public static void MainTest(string[] args)
{
int V1 = int.Parse(args[0]);
int V2 = int.Parse(args[1]);
int E = int.Parse(args[2]);
int F = int.Parse(args[3]);
BipartiteX b;
// create random bipartite graph with V1 vertices on left side,
// V2 vertices on right side, and E edges; then add F random edges
Graph G = GraphGenerator.Bipartite(V1, V2, E);
Console.WriteLine("Graph is {0}\n", G);
b = new BipartiteX(G);
BipartiteXReport(b);
for (int i = 0; i < F; i++)
{
int v = StdRandom.Uniform(V1 + V2);
int w = StdRandom.Uniform(V1 + V2);
G.AddEdge(v, w);
}
Console.WriteLine("After adding {0} random edges", F);
Console.WriteLine("Graph is {0}\n", G);
b = new BipartiteX(G);
BipartiteXReport(b);
}
private int[] edgeTo; // edgeTo[v] = w if v-w is last edge on path to w
/// <summary>
/// Determines a maximum matching (and a minimum vertex cover)
/// in a bipartite graph.</summary>
/// <param name="G">the bipartite graph</param>
/// <exception cref="ArgumentException">if <c>G</c> is not bipartite</exception>
///
public BipartiteMatching(Graph G)
{
bipartition = new BipartiteX(G);
if (!bipartition.IsBipartite)
{
throw new ArgumentException("graph is not bipartite");
}
numVertices = G.V;
// initialize empty matching
mate = new int[numVertices];
for (int v = 0; v < numVertices; v++)
{
mate[v] = UNMATCHED;
}
// alternating path algorithm
while (hasAugmentingPath(G))
{
// find one endpoint t in alternating path
int t = -1;
for (int v = 0; v < numVertices; v++)
{
if (!IsMatched(v) && edgeTo[v] != -1)
{
t = v;
break;
}
}
// update the matching according to alternating path in edgeTo[] array
for (int v = t; v != -1; v = edgeTo[edgeTo[v]])
{
int w = edgeTo[v];
mate[v] = w;
mate[w] = v;
}
cardinality++;
}
// find min vertex cover from marked[] array
inMinVertexCover = new bool[numVertices];
for (int v = 0; v < numVertices; v++)
{
if (bipartition.Color(v) && !marked[v])
{
inMinVertexCover[v] = true;
}
if (!bipartition.Color(v) && marked[v])
{
inMinVertexCover[v] = true;
}
}
Debug.Assert(certifySolution(G));
}
private static void BipartiteXReport(BipartiteX b)
{
if (b.IsBipartite)
{
Graph G = b.G;
Console.WriteLine("Graph is bipartite");
for (int v = 0; v < G.V; v++)
{
Console.WriteLine(v + ": " + b.Color(v));
}
}
else
{
Console.Write("Graph has an odd-length cycle: ");
foreach (int x in b.OddCycle())
{
Console.Write(x + " ");
}
}
Console.WriteLine();
}
private int[] distTo; // distTo[v] = number of edges on shortest path to v
/// <summary>
/// Determines a maximum matching (and a minimum vertex cover)
/// in a bipartite graph.</summary>
/// <param name="G">the bipartite graph</param>
/// <exception cref="ArgumentException">if <c>G</c> is not bipartite</exception>
///
public HopcroftKarp(Graph G)
{
bipartition = new BipartiteX(G);
if (!bipartition.IsBipartite)
{
throw new ArgumentException("graph is not bipartite");
}
// initialize empty matching
this.V = G.V;
mate = new int[V];
for (int v = 0; v < V; v++)
{
mate[v] = UNMATCHED;
}
// the call to hasAugmentingPath() provides enough info to reconstruct level graph
while (hasAugmentingPath(G))
{
// to be able to iterate over each adjacency list, keeping track of which
// vertex in each adjacency list needs to be explored next
IEnumerator <int>[] adj = new IEnumerator <int> [G.V];
for (int v = 0; v < G.V; v++)
{
adj[v] = G.Adj(v).GetEnumerator();
}
// for each unmatched vertex s on one side of bipartition
for (int s = 0; s < V; s++)
{
if (IsMatched(s) || !bipartition.Color(s))
{
continue; // or use distTo[s] == 0
}
// find augmenting path from s using nonrecursive DFS
LinkedStack <int> path = new LinkedStack <int>();
path.Push(s);
while (!path.IsEmpty)
{
int v = path.Peek();
// retreat, no more edges in level graph leaving v
if (!adj[v].MoveNext())
{
path.Pop();
}
// advance
else
{
// process edge v-w only if it is an edge in level graph
int w = adj[v].Current;
if (!isLevelGraphEdge(v, w))
{
continue;
}
// add w to augmenting path
path.Push(w);
// augmenting path found: update the matching
if (!IsMatched(w))
{
// Console.WriteLine("augmenting path: " + toString(path));
while (!path.IsEmpty)
{
int x = path.Pop();
int y = path.Pop();
mate[x] = y;
mate[y] = x;
}
cardinality++;
}
}
}
}
}
// also find a min vertex cover
inMinVertexCover = new bool[V];
for (int v = 0; v < V; v++)
{
if (bipartition.Color(v) && !marked[v])
{
inMinVertexCover[v] = true;
}
if (!bipartition.Color(v) && marked[v])
{
inMinVertexCover[v] = true;
}
}
Debug.Assert(certifySolution(G));
}