rename maxCarBiMatch.cpp to kuhn.cpp

1 files changed, 25 insertions, 0 deletions

diff --git a/content/graph/kuhn.cpp b/content/graph/kuhn.cpp
new file mode 100644
index 0000000..e928387
--- /dev/null
+++ b/content/graph/kuhn.cpp
@@ -0,0 +1,25 @@
+vector<vector<int>> adj;
+vector<int> pairs; // Der gematchte Knoten oder -1.
+vector<bool> visited;
+
+bool dfs(int v) {
+	if (visited[v]) return false;
+	visited[v] = true;
+	for (int u : adj[v]) if (pairs[u] < 0 || dfs(pairs[u])) {
+		pairs[u] = v; pairs[v] = u; return true;
+	}
+	return false;
+}
+
+int kuhn(int l) { // l = #Knoten links.
+	pairs.assign(sz(adj), -1);
+	int ans = 0;
+	// Greedy Matching. Optionale Beschleunigung.
+	for (int v = 0; v < l; v++) for (int u : adj[v])
+		if (pairs[u] < 0) {pairs[u] = v; pairs[v] = u; ans++; break;}
+	for (int v = 0; v < l; v++) if (pairs[v] < 0) {
+		visited.assign(l, false);
+		ans += dfs(v);
+	}
+	return ans; // Größe des Matchings.
+}