1, node2) == false)
{
Graph.MakeConnection(node1, node2);
Graph.OnChange();
}
else
{
Graph.RemoveConnection(node1, node2);
Graph.OnChange();
}
}
public static DirectedGraphList ConvertToSList(DirectedGraphMatrix from)
{
DirectedGraphList x = new DirectedGraphList(from.NodesNr);
for (int i = 0; i < from.NodesNr; i++)
{
for (int j = 0; j < from.NodesNr; j++)
{
if (from.GetConnection(i, j))
{
x.MakeConnection(i, j);
}
x.setWeight(i, j, from.getWeight(i, j));
}
}
return(x);
}
public static DirectedGraphMatrix CreateRandomDirectedWeights(DirectedGraphMatrix f, int minWeight = -5, int maxWeight = 20)
{
Random r = new Random();
DirectedGraphMatrix ret = new DirectedGraphMatrix(f.NodesNr);
for (int k = 0; k < f.NodesNr; k++)
{
for (int p = 0; p < f.NodesNr; p++)
{
if (f.GetConnection(k, p))
{
ret.MakeConnection(k, p, r.Next(minWeight, maxWeight + 1));
}
}
}
return(ret);
}
/// <summary>
/// Implementacja algorytmu Floyda-Warshalla
/// </summary>
/// <param name="g"></param> Graf ktory jest spojny. Ten algorytm dziala takze dla grafow niespojnych w przeciwienstwie do johnsona
/// <returns></returns> Macierz odleglosci miedzy wszystkimi wierzcholkami
public static int[,] FloydWarshall(DirectedGraphMatrix graph)
{
int nodes = graph.NodesNr;
int[,] distances = new int[nodes, nodes];
int w = 0;
const int INF = int.MaxValue - 10000;
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
distances[i, j] = INF;
if (graph.GetConnection(i, j))
{
distances[i, j] = graph.getWeight(i, j);
}
}
distances[i, i] = 0;
}
for (int k = 0; k < nodes; ++k)
{
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
if (k == i || k == j || i == j)
{
continue;
}
if ((distances[i, k] == INF) || (distances[k, j] == INF))
{
continue;
}
w = distances[i, k] + distances[k, j];
if (distances[i, j] > w)
{
distances[i, j] = w;
}
}
}
}
return(distances);
}
/// <summary>
/// Transpozycja macierzy sasiedztwa
/// potrzebna do algorytmu Kosaraju
/// </summary>
/// <param name="from"></param>
/// <returns>Graf z transponowana macierza sasiedztwa</returns>
public static DirectedGraphMatrix transpose(DirectedGraphMatrix from)
{
int[,] t = new int[from.NodesNr, from.NodesNr];
for (int i = 0; i < from.NodesNr; i++)
{
for (int j = 0; j < from.NodesNr; j++)
{
if (from.GetConnection(i, j))
{
t[j, i] = 1;
}
else
{
t[j, i] = 0;
}
}
}
return(new DirectedGraphMatrix(from.NodesNr, t));
}
/// <summary>
/// Tworzy graf maxymalnie spojny
/// </summary>
/// <param name="f">graf</param>
/// <returns>max spojny graf</returns>
public static DirectedGraphMatrix Directedmaxspojny(DirectedGraphMatrix f)
{
List <List <int> > sp = spojne(f);
int k = 0;
for (int i = 0; i < sp.Count; i++)
{
if (sp[i].Count >= sp[k].Count)
{
k = i;
}
}
List <int> q = sp[k];
int[,] t = new int[q.Count, q.Count];
k = 0;
int l;
for (int i = 0; i < f.NodesNr; i++)
{
l = 0;
if (!q.Contains(i))
{
continue;
}
for (int j = 0; j < f.NodesNr; j++)
{
if (!q.Contains(j))
{
continue;
}
if (f.GetConnection(i, j))
{
t[k, l] = 1;
}
l++;
}
k++;
}
return(new DirectedGraphMatrix(q.Count, t));
}
/// <summary>
/// Implementacja algorytmu Johnsona, korzysta z algorytmow Bellmana-Forda i Dijkstry
/// </summary>
/// <param name="g"></param> Musi to byc graf skierowany ktory ma juz randomowe wagi i musi byc on spojny(WAŻNE)!!!!
/// Mozna np stworzyc graf skierowany, wydobyc z niego skladowa maksymalnie spojna i nadać jej randomowe wagi
/// <returns></returns> Macierz odleglosci miedzy wszystkimi wierzcholkami
public static int[,] Johnson(DirectedGraphMatrix graph)
{
try
{
int nodes = graph.NodesNr;
int[,] distances = new int[nodes, nodes];
int[] d = new int[nodes];
const int INF = int.MaxValue - 10000;
int[,] wagi = new int[nodes, nodes];
int q = nodes + 1;
int[,] new_connect = new int[q, q];
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
new_connect[i, j] = graph.getConnect(i, j);
wagi[i, j] = graph.getWeight(i, j);
}
}
DirectedGraphMatrix dgraph = new DirectedGraphMatrix(q, new_connect);
for (int i = 0; i < q - 1; ++i)
{
dgraph.MakeConnection(q - 1, i, 0);
dgraph.setWeight(i, q - 1, INF);
for (int j = 0; j < q - 1; ++j)
{
dgraph.setWeight(i, j, graph.getWeight(i, j));
}
}
List <List <int> > bellman = new List <List <int> >();
for (int i = 0; i < nodes; ++i)
{
bellman.Add(BellmanFord(dgraph, q - 1, i));
d[i] = pathWeight(dgraph, bellman[i]);
if (ujemnyCykl(graph, wagi))
{
throw new Exception("Algorytm Johnsona zostal zatrzymany.");
}
}
for (int i = 0; i < q - 1; ++i)
{
for (int j = 0; j < q - 1; ++j)
{
if (dgraph.GetConnection(i, j))
{
dgraph.setWeight(i, j, dgraph.getWeight(i, j) + d[i] - d[j]);
}
}
}
int[,] last_connect = new int[nodes, nodes];
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
last_connect[i, j] = dgraph.getConnect(i, j);
}
}
DirectedGraphMatrix lgraph = new DirectedGraphMatrix(nodes, last_connect);
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
lgraph.setWeight(i, j, dgraph.getWeight(i, j));
}
}
distances = distancesDirectedMatrix(lgraph);
for (int i = 0; i < nodes; ++i)
{
for (int j = 0; j < nodes; ++j)
{
distances[i, j] = distances[i, j] - d[i] + d[j];
}
}
return(distances);
}
catch (Exception)
{
Console.WriteLine("Algorytm Johnsona zatrzymany z powodu ujemnego cyklu w grafie.");
return(new int[5, 5]);
}
}
/// <summary>
/// Bellman ford
/// </summary>
/// <param name="g"></param>
/// <param name="start">skad</param>
/// <param name="finish">dokad</param>
/// <returns>lista wierzcholkow po ktorych otrzymamy najkrotsza sciezke start /rest/ finish</returns>
public static List <int> BellmanFord(DirectedGraphMatrix g, int start, int finish)
{
const int INF = int.MaxValue - 1000; //uzywam jako nieskonczonosci
var map = new Dictionary <int, Tuple <int, int> >(); //nr wierzch. < odleglosc, skad przyszedl >
for (int i = 0; i < g.NodesNr; i++)
{
if (i == start)
{
map.Add(i, new Tuple <int, int>(0, -1));
}
else
{
map.Add(i, new Tuple <int, int>(INF, -1));
}
}
var con = new List <Tuple <int, int, int> >();//lista polaczen skad / dokad / waga
for (int i = 0; i < g.NodesNr; i++)
{
for (int j = 0; j < g.NodesNr; j++)
{
if (g.GetConnection(i, j))
{
con.Add(new Tuple <int, int, int>(i, j, g.getWeight(i, j)));
}
}
}
for (int i = 0; i < g.NodesNr - 1; i++)
{
for (int j = 0; j < con.Count; j++)
{
if (map[con[j].Item2].Item1 == INF && map[con[j].Item1].Item1 == INF)//pozbywam sie operacji na nieskonczonosciach
{
continue;
}
if (map[con[j].Item2].Item1 > map[con[j].Item1].Item1 + con[j].Item3)//relaksacja
{
map[con[j].Item2] = new Tuple <int, int>(map[con[j].Item1].Item1 + con[j].Item3, con[j].Item1);
}
}
}
//sprawdzenie czy istnieje cykl ujemny
//jesli wykona sie warunek istnieje ujemny
for (int j = 0; j < con.Count; j++)
{
if (map[con[j].Item2].Item1 > map[con[j].Item1].Item1 + con[j].Item3) //relaksacja
{
return(null); //jesli relaksacja jest możliwa po V-1 przejściach istnieje cykl ujemny
}
}
//sciezka wynikowa
List <int> path = new List <int>();
recBellman(map, path, start, finish); //sciezke otrzymamy od konca
if (path.Count == 1) //brak sciezki
{
return(null);
}
path.Reverse();
return(path);
}
