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Submission #967325

# Submission time Handle Problem Language Result Execution time Memory
967325 2024-04-21T21:20:03 Z four_specks Beads and wires (APIO14_beads) C++17
100 / 100
 133 ms 36576 KB 
#include <bits/stdc++.h>

using namespace std;

namespace {

template <typename Fun>
struct YCombinator {
  template <typename T>
  YCombinator(T &&_fun) : fun(forward<T>(_fun)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) {
    return fun(ref(*this), forward<Args>(args)...);
  }

 private:
  Fun fun;
};

template <typename T>
YCombinator(T &&) -> YCombinator<decay_t<T>>;

}  // namespace

void solve() {
  int n;
  cin >> n;
  vector<vector<pair<int, long>>> adj(n);
  long low = -1;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    long x;
    cin >> u >> v >> x;
    --u;
    --v;
    adj[u].emplace_back(v, x);
    adj[v].emplace_back(u, x);
    low -= x;
  }
  // root at a leaf
  int root = -1;
  for (int u = 0; u < n; u++) {
    if ((int)adj[u].size() == 1) {
      root = u;
      break;
    }
  }
  // dp[u][0] = max val such that it is root and no splitting
  // dp[u][1] = max val such that it is root and has splitting
  // dp[u][2] = max val such that it is connected to parent and no splitting
  // dp[u][3] = max val such that it is connected to parent and has splitting
  vector<array<long, 4>> dp(n);
  YCombinator([&](auto self, int u, int p) -> void {
    vector<pair<int, long>> ch;
    for (auto [v, x] : adj[u]) {
      if (v != p) {
        ch.emplace_back(v, x);
        self(v, u);
      }
    }
    int k = (int)ch.size();
    vector<long> com(k);
    for (int i = 0; i < k; i++) {
      auto [v, x] = ch[i];
      com[i] = max(dp[v][0], x + dp[v][2]);
    }
    vector<long> pref(k + 1), suff(k + 1);
    for (int i = 0; i < k; i++) {
      pref[i + 1] = pref[i] + com[i];
    }
    for (int i = k - 1; i >= 0; i--) {
      suff[i] = suff[i + 1] + com[i];
    }
    dp[u][0] = pref[k];
    dp[u][1] = low;
    if (k >= 2) {
      // if split at u, can split in atmost one subtree of u
      array<long, 3> can;
      can.fill(2 * low);
      for (int i = 0; i < k; i++) {
        auto [v, x] = ch[i];
        can[2] = max(can[2] + com[i], max(can[0] + (x + max(dp[v][0], dp[v][1])), can[1] + (x + dp[v][0])));
        can[0] = max(can[0] + com[i], pref[i] + (x + dp[v][0]));
        can[1] = max(can[1] + com[i], pref[i] + (x + dp[v][1]));
      }
      dp[u][1] = max(dp[u][1], can[2]);
    }
    for (int i = 0; i < k; i++) {
      auto [v, x] = ch[i];
      dp[u][1] = max(dp[u][1], pref[i] + max(dp[v][1], x + dp[v][3]) + suff[i + 1]);
    }
    dp[u][2] = low;
    for (int i = 0; i < k; i++) {
      auto [v, x] = ch[i];
      dp[u][2] = max(dp[u][2], pref[i] + (x + dp[v][0]) + suff[i + 1]);
    }
    dp[u][3] = low;
    for (int i = 0; i < k; i++) {
      auto [v, x] = ch[i];
      dp[u][3] = max(dp[u][3], pref[i] + (x + dp[v][1]) + suff[i + 1]);
    }
  })(root, -1);
  long ans = max(dp[root][0], dp[root][1]);
  cout << ans << '\n';
}

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

  solve();

  return 0;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 456 KB Output is correct
22 Correct 0 ms 348 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 456 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 4 ms 912 KB Output is correct
24 Correct 2 ms 1112 KB Output is correct
25 Correct 3 ms 860 KB Output is correct
26 Correct 4 ms 1628 KB Output is correct
27 Correct 4 ms 1624 KB Output is correct
28 Correct 4 ms 2260 KB Output is correct
29 Correct 4 ms 1884 KB Output is correct
30 Correct 4 ms 1880 KB Output is correct
31 Correct 5 ms 2396 KB Output is correct

Subtask #4
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 456 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 4 ms 912 KB Output is correct
24 Correct 2 ms 1112 KB Output is correct
25 Correct 3 ms 860 KB Output is correct
26 Correct 4 ms 1628 KB Output is correct
27 Correct 4 ms 1624 KB Output is correct
28 Correct 4 ms 2260 KB Output is correct
29 Correct 4 ms 1884 KB Output is correct
30 Correct 4 ms 1880 KB Output is correct
31 Correct 5 ms 2396 KB Output is correct
32 Correct 21 ms 6492 KB Output is correct
33 Correct 20 ms 6492 KB Output is correct
34 Correct 20 ms 6524 KB Output is correct
35 Correct 113 ms 25188 KB Output is correct
36 Correct 126 ms 25196 KB Output is correct
37 Correct 130 ms 25096 KB Output is correct
38 Correct 102 ms 31380 KB Output is correct
39 Correct 94 ms 28460 KB Output is correct
40 Correct 100 ms 27952 KB Output is correct
41 Correct 133 ms 36576 KB Output is correct