private int[] distTo; // distTo[v] = number of edges on shortest path to v
/**
* Determines a maximum matching (and a minimum vertex cover)
* in a bipartite graph.
*
* @param G the bipartite graph
* @throws IllegalArgumentException if {@code G} is not bipartite
*/
public HopcroftKarp(Graph G) {
bipartition = new BipartiteX(G);
if (!bipartition.isBipartite()) {
throw new IllegalArgumentException("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
Iterator<Integer>[] adj = (Iterator<Integer>[]) new Iterator[G.V()];
for (int v = 0; v < G.V(); v++)
adj[v] = G.adj(v).iterator();
// 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
Stack<Integer> path = new Stack<Integer>();
path.push(s);
while (!path.isEmpty()) {
int v = path.peek();
// retreat, no more edges in level graph leaving v
if (!adj[v].hasNext())
path.pop();
// advance
else {
// process edge v-w only if it is an edge in level graph
int w = adj[v].next();
if (!isLevelGraphEdge(v, w)) continue;
// add w to augmenting path
path.push(w);
// augmenting path found: update the matching
if (!isMatched(w)) {
// StdOut.println("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 boolean[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;
}
assert certifySolution(G);
}
// is the edge v-w a forward edge not in the matching or a reverse edge in the matching?
private boolean isResidualGraphEdge(int v, int w) {
if ((mate[v] != w) && bipartition.color(v)) return true;
if ((mate[v] == w) && !bipartition.color(v)) return true;
return false;
}