Submission #1082927

#	Time	Username	Problem	Language	Result	Execution time	Memory
1082927		avighna	Aesthetic (NOI20_aesthetic)	C++17	51 / 100	2060 ms	65052 KiB

Aesthetic

#include <bits/stdc++.h>

typedef long long ll;

struct To {
  ll v, w;
  ll i;
};

const ll inf = 1e15;

int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);

  ll n, m;
  std::cin >> n >> m;
  std::vector<std::vector<To>> adj(n + 1);
  std::vector<ll> roads(m);
  std::vector<std::pair<ll, ll>> edges;
  for (ll i = 0, u, v, w; i < m; ++i) {
    std::cin >> u >> v >> w;
    adj[u].push_back({v, w, i});
    adj[v].push_back({u, w, i});
    roads[i] = w;
    edges.push_back({u, v});
  }

  if (m == n - 1) {
    // there will only be one path
    std::set<ll> edges;
    std::function<bool(ll, ll)> dfs;
    ll def = 0;
    dfs = [&](ll node, ll par) {
      if (node == n) {
        return true;
      }
      for (auto &[ch, w, i] : adj[node]) {
        if (ch == par) {
          continue;
        }
        if (dfs(ch, node)) {
          edges.insert(i);
          def += w;
          return true;
        }
      }
      return false;
    };
    dfs(1, 0);

    ll ans = def;
    ll worst_road = roads[m - 1];
    for (ll i = m - 2; i >= 0; --i) {
      if (edges.count(i)) {
        ans = std::max(ans, def + worst_road);
      }
      worst_road = std::max(worst_road, roads[i]);
    }
    std::cout << ans << '\n';

    return 0;
  }

  if (m == n) {
    // find the cycle
    std::vector<std::pair<ll, ll>> up(n + 1);
    std::function<void(ll, ll)> dfs;
    std::vector<bool> vis(n + 1);
    bool found = false;
    ll begin_node = -1;
    dfs = [&](ll node, ll par) {
      if (found) {
        return;
      }
      if (vis[node]) {
        return;
      }
      vis[node] = true;
      for (auto &[ch, w, i] : adj[node]) {
        if (ch == par) {
          continue;
        }
        up[ch] = {node, i};
        if (vis[ch]) {
          begin_node = node;
          found = true;
          return;
        }
        dfs(ch, node);
        if (found) {
          return;
        }
      };
    };
    dfs(1, 0);
    std::set<ll> cycle_edegs;
    ll tot_cyc_wt = 0;
    if (found) {
      vis.assign(n + 1, false);
      while (!vis[begin_node]) {
        vis[begin_node] = true;
        cycle_edegs.insert(up[begin_node].second);
        tot_cyc_wt += roads[up[begin_node].second];
        begin_node = up[begin_node].first;
      }
    }

    std::set<ll> shortest_path_edges;
    ll shortest_cyc_wt = 0;
    ll def = 0;
    auto sssp = [&]() {
      std::vector<ll> ans(n + 1, inf);
      std::vector<bool> vis(n + 1);
      std::vector<std::pair<ll, ll>> up(n + 1);
      std::priority_queue<std::pair<ll, ll>> pq;
      pq.push({0, 1});
      while (!pq.empty()) {
        auto [d, node] = pq.top();
        d *= -1;
        pq.pop();
        if (vis[node]) {
          continue;
        }
        vis[node] = true;
        for (auto [ch, w, cur_i] : adj[node]) {
          if (ans[ch] > d + w) {
            up[ch] = {node, cur_i};
            ans[ch] = d + w;
            pq.push({-ans[ch], ch});
          }
        }
      }
      def = ans[n];
      ll end = n;
      while (end != 1) {
        shortest_path_edges.insert(up[end].second);
        if (cycle_edegs.count(up[end].second)) {
          shortest_cyc_wt += roads[up[end].second];
        }
        end = up[end].first;
      }
    };
    sssp();

    ll ans = def;
    ll worst_road = roads[m - 1];
    for (ll i = m - 2; i >= 0; --i) {
      if (shortest_path_edges.count(i)) {
        if (cycle_edegs.count(i)) {
          ans = std::max(ans, std::min(def + worst_road,
                                       def - 2 * shortest_cyc_wt + tot_cyc_wt));
        } else {
          ans = std::max(ans, def + worst_road);
        }
      }
      worst_road = std::max(worst_road, roads[i]);
    }
    std::cout << ans << '\n';

    return 0;
  };

  if (*std::max_element(roads.begin(), roads.end()) == 1 and
      *std::min_element(roads.begin(), roads.end()) == 1) {
    // w_i = 1
    auto sssp = [&](ll node) {
      std::vector<ll> ans(n + 1, inf);
      std::vector<bool> vis(n + 1);
      std::priority_queue<std::pair<ll, ll>> pq;
      ans[node] = 0;
      pq.push({0, node});
      while (!pq.empty()) {
        auto [d, node] = pq.top();
        d *= -1;
        pq.pop();
        if (vis[node]) {
          continue;
        }
        vis[node] = true;
        for (auto [ch, w, cur_i] : adj[node]) {
          if (ans[ch] > d + w) {
            ans[ch] = d + w;
            pq.push({-ans[ch], ch});
          }
        }
      }
      return ans;
    };

    auto sssp1 = sssp(1);
    auto ssspn = sssp(n);
    std::set<ll> special_edges;
    std::map<std::pair<ll, ll>, ll> edge_starts;
    for (ll i = 0; i < edges.size(); ++i) {
      auto [u, v] = edges[i];
      if (std::min(sssp1[u] + 1 + ssspn[v], sssp1[v] + 1 + ssspn[u]) ==
          sssp1[n]) {
        special_edges.insert(i);
        if (sssp1[u] + 1 + ssspn[v] == sssp1[n]) {
          edge_starts[{sssp1[u], ssspn[v]}]++;
        } else {
          edge_starts[{sssp1[v], ssspn[u]}]++;
        }
      }
    }

    ll ans = sssp1[n];
    for (ll i = 0; i <= m - 2; ++i) {
      auto [u, v] = edges[i];
      if (special_edges.count(i) and
          ((edge_starts[{sssp1[u], ssspn[v]}] == 1 and
            sssp1[u] + 1 + ssspn[v] == sssp1[n]) or
           (edge_starts[{sssp1[v], sssp1[u]}] == 1 and
            sssp1[v] + 1 + ssspn[u]))) {
        ans = std::max(ans, sssp1[n] + 1);
      }
    }
    std::cout << ans << '\n';
    return 0;
  }

  // exclude edge i
  auto sssp = [&](ll i, ll add) {
    std::vector<ll> ans(n + 1, inf);
    std::vector<bool> vis(n + 1);
    std::priority_queue<std::pair<ll, ll>> pq;
    pq.push({0, 1});
    while (!pq.empty()) {
      auto [d, node] = pq.top();
      d *= -1;
      pq.pop();
      if (vis[node]) {
        continue;
      }
      vis[node] = true;
      for (auto [ch, w, cur_i] : adj[node]) {
        if (cur_i == i) {
          w += add;
        }
        if (ans[ch] > d + w) {
          ans[ch] = d + w;
          pq.push({-ans[ch], ch});
        }
      }
    }
    return ans;
  };

  ll def = sssp(-1, 0)[n];
  ll ans = def;
  ll worst_road = roads[m - 1];
  for (ll i = m - 2; i >= 0; --i) {
    ans = std::max(ans, sssp(i, worst_road)[n]);
    worst_road = std::max(worst_road, roads[i]);
  }
  std::cout << ans << '\n';
}

Compilation message (stderr)

Aesthetic.cpp: In function 'int main()':
Aesthetic.cpp:195:22: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  195 |     for (ll i = 0; i < edges.size(); ++i) {
      |                    ~~^~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 8 / 8
• Subtask 3: 7 / 7
• Subtask 4: 15 / 15
• Subtask 5: 16 / 16
• Subtask 6: 0 / 22
• Subtask 7: 0 / 27