feat: update to new kactl hopcroft_karp

Author: dariasc

lib/flow/hopcroft_karp.h

@@ -1,49 +1,29 @@
 #include "../template.h"
 /* -
 name = "Hopcroft Karp"
+source = "https://github.com/kth-competitive-programming/kactl/blob/main/content/graph/HopcroftKarp.h"
 [info]
-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` 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, or `-1` if it's not matched."
-usage = "`vi btoa(m, -1); hopcroftKarp(g, btoa);`"
+description = "Fast bipartite matching algorithm. Graph $g$ should be a list 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 r(m, -1); hopcroftKarp(g, r);`"
 time = "$O\\(sqrt(V) E\\)$" 
 - */
-bool dfs(int a, int L, vec<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(vec<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);
-    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);
-    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);
-    }
-    rep(a,0,sz(g))
-      res += dfs(a, 0, g, btoa, A, B);
-  }
+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];
+		}
+		if (!f) return res;
+		rep(i,0,n) if (l[i] == -1) res += dfs(dfs, i);
+	}
 }