From 5f9b1033c7d4ce5ffe4aaa9e000496aca2ad2a1b Mon Sep 17 00:00:00 2001
From: Baoshuo Ren <i@baoshuo.ren>
Date: Sat, 12 Mar 2022 08:54:56 +0800
Subject: [PATCH] =?UTF-8?q?2172.=20Dinic/ISAP=E6=B1=82=E6=9C=80=E5=A4=A7?=
 =?UTF-8?q?=E6=B5=81?=
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https://www.acwing.com/problem/content/submission/code_detail/11826004/
---
 AcWing/2172/2172.cpp | 86 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 86 insertions(+)
 create mode 100644 AcWing/2172/2172.cpp

diff --git a/AcWing/2172/2172.cpp b/AcWing/2172/2172.cpp
new file mode 100644
index 00000000..7eeea751
--- /dev/null
+++ b/AcWing/2172/2172.cpp
@@ -0,0 +1,86 @@
+#include <cstring>
+#include <iostream>
+#include <queue>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+int n, m, s, t, flow, ans;
+
+const int N = 10005,
+          M = 100005;
+
+// Graph
+int idx, head[N], edge[M << 1], ver[M << 1], next[M << 1];
+
+void add(int u, int v, int w) {
+    next[idx] = head[u];
+    edge[idx] = w;
+    ver[idx] = v;
+    head[u] = idx++;
+}
+
+// Dinic
+int d[N], cur[N];
+
+bool bfs() {
+    memset(d, 0x00, sizeof(d));
+    std::queue<int> q;
+    q.push(s);
+    d[s] = 1;
+    cur[s] = head[s];
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+        for (int i = head[u]; ~i; i = next[i]) {
+            int v = ver[i],
+                w = edge[i];
+            if (w && !d[v]) {
+                d[v] = d[u] + 1;
+                cur[v] = head[v];
+                if (v == t) return true;
+                q.push(v);
+            }
+        }
+    }
+    return false;
+}
+
+int dinic(int u, int limit) {
+    if (u == t) return limit;
+
+    int flow = 0;
+    for (int i = cur[u]; ~i && flow < limit; i = next[i]) {
+        cur[u] = i;
+
+        int v = ver[i];
+        if (d[v] == d[u] + 1 && edge[i]) {
+            int k = dinic(v, std::min(edge[i], limit - flow));
+            if (!k) d[v] = 0;
+            edge[i] -= k;
+            edge[i ^ 1] += k;
+            flow += k;
+        }
+    }
+    return flow;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    memset(head, 0xff, sizeof(head));
+    cin >> n >> m >> s >> t;
+    for (int i = 1; i <= m; i++) {
+        int u, v, w;
+        cin >> u >> v >> w;
+        add(u, v, w);
+        add(v, u, 0);
+    }
+
+    while (bfs()) {
+        while (flow = dinic(s, 0x3f3f3f3f)) ans += flow;
+    }
+
+    cout << ans << endl;
+    return 0;
+}