Added implementation of Dinic's (#82)

Author: Chillee

content/graph/Dinic.h

@@ -0,0 +1,50 @@
+/**
+ * Author: chilli
+ * Date: 2019-04-26
+ * License: CC0
+ * Source: https://cp-algorithms.com/graph/dinic.html
+ * Description: Flow algorithm with guaranteed complexity $O(V^2E)$.
+ * $O(\sqrt{V}E)$ for bipartite graphs, $O(\min(V^{1/2}, E^{2/3})E))$ for unit graphs.
+ * To obtain the actual flow, look at positive values only.
+ * Status: Tested on SPOJ FASTFLOW and SPOJ MATCHING
+ */
+struct Dinic {
+	struct Edge {
+		int to, rev;
+		ll c, f;
+	};
+	vi lvl, ptr, q;
+	vector<vector<Edge>> adj;
+	Dinic(int n) : lvl(n), ptr(n), q(n), adj(n) {}
+	void addEdge(int a, int b, ll c, int rcap = 0) {
+		adj[a].push_back({b, sz(adj[b]), c, 0});
+		adj[b].push_back({a, sz(adj[a]) - 1, rcap, 0});
+	}
+	ll dfs(int v, int t, ll f) {
+		if (v == t || !f) return f;
+		for (int& i = ptr[v]; i < sz(adj[v]); i++) {
+			Edge& e = adj[v][i];
+			if (lvl[e.to] == lvl[v] + 1)
+				if (ll p = dfs(e.to, t, min(f, e.c - e.f))) {
+					e.f += p, adj[e.to][e.rev].f -= p;
+					return p;
+				}
+		}
+		return 0;
+	}
+	ll calc(int s, int t) {
+		ll flow = 0; q[0] = s;
+		do {
+			lvl = ptr = vi(sz(q));
+			int qi = 0, qe = lvl[s] = 1;
+			while (qi < qe && !lvl[t]) {
+				int v = q[qi++];
+				trav(e, adj[v])
+					if (!lvl[e.to] && e.f < e.c)
+						q[qe++] = e.to, lvl[e.to] = lvl[v] + 1;
+			}
+			while (ll p = dfs(s, t, LLONG_MAX)) flow += p;
+		} while (lvl[t]);
+		return flow;
+	}
+};

content/graph/chapter.tex

@@ -12,6 +12,7 @@ \section{Network flow}
 	\kactlimport{PushRelabel.h}
 	\kactlimport{MinCostMaxFlow.h}
 	\kactlimport{EdmondsKarp.h}
+	% \kactlimport{Dinic.h}
 	\kactlimport{MinCut.h}
 	\kactlimport{GlobalMinCut.h}