rename Dinic to Dinitz

1 files changed, 57 insertions, 0 deletions

diff --git a/content/graph/dinitzScaling.cpp b/content/graph/dinitzScaling.cpp
new file mode 100644
index 0000000..fd82296
--- /dev/null
+++ b/content/graph/dinitzScaling.cpp
@@ -0,0 +1,57 @@
+struct Edge {
+	int to, rev;
+	ll f, c;
+};
+
+vector<vector<Edge>> adj;
+int s, t;
+vector<int> pt, dist;
+
+void addEdge(int u, int v, ll c) {
+	adj[u].push_back({v, (int)ssize(adj[v]), 0, c});
+	adj[v].push_back({u, (int)ssize(adj[u]) - 1, 0, 0});
+}
+
+bool bfs(ll lim) {
+	dist.assign(ssize(adj), -1);
+	dist[s] = 0;
+	queue<int> q({s});
+	while (!q.empty() && dist[t] < 0) {
+		int v = q.front(); q.pop();
+		for (Edge& e : adj[v]) {
+			if (dist[e.to] < 0 && e.c - e.f >= lim) {
+				dist[e.to] = dist[v] + 1;
+				q.push(e.to);
+	}}}
+	return dist[t] >= 0;
+}
+
+ll dfs(int v, ll flow) {
+	if (v == t || flow == 0) return flow;
+	for (; pt[v] < ssize(adj[v]); pt[v]++) {
+		Edge& e = adj[v][pt[v]];
+		if (dist[e.to] != dist[v] + 1) continue;
+		ll cur = dfs(e.to, min(e.c - e.f, flow));
+		if (cur > 0) {
+			e.f += cur;
+			adj[e.to][e.rev].f -= cur;
+			return cur;
+	}}
+	return 0;
+}
+
+ll maxFlow(int source, int target) {
+	s = source, t = target;
+	ll flow = 0;
+	// lim = 1 may be faster if capacities are small
+	for (ll lim = (1LL << 62); lim >= 1; lim /= 2) {
+		while (bfs(lim)) {
+			pt.assign(ssize(adj), 0);
+			ll cur;
+			do {
+				cur = dfs(s, lim);
+				flow += cur;
+			} while (cur > 0);
+	}}
+	return flow;
+}