teamnote history merge

2024fall/source/Graph/MCMF.cpp

@@ -0,0 +1,79 @@
+struct Edge
+{
+    int to, cap, now;
+    ll cost;
+    Edge* rev;
+    Edge(int to,int cap, ll cost)
+        :to(to), cap(cap), now(0), cost(cost){}
+    int left(){return cap - now;}
+    ll flow(int f)
+        {now += f; rev->now -= f; return cost * f;}
+    void reset(){now = 0;}
+};
+vector<Edge*> adj[N];
+Edge* hist[N]; ll dist[N]; bool inQueue[N], chk[N];
+bool spfa(int s, int t)
+{
+    memset(dist, 0, sizeof(dist));
+    memset(chk, 0, sizeof(chk)); chk[s] = true;
+
+    queue<int> q;
+    memset(inQueue, 0, sizeof(inQueue));
+    q.push(s); inQueue[s] = true;
+
+    while(!q.empty())
+    {
+        int now = q.front();
+        q.pop(); inQueue[now] = false;
+
+        for(auto e : adj[now])
+        {
+            int next = e->to;
+            if(e->left() > 0 and
+                  (chk[next] == false
+                         or dist[next] > dist[now] + e->cost))
+            {
+                chk[next] = true;
+                dist[next] = dist[now] + e->cost;
+                hist[next] = e;
+                if(!inQueue[next])
+                    q.push(next), inQueue[next] = true;
+            }
+        }
+    }
+    return chk[t];
+}
+// cost가 들어가면 항상 단방향만 가능하다. (양방향 : 2번 connect)
+void connect(int from, int to, int cap, ll cost)
+{
+    Edge *fw, *bw;
+    fw = new Edge(to, cap, cost);
+    bw = new Edge(from, 0, -cost);
+    fw->rev = bw; bw->rev = fw;
+    adj[from].push_back(fw);
+    adj[to].push_back(bw);
+}
+//maximum matching & minimum cost
+pair<ll, ll> flow(int S,int T)
+{
+    ll ans = 0; ll cost = 0;
+    while(spfa(S, T))
+    {
+        int m = 2e9;
+
+        int now = T;
+        while(S != now)
+        {
+            m = min(m, hist[now]->left());
+            now = hist[now]->rev->to;
+        }
+        now = T;
+        while(S != now)
+        {
+            cost += hist[now]->flow(m);
+            now = hist[now]->rev->to;
+        }
+        ans += m;
+    }
+    return {ans, cost};
+}