Add dinic

lib/Graph/dinic.h

@@ -0,0 +1,79 @@
+#pragma once
+#include "graph.h"
+#include "template.h"
+
+template <typename T>
+class Dinic {
+ private:
+  int V;  // 頂点数
+  vector<T> minCost;
+  vector<int> iter;
+  AdjList<T> graph;
+  const T INF = numeric_limits<T>::max() / 10;
+  bool Bfs(int s, int t);
+  T Dfs(int idx, const int t, T flow);
+
+ public:
+  explicit Dinic(int n);
+  void AddEdge(int from, int to, T cost);
+  T Run(int s, int t);
+};
+
+template <typename T>
+Dinic<T>::Dinic(int n) : V(n), graph(n) {}
+
+template <typename T>
+void Dinic<T>::AddEdge(int from, int to, T cost) {
+  graph[from].push_back(Edge<T>(static_cast<int>(graph[to].size()), to, cost));
+  graph[to].push_back(
+      Edge<T>(static_cast<int>(graph[from].size() - 1), from, 0));
+}
+
+template <typename T>
+bool Dinic<T>::Bfs(int s, int t) {
+  minCost.assign(graph.size(), -1);
+  queue<int> que;
+  minCost[s] = 0;
+  que.push(s);
+  while (!que.empty()) {
+    int p = que.front();
+    que.pop();
+    for (auto &e : graph[p]) {
+      if (e.cost > 0 && minCost[e.to] < 0) {
+        minCost[e.to] = minCost[p] + 1;
+        que.push(e.to);
+      }
+    }
+  }
+  return (minCost[t] != -1);
+}
+
+template <typename T>
+T Dinic<T>::Dfs(int idx, const int t, T flow) {
+  if (idx == t) return flow;
+  for (int &i = iter[idx]; i < graph[idx].size(); ++i) {
+    Edge<T> &e = graph[idx][i];
+    if (e.cost > 0 && minCost[idx] < minCost[e.to]) {
+      T d = Dfs(e.to, t, min(flow, e.cost));
+      if (d > 0) {
+        e.cost -= d;
+        graph[e.to][e.from].cost += d;
+        return d;
+      }
+    }
+  }
+  return 0;
+}
+
+template <typename T>
+T Dinic<T>::Run(int s, int t) {
+  T flow = 0;
+  while (Bfs(s, t)) {
+    iter.assign(graph.size(), 0);
+    T f = 0;
+    while ((f = Dfs(s, t, INF)) > 0) {
+      flow += f;
+    }
+  }
+  return flow;
+}