From cb5bd9618e6115da564bdf523c0da4d4b307d0f6 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Sat, 4 Feb 2023 15:39:58 +0800
Subject: [PATCH] F - Minimal k-covering

https://codeforces.com/contest/976/submission/192117447
---
 Codeforces/976/F/F.cpp | 179 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 179 insertions(+)
 create mode 100644 Codeforces/976/F/F.cpp

diff --git a/Codeforces/976/F/F.cpp b/Codeforces/976/F/F.cpp
new file mode 100644
index 00000000..633ff338
--- /dev/null
+++ b/Codeforces/976/F/F.cpp
@@ -0,0 +1,179 @@
+#include <iostream>
+#include <algorithm>
+#include <queue>
+#include <utility>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2005,
+          M = 4005;
+const int INF = 0x3f3f3f3f;
+
+int n1, n2, n, m, s, t, deg[N << 1];
+int idx, head[N << 1], ver[M << 3], edge[M << 3], next[M << 3];
+std::pair<int, int> edges[M];
+int id[M], dis[N << 1], cur[N << 1];
+
+void add(int u, int v, int w) {
+    next[idx] = head[u];
+    ver[idx] = v;
+    edge[idx] = w;
+    head[u] = idx++;
+}
+
+bool bfs() {
+    std::fill(std::begin(dis), std::end(dis), 0);
+
+    std::queue<int> q;
+
+    q.emplace(s);
+    dis[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 && !dis[v]) {
+                dis[v] = dis[u] + 1;
+                cur[v] = head[v];
+
+                if (v == t) return true;
+
+                q.emplace(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],
+            w = edge[i];
+
+        if (w && dis[v] == dis[u] + 1) {
+            int k = dinic(v, std::min(w, limit - flow));
+
+            if (!k) dis[v] = 0;
+
+            edge[i] -= k;
+            edge[i ^ 1] += k;
+            flow += k;
+        }
+    }
+
+    return flow;
+}
+
+void solve(int x) {
+    idx = 0;
+    std::fill(std::begin(head), std::end(head), -1);
+
+    s = 0, t = n + 1;
+
+    if (n1 < n2) {
+        for (int i = 1; i <= n1; i++) {
+            add(s, i, x);
+            add(i, s, 0);
+        }
+
+        for (int i = n1 + 1; i <= n; i++) {
+            add(i, t, x);
+            add(t, i, 0);
+        }
+
+        for (int i = 1; i <= m; i++) {
+            int u = edges[i].first,
+                v = edges[i].second;
+
+            id[i] = idx;
+            add(u, v, 1);
+            add(v, u, 0);
+        }
+    } else {
+        for (int i = 1; i <= n1; i++) {
+            add(i, t, x);
+            add(t, i, 0);
+        }
+
+        for (int i = n1 + 1; i <= n; i++) {
+            add(s, i, x);
+            add(i, s, 0);
+        }
+
+        for (int i = 1; i <= m; i++) {
+            int u = edges[i].first,
+                v = edges[i].second;
+
+            id[i] = idx;
+            add(v, u, 1);
+            add(u, v, 0);
+        }
+    }
+
+    while (bfs()) {
+        while (dinic(s, INF)) {}
+    }
+
+    for (int i = head[s]; ~i; i = next[i]) {
+        edge[i] = INF;
+    }
+
+    while (bfs()) {
+        while (dinic(s, INF)) {}
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n1 >> n2 >> m;
+
+    n = n1 + n2;
+
+    for (int i = 1, u, v; i <= m; i++) {
+        cin >> u >> v;
+
+        v += n1;
+        edges[i] = {u, v};
+        deg[u]++, deg[v]++;
+    }
+
+    int min = *std::min_element(deg + 1, deg + 1 + n);
+
+    for (int k = 0; k <= min; k++) {
+        std::vector<int> used_edges;
+
+        solve(k);
+
+        for (int i = 1; i <= m; i++) {
+            if (edge[id[i]] == 0) {
+                used_edges.emplace_back(i);
+            }
+        }
+
+        cout << used_edges.size() << ' ';
+
+        for (int x : used_edges) {
+            cout << x << ' ';
+        }
+
+        cout << endl;
+    }
+
+    return 0;
+}