From 57bb611284c40de7203759d184c8f8b8142ca752 Mon Sep 17 00:00:00 2001
From: Kyungmo Ku <46951576+Pentagon03@users.noreply.github.com>
Date: Fri, 2 Aug 2024 23:13:35 +0900
Subject: [PATCH] Create MCMF.cpp

---
 Flow/MCMF.cpp | 81 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 81 insertions(+)
 create mode 100644 Flow/MCMF.cpp

diff --git a/Flow/MCMF.cpp b/Flow/MCMF.cpp
new file mode 100644
index 0000000..a266f13
--- /dev/null
+++ b/Flow/MCMF.cpp
@@ -0,0 +1,81 @@
+// hijkl2e, https://www.acmicpc.net/source/62155473
+template<typename Cap, typename Cost>
+class mcf_graph {
+public:
+	using edge = tuple<int, Cap, int, Cost>;
+    Cost mxcost{};
+	mcf_graph(int V) : G(V), d(V), last(V), vst(V){ }
+	void add_edge(int u, int v, int cap, int cost, bool directed = true) {
+		G[u].push_back(E.size());
+		E.push_back({v, cap, 0, cost});
+		G[v].push_back(E.size());
+		E.push_back({u, 0, 0, -cost});
+		if (!directed) add_edge(v, u, cap, cost);
+	}
+    using pr = pair<Cap, Cost>;
+    vector<pr> slope(int s, int t, Cost max_cost){
+        mxcost = max_cost;
+        Cap mf{};
+        vector<pr> ans({pr{mf, tcost}});
+		while (spfa(s, t)) {
+			fill(last.begin(), last.end(), 0);
+			while (int f = dfs(s, t)) {
+				mf += f;
+                ans.push_back({mf, tcost});
+			}
+		}
+		return ans;
+    }
+	pr flow(int s, int t, Cost max_cost) {
+        return slope(s, t, max_cost).back();
+	}
+private:
+	bool spfa(int s, int t) {
+		fill(d.begin(), d.end(), mxcost);
+		queue<int> q;
+		d[s] = 0, vst[s] = true;
+		q.push(s);
+		while (q.size()) {
+			int u = q.front(); q.pop();
+			vst[u] = false;
+			for (int idx : G[u]) {
+				auto &[v, cap, flow, cost] = E[idx];
+				if (d[v] > d[u] + cost && flow < cap) {
+					d[v] = d[u] + cost;
+					if (!vst[v]) {
+						vst[v] = true;
+						q.push(v);
+					}
+				}
+			}
+		}
+		return d[t] < mxcost;
+	}
+	Cap dfs(int u, int t, int f = inf) {
+		if (u == t) {
+			return f;
+		}
+		vst[u] = true;
+		for (int &i = last[u]; i < G[u].size(); ++i) {
+			auto &[v, cap, flow, cost] = E[G[u][i]];
+			if (!vst[v] && d[v] == d[u] + cost && flow < cap) {
+				if (Cap pushed = dfs(v, t, min(f, cap - flow))) {
+					tcost += pushed * cost;
+					flow += pushed;
+					auto &rflow = get<2>(E[G[u][i] ^ 1]);
+					rflow -= pushed;
+					vst[u] = false;
+					return pushed;
+				}
+			}
+		}
+		vst[u] = false;
+		return 0;
+	}
+	vector<edge> E;
+	vector<vector<int>> G;
+	vector<Cost> d;
+	vector<int> last;
+	vector<bool> vst;
+	Cost tcost{};
+};