Submission #403977

#	Time	Username	Problem	Language	Result	Execution time	Memory
403977		rama_pang	Love Polygon (BOI18_polygon)	C++17	100 / 100	319 ms	36376 KiB

polygon

#include <bits/stdc++.h>
using namespace std;

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N;
  cin >> N;
  vector<int> to(N);

  const auto GetName = [&](string s) {
    static map<string, int> mp;
    if (mp.count(s)) return mp[s];
    return mp[s] = mp.size();
  };

  for (int i = 0; i < N; i++) {
    string s, t;
    cin >> s >> t;
    int u = GetName(s);
    int v = GetName(t);
    to[u] = v;
  }

  if (N & 1) {
    cout << -1 << '\n';
    return 0;
  }

  const auto SolveTree = [&](vector<int> nodes) -> int {
    static vector<int> dp0(N), dp1(N);
    static vector<vector<int>> adj(N);
    for (auto u : nodes) adj[u].clear();

    int root = -1;
    for (auto u : nodes) {
      if (to[u] == u) {
        assert(root == -1);
        root = u;
      } else {
        adj[to[u]].emplace_back(u);
      }
    }

    const auto Dfs = [&](const auto &self, int u) -> void {
      // If we don't use arrow on v:
      // - Must use arrow on u
      // - Must use arrow on other children of u
      // - Must use arrow on children of v
      // dp0[u] = don't use arrow on u
      // dp1[u] = use arrow on u
      dp0[u] = 0;
      dp1[u] = to[u] == u ? -1e9 : 1;

      int sum0 = 0;
      for (auto v : adj[u]) {
        self(self, v);
        sum0 += dp0[v];
      }
      dp0[u] += sum0;
      dp1[u] += sum0;
      for (auto v : adj[u]) {
        dp0[u] = max(dp0[u], sum0 - dp0[v] + dp1[v]);
      }
    };

    assert(root != -1);
    Dfs(Dfs, root);
    return max(dp0[root], dp1[root]);
  };

  const auto SolveForest = [&](vector<int> nodes) -> int {
    static vector<int> vis(N);
    static vector<vector<int>> adj(N);
    for (auto u : nodes) vis[u] = 0;
    for (auto u : nodes) adj[u].clear();

    for (auto u : nodes) {
      adj[u].emplace_back(to[u]);
      adj[to[u]].emplace_back(u);
    }

    int ans = 0;
    for (auto i : nodes) if (!vis[i]) {
      vis[i] = 1;
      vector<int> que = {i};
      for (int j = 0; j < int(que.size()); j++) {
        int u = que[j];
        for (auto v : adj[u]) if (!vis[v]) {
          vis[v] = 1;
          que.emplace_back(v);
        }
      }
      ans += SolveTree(que);
    }

    return ans;
  };

  const auto Solve = [&](vector<int> nodes) -> int {
    static vector<int> indeg(N);
    static vector<int> in_cycle(N);
    for (auto u : nodes) indeg[u] = 0;
    for (auto u : nodes) in_cycle[u] = 1;

    for (auto u : nodes) {
      indeg[to[u]]++;
    }

    vector<int> que;
    for (auto u : nodes) {
      if (indeg[u] == 0) {
        que.emplace_back(u);
      }
    }

    for (int i = 0; i < int(que.size()); i++) {
      int u = que[i];
      int v = to[u];
      indeg[v]--;
      in_cycle[u] = 0;
      if (indeg[v] == 0) {
        que.emplace_back(v);
      }
    }

    vector<int> cyc;
    for (auto u : nodes) if (in_cycle[u]) {
      cyc.emplace_back(u);
    }

    if (cyc.size() == 1) {
      return SolveTree(nodes);
    } else {
      int u = cyc[0];
      int v = to[u];
      assert(u != v);

      // Don't use (u, v)
      to[u] = u;
      int ans_1 = SolveTree(nodes);
      to[u] = v;

      // Use (u, v)
      vector<int> nn = nodes;
      nn.erase(find(begin(nn), end(nn), u));
      nn.erase(find(begin(nn), end(nn), v));
      for (auto x : nn) {
        if (to[x] == u || to[x] == v) {
          to[x] = x;
        }
      }
      int ans_2 = (to[u] == v) + (to[v] == u) + SolveForest(nn);

      return max(ans_1, ans_2);
    }
  };

  int ans = 0;
  vector<int> vis(N);
  vector<vector<int>> adj(N);
  for (int i = 0; i < N; i++) {
    adj[i].emplace_back(to[i]);
    adj[to[i]].emplace_back(i);
  }

  for (int i = 0; i < N; i++) if (!vis[i]) {
    vis[i] = 1;
    vector<int> que = {i};
    for (int j = 0; j < int(que.size()); j++) {
      int u = que[j];
      for (auto v : adj[u]) if (!vis[v]) {
        vis[v] = 1;
        que.emplace_back(v);
      }
    }
    ans += Solve(que);
  }

  cout << N - ans << '\n';
  return 0;
}

• Subtask 1: 21 / 21
• Subtask 2: 25 / 25
• Subtask 3: 29 / 29
• Subtask 4: 25 / 25