Add graph/edmonds-karp.cc

Signed-off-by: subcrip <contact@subc.rip>

graph/edmonds-karp.cc

@@ -0,0 +1,55 @@
+struct edmonds_karp {
+    struct edge {
+        int to;
+        ll cap;
+        ll flow;
+        pair<int, int> rev;
+    };
+
+    vector<vector<edge>> edges;
+
+    edmonds_karp(int n) : edges(n + 1) {}
+
+    void add_edge(int from, int to, ll cap) {
+        edges[from].push_back({to, cap, 0, make_pair(to, int(edges[to].size()))});
+        edges[to].push_back({from, 0, 0, make_pair(from, int(edges[from].size() - 1))});
+    }
+
+    ll run(int s, int t) {
+        int n = edges.size();
+        vector<pii> pa_(n + 1);
+        ll res = 0;
+        while (1) {
+            vector<ll> pf(n + 1);
+            deque<int> dq;
+            dq.emplace_back(s);
+            pf[s] = LLONG_MAX;
+            while (dq.size()) {
+                int v = dq.front(); dq.pop_front();
+                for (auto&& [i, ne] : enumerate(edges[v])) {
+                    if (pf[ne.to] == 0 and ne.cap > ne.flow) {
+                        pf[ne.to] = min(pf[v], ne.cap - ne.flow);
+                        pa_[ne.to] = {v, i};
+                        dq.emplace_back(ne.to);
+                    }
+                }
+                if (pf[t] != 0) {
+                    break;
+                }
+            }
+            if (pf[t] == 0) {
+                break;
+            }
+            int p = t;
+            while (pa_[p].first != 0) {
+                auto [x, y] = pa_[p];
+                edges[x][y].flow += pf[t];
+                auto [z, w] = edges[x][y].rev;
+                edges[z][w].flow -= pf[t];
+                p = x;
+            }
+            res += pf[t];
+        }
+        return res;
+    }
+};