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Submission #646009

# Submission time Handle Problem Language Result Execution time Memory
646009 2022-09-28T13:29:34 Z Alex_tz307 Paths (RMI21_paths) C++17
100 / 100
 461 ms 34660 KB 
#include <bits/stdc++.h>

using namespace std;

const int kN = 1e5;
int n, k;
int64_t sumK, sol[1 + kN];
pair<int64_t, int> dmax[1 + kN];
vector<pair<int, int>> g[1 + kN];
set<pair<int64_t, int>> paths[1 + kN];
multiset<int64_t> low, big;

void fix() {
  while ((int)big.size() < k && !low.empty()) {
    auto it = --low.end();
    big.emplace(*it);
    sumK += *it;
    low.erase(it);
  }

  if (low.empty() || big.empty()) {
    return;
  }

  int64_t last = *(--low.end()), first = *big.begin();
  while (first < last) {
    big.erase(big.begin());
    low.erase(--low.end());
    low.emplace(first);
    sumK -= first;
    big.emplace(last);
    sumK += last;
    last = *(--low.end());
    first = *big.begin();
  }
}

void add(int64_t x) {
  if ((int)big.size() < k) {
    big.emplace(x);
    sumK += x;
  } else {
    low.emplace(x);
    fix();
  }
}

void rem(int64_t x) {
  if (low.count(x)) {
    low.erase(low.find(x));
  } else {
    big.erase(big.find(x));
    sumK -= x;
    fix();
  }
}

void dfs1(int u, int par) {
  for (auto it : g[u]) {
    int v, w;
    tie(v, w) = it;

    if (v != par) {
      dfs1(v, u);

      if (paths[v].empty()) {
        paths[u].emplace(w, v);
      } else {
        paths[u].emplace((--paths[v].end())->first + w, v);
      }
    }
  }
}

void dfs2(int u, int par) {
  sol[u] = sumK;

  for (auto it : g[u]) {
    int v, w;
    tie(v, w) = it;

    if (v != par) {
      auto it1 = --paths[u].end();
      pair<int64_t, int> path1, removed{-1, -1};

      if (it1->second == v) {
        if ((int)paths[u].size() == 1) {
          path1 = {w, u};
        } else {
          auto it2 = --it1;
          path1 = {it2->first + w, u};
          removed = *it2;
        }
      } else {
        path1 = {it1->first + w, u};
        removed = *it1;
      }

      paths[v].emplace(path1);
      add(path1.first);
      if (removed.first != -1) {
        rem(removed.first);
      }

      pair<int64_t, int> path2{dmax[v].first + w, v};
      rem(path2.first);
      paths[v].emplace(dmax[v]);
      add(dmax[v].first);

      dfs2(v, u);

      rem(path1.first);
      if (removed.first != -1) {
        add(removed.first);
      }

      add(path2.first);
      rem(dmax[v].first);
    }
  }
}

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

  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    g[u].emplace_back(v, w);
    g[v].emplace_back(u, w);
  }

  dfs1(1, 0);

  for (int i = 1; i <= n; ++i) {
    if (!paths[i].empty()) {
      auto it = *(--paths[i].end());
      dmax[i] = it;
      if (i != 1) {
        paths[i].erase(it);
      }
    }

    for (auto it : paths[i]) {
      add(it.first);
    }

    while ((int)paths[i].size() > 1 + (i == 1)) {
      paths[i].erase(paths[i].begin());
    }
  }

  dfs2(1, 0);

  for (int i = 1; i <= n; ++i) {
    cout << sol[i] << '\n';
  }

  return 0;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct
3 Correct 5 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 6 ms 7380 KB Output is correct
7 Correct 6 ms 7380 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct
3 Correct 5 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 6 ms 7380 KB Output is correct
7 Correct 6 ms 7380 KB Output is correct
8 Correct 8 ms 7524 KB Output is correct
9 Correct 6 ms 7644 KB Output is correct
10 Correct 8 ms 7508 KB Output is correct
11 Correct 8 ms 7508 KB Output is correct
12 Correct 8 ms 7508 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct
3 Correct 5 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 6 ms 7380 KB Output is correct
7 Correct 6 ms 7380 KB Output is correct
8 Correct 8 ms 7524 KB Output is correct
9 Correct 6 ms 7644 KB Output is correct
10 Correct 8 ms 7508 KB Output is correct
11 Correct 8 ms 7508 KB Output is correct
12 Correct 8 ms 7508 KB Output is correct
13 Correct 11 ms 7784 KB Output is correct
14 Correct 10 ms 7892 KB Output is correct
15 Correct 9 ms 7716 KB Output is correct
16 Correct 9 ms 7808 KB Output is correct
17 Correct 11 ms 7776 KB Output is correct
18 Correct 8 ms 7764 KB Output is correct
19 Correct 9 ms 7764 KB Output is correct

Subtask #5
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 368 ms 31148 KB Output is correct
2 Correct 357 ms 33884 KB Output is correct
3 Correct 204 ms 27684 KB Output is correct
4 Correct 325 ms 30952 KB Output is correct
5 Correct 390 ms 32296 KB Output is correct
6 Correct 368 ms 30780 KB Output is correct

Subtask #6
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct
3 Correct 5 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 6 ms 7380 KB Output is correct
7 Correct 6 ms 7380 KB Output is correct
8 Correct 8 ms 7524 KB Output is correct
9 Correct 6 ms 7644 KB Output is correct
10 Correct 8 ms 7508 KB Output is correct
11 Correct 8 ms 7508 KB Output is correct
12 Correct 8 ms 7508 KB Output is correct
13 Correct 11 ms 7784 KB Output is correct
14 Correct 10 ms 7892 KB Output is correct
15 Correct 9 ms 7716 KB Output is correct
16 Correct 9 ms 7808 KB Output is correct
17 Correct 11 ms 7776 KB Output is correct
18 Correct 8 ms 7764 KB Output is correct
19 Correct 9 ms 7764 KB Output is correct
20 Correct 368 ms 31148 KB Output is correct
21 Correct 357 ms 33884 KB Output is correct
22 Correct 204 ms 27684 KB Output is correct
23 Correct 325 ms 30952 KB Output is correct
24 Correct 390 ms 32296 KB Output is correct
25 Correct 368 ms 30780 KB Output is correct
26 Correct 409 ms 31732 KB Output is correct
27 Correct 381 ms 33944 KB Output is correct
28 Correct 393 ms 34660 KB Output is correct
29 Correct 224 ms 27988 KB Output is correct
30 Correct 356 ms 31408 KB Output is correct
31 Correct 434 ms 30404 KB Output is correct
32 Correct 409 ms 32904 KB Output is correct
33 Correct 461 ms 31680 KB Output is correct
34 Correct 214 ms 27424 KB Output is correct
35 Correct 378 ms 31508 KB Output is correct
36 Correct 348 ms 34148 KB Output is correct