From 37bf6f1d9ad812ec84093bd56739375c9c6a4bd5 Mon Sep 17 00:00:00 2001
From: Macesuted <i@macesuted.moe>
Date: Fri, 4 Oct 2024 19:50:19 +0800
Subject: [PATCH] QOJ: Stop the Castle 2

---
 QOJ/9424.cpp | 144 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 144 insertions(+)
 create mode 100644 QOJ/9424.cpp

diff --git a/QOJ/9424.cpp b/QOJ/9424.cpp
new file mode 100644
index 0000000..48a6649
--- /dev/null
+++ b/QOJ/9424.cpp
@@ -0,0 +1,144 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+
+#define maxn 200005
+
+typedef pair<int, int> pii;
+
+class Dinic {
+   private:
+    struct Edge {
+        int to, cap, rev, id;
+    };
+
+    vector<vector<Edge>> graph;
+    vector<vector<Edge>::iterator> cur;
+    vector<int> dist;
+    queue<int> que;
+    int n, S, T;
+
+    bool bfs(void) {
+        for (int i = 1; i <= n; i++) dist[i] = INT_MAX, cur[i] = graph[i].begin();
+        que.push(S), dist[S] = 0;
+        while (!que.empty()) {
+            int p = que.front();
+            que.pop();
+            for (auto i : graph[p])
+                if (dist[i.to] > dist[p] + 1 && i.cap) dist[i.to] = dist[p] + 1, que.push(i.to);
+        }
+        return dist[T] != INT_MAX;
+    }
+    int dfs(int p, int rest) {
+        if (p == T) return rest;
+        int used = 0, c;
+        for (auto i = cur[p]; i != graph[p].end() && rest; i++) {
+            cur[p] = i;
+            if (!i->cap || dist[i->to] != dist[p] + 1) continue;
+            if (!(c = dfs(i->to, min(rest, i->cap)))) dist[i->to] = -1;
+            used += c, rest -= c, i->cap -= c, graph[i->to][i->rev].cap += c;
+        }
+        return used;
+    }
+
+   public:
+    vector<bool> avai;
+    set<int> edges[2];
+
+    void resize(int _n) { return n = _n, graph.resize(n + 1), cur.resize(n + 1), dist.resize(n + 1), avai.resize(n + 1); }
+    void addEdge(int from, int to, int cap, int id) {
+        return graph[from].push_back(Edge{to, cap, (int)graph[to].size(), id}),
+               graph[to].push_back(Edge{from, 0, (int)graph[from].size() - 1, 0});
+    }
+    int solve(int _S, int _T) {
+        S = _S, T = _T;
+        int flow = 0;
+        while (bfs()) flow += dfs(S, INT_MAX);
+        for (int i = 1; i <= n; i++)
+            for (auto j : graph[i])
+                if (j.id) edges[!j.cap].insert(j.id);
+        return flow;
+    }
+};
+
+map<int, set<pii>> R, C;
+int nx[maxn], ny[maxn];
+bool vis[maxn];
+vector<int> rec[maxn];
+
+void solve(void) {
+    R.clear(), C.clear();
+
+    int n, m, k;
+    cin >> n >> m >> k;
+
+    Dinic dnc;
+    int S = 2 * n + 1, T = S + 1;
+    dnc.resize(T);
+
+    for (int i = 1, x, y; i <= n; i++)
+        cin >> x >> y, R[x].emplace(y, i), C[y].emplace(x, i), dnc.addEdge(S, i, 1, 0), dnc.addEdge(n + i, T, 1, 0);
+    for (int i = 1; i <= 2 * n; i++) rec[i].clear(), vis[i] = false;
+    int ans = 0;
+    for (auto &i : R) ans += (int)i.second.size() - 1;
+    for (auto &i : C) ans += (int)i.second.size() - 1;
+    for (int i = 1, x, y; i <= m; i++) {
+        cin >> x >> y, nx[i] = -1, ny[i] = -1;
+        if (R.count(x)) {
+            auto p = R[x].lower_bound({y, 0});
+            if (p != R[x].begin() && p != R[x].end()) dnc.avai[nx[i] = p->second] = true;
+        }
+        if (C.count(y)) {
+            auto p = C[y].lower_bound({x, 0});
+            if (p != C[y].begin() && p != C[y].end()) dnc.avai[ny[i] = n + p->second] = true;
+        }
+        if (nx[i] != -1 && ny[i] != -1) dnc.addEdge(nx[i], ny[i], 1, i);
+    }
+    // cerr << "! " << ans << endl;
+    int cnt = m - k, flow = dnc.solve(S, T);
+    if (flow >= cnt) {
+        cout << ans - cnt * 2 << endl;
+        for (int i = 1; i <= m; i++)
+            if (!dnc.edges[1].count(i) || !cnt)
+                cout << i << ' ';
+            else
+                cnt--;
+        cout << endl;
+        return;
+    }
+    cnt -= flow, ans -= flow * 2;
+    for (int i = 1; i <= m; i++)
+        if (!dnc.edges[1].count(i)) {
+            if (nx[i] != -1) rec[nx[i]].push_back(i);
+            if (ny[i] != -1) rec[ny[i]].push_back(i);
+        } else
+            vis[nx[i]] = vis[ny[i]] = true;
+    // cerr << "# " << cnt << endl;
+    for (int i = 1; i <= m; i++) {
+        if (dnc.edges[1].count(i)) continue;
+        if (nx[i] != -1 && !vis[nx[i]] && cnt) vis[nx[i]] = true, dnc.edges[1].insert(i), ans--, cnt--;
+        if (ny[i] != -1 && !vis[ny[i]] && cnt) vis[ny[i]] = true, dnc.edges[1].insert(i), ans--, cnt--;
+    }
+    // cerr << "# " << cnt << endl;
+    for (int i = 1; i <= m; i++)
+        if (!dnc.edges[1].count(i) && cnt) dnc.edges[1].insert(i), cnt--;
+
+    // cerr << "###" << endl;
+    cout << ans << endl;
+    for (int i = 1; i <= m; i++)
+        if (!dnc.edges[1].count(i)) cout << i << ' ';
+    cout << endl;
+
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
+
+    int _ = 1;
+    cin >> _;
+    while (_--) solve();
+
+    return 0;
+}
\ No newline at end of file