Shorter and faster Hopcroft-Karp implementation (#308)

Author: ahsoltan

content/graph/hopcroftKarp.h

@@ -1,61 +1,34 @@
 /**
- * Author: Chen Xing
- * Date: 2009-10-13
+ * Author: Adam Soltan
+ * Date: 2026-01-13
  * License: CC0
- * Source: N/A
  * Description: Fast bipartite matching algorithm. Graph $g$ should be a list
- * of neighbors of the left partition, and $btoa$ should be a vector full of
- * -1's of the same size as the right partition. Returns the size of
- * the matching. $btoa[i]$ will be the match for vertex $i$ on the right side,
+ * of neighbors of the left partition, and $r$ should be a vector full of
+ * $-1$'s of the same size as the right partition. Returns the size of
+ * the matching. $r[i]$ will be the match for vertex $i$ on the right side,
  * or $-1$ if it's not matched.
- * Usage: vi btoa(m, -1); hopcroftKarp(g, btoa);
- * Time: O(\sqrt{V}E)
- * Status: stress-tested by MinimumVertexCover, and tested on oldkattis.adkbipmatch and SPOJ:MATCHING
+ * Time: O(E \sqrt{V})
+ * Status: stress-tested by MinimumVertexCover and tested on Library Checker
  */
 #pragma once
 
-bool dfs(int a, int L, vector<vi>& g, vi& btoa, vi& A, vi& B) {
-	if (A[a] != L) return 0;
-	A[a] = -1;
-	for (int b : g[a]) if (B[b] == L + 1) {
-		B[b] = 0;
-		if (btoa[b] == -1 || dfs(btoa[b], L + 1, g, btoa, A, B))
-			return btoa[b] = a, 1;
-	}
-	return 0;
-}
-
-int hopcroftKarp(vector<vi>& g, vi& btoa) {
-	int res = 0;
-	vi A(g.size()), B(btoa.size()), cur, next;
-	for (;;) {
-		fill(all(A), 0);
-		fill(all(B), 0);
-		/// Find the starting nodes for BFS (i.e. layer 0).
-		cur.clear();
-		for (int a : btoa) if(a != -1) A[a] = -1;
-		rep(a,0,sz(g)) if(A[a] == 0) cur.push_back(a);
-		/// Find all layers using bfs.
-		for (int lay = 1;; lay++) {
-			bool islast = 0;
-			next.clear();
-			for (int a : cur) for (int b : g[a]) {
-				if (btoa[b] == -1) {
-					B[b] = lay;
-					islast = 1;
-				}
-				else if (btoa[b] != a && !B[b]) {
-					B[b] = lay;
-					next.push_back(btoa[b]);
-				}
-			}
-			if (islast) break;
-			if (next.empty()) return res;
-			for (int a : next) A[a] = lay;
-			cur.swap(next);
+int hopcroftKarp(vector<vi>& g, vi& r) {
+	int n = sz(g), res = 0;
+	vi l(n, -1), q(n), d(n);
+	auto dfs = [&](auto f, int u) -> bool {
+		int t = exchange(d[u], 0) + 1;
+		for (int v : g[u])
+			if (r[v] == -1 || (d[r[v]] == t && f(f, r[v])))
+				return l[u] = v, r[v] = u, 1;
+		return 0;
+	};
+	for (int t = 0, f = 0;; t = f = 0, d.assign(n, 0)) {
+		rep(i,0,n) if (l[i] == -1) q[t++] = i, d[i] = 1;
+		rep(i,0,t) for (int v : g[q[i]]) {
+			if (r[v] == -1) f = 1;
+			else if (!d[r[v]]) d[r[v]] = d[q[i]] + 1, q[t++] = r[v];
 		}
-		/// Use DFS to scan for augmenting paths.
-		rep(a,0,sz(g))
-			res += dfs(a, 0, g, btoa, A, B);
+		if (!f) return res;
+		rep(i,0,n) if (l[i] == -1) res += dfs(dfs, i);
 	}
 }