From 38091746483e481f3ab4157f736735def7a23f0b Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Sat, 18 May 2024 22:47:27 +0800
Subject: [PATCH] Add graph/mcmf.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 graph/mcmf.cc | 77 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 graph/mcmf.cc

diff --git a/graph/mcmf.cc b/graph/mcmf.cc
new file mode 100644
index 0000000..ec0b030
--- /dev/null
+++ b/graph/mcmf.cc
@@ -0,0 +1,77 @@
+struct mcmf {
+    struct edge {
+        int to;
+        ll cap;
+        ll flow;
+        ll cost;
+        int rev;
+    };
+
+    vector<vector<edge>> edges;
+    vector<ll> dis;
+    vector<bool> vis;
+    ll ret;
+
+    mcmf(int n) : edges(n + 1), dis(n + 1), vis(n + 1) {}
+
+    void add_edge(int from, int to, ll cap, ll cost) {
+        edges[from].push_back({ to, cap, 0, cost, int(edges[to].size()) });
+        edges[to].push_back({ from, 0, 0, -cost, int(edges[from].size() - 1)});
+    }
+
+    bool sp(int s, int t) {
+        dis.assign(edges.size(), INFLL);
+        dis[s] = 0;
+        int n = edges.size();
+        int f = 1;
+        while (f) {
+            f = 0;
+            for (int i = 0; i < n; ++i) {
+                for (auto&& [to, cap, flow, cost, rev] : edges[i]) {
+                    if (cap > flow and dis[to] > dis[i] + cost) {
+                        dis[to] = dis[i] + cost;
+                        f = 1;
+                    }
+                }
+            }
+        }
+        return dis[t] != INFLL;
+    }
+
+    ll dfs(int s, int t, ll cap) {
+        if (vis[s]) {
+            return 0;
+        }
+        vis[s] = 1;
+        if (s == t) {
+            return cap;
+        }
+        ll res = 0;
+        int n = edges[s].size();
+        for (int i = 0; i < n; ++i) {
+            auto e = edges[s][i];
+            if (e.cap > e.flow and dis[e.to] == dis[s] + e.cost) {
+                ll nw = dfs(e.to, t, min(cap - res, e.cap - e.flow));
+                edges[s][i].flow += nw;
+                edges[e.to][e.rev].flow -= nw;
+                res += nw;
+                ret += nw * e.cost;
+                if (res == cap) {
+                    return res;
+                }
+            }
+        }
+        return res;
+    }
+
+    // returns: (flow, cost)
+    pll run(int s, int t) {
+        ll res = 0; ret = 0;
+        while (sp(s, t)) {
+            vis.assign(edges.size(), 0);
+            ll curr = dfs(s, t, LLONG_MAX);
+            res += curr;
+        }
+        return { res, ret };
+    }
+};