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Submission #219759

# Submission time Handle Problem Language Result Execution time Memory
219759 2020-04-06T09:26:49 Z rama_pang Designated Cities (JOI19_designated_cities) C++14
100 / 100
 1316 ms 36056 KB 
#include <bits/stdc++.h>
using namespace std;
using lint = long long;

struct edge_t {
  int v;
  int away;
  int come;
  edge_t() {}
  edge_t(int v, int a, int c) : v(v), away(a), come(c) {}
};

int N;
vector<vector<edge_t>> adj;

vector<lint> Answer;
vector<lint> BaseCost; // BaseCost[i] = sum of all edges going to i (root at i), so we do not need to consider them afterwards
vector<bool> processed; // processed as R, done via centroid decomposition

vector<int> sz; // subtree size
vector<lint> optimal; // maximum weighted depth

void GenerateBaseCost() {
  vector<lint> dp(N);
  function<void(int, int)> dfs = [&](int n, int p) {
    for (const auto &i : adj[n]) if (i.v != p) {
      dfs(i.v, n);
      dp[n] += dp[i.v] + i.come;
    }
  };

  function<void(int, int)> reroot = [&](int n, int p) {
    BaseCost[n] = dp[n];
    for (const auto &i : adj[n]) if (i.v != p) {
      dp[n] -= dp[i.v] + i.come;
      dp[i.v] += dp[n] + i.away;
      reroot(i.v, n);
      dp[i.v] -= dp[n] + i.away;
      dp[n] += dp[i.v] + i.come;
    }
  };

  dfs(0, -1);
  reroot(0, -1);

}

int Centroid(int n) {
  function<void(int, int)> dfs = [&](int n, int p) {
    sz[n] = 1;
    for (const auto &i : adj[n]) if (i.v != p && !processed[i.v]) {
      dfs(i.v, n);
      sz[n] += sz[i.v];
    }
  };

  dfs(n, -1);
  int cur = n, p = -1;
  while (true) {
    pair<int, int> mx = {-1, -1};
    for (const auto &i : adj[cur]) if (i.v != p && !processed[i.v]) {
      mx = max(mx, {sz[i.v], i.v});
    }
    if (mx.first * 2 <= sz[n]) {
      return cur;
    }
    p = cur;
    cur = mx.second;
  }
}

void Solve(int R) {
  function<lint(int, int, vector<lint>&)> dfs = [&](int n, int p, vector<lint> &v) {
    lint cur = 0;
    for (const auto &i : adj[n]) if (i.v != p && !processed[i.v]) {
      lint nxt = dfs(i.v, n, v) + i.away;
      if (cur < nxt) swap(cur, nxt);
      if (nxt > 0) v.emplace_back(nxt);
    }
    return cur;
  };

  vector<lint> all;
  for (const auto &i : adj[R]) if (!processed[i.v]) {
    optimal[i.v] = dfs(i.v, R, all) + i.away;
    all.emplace_back(optimal[i.v]);
  }
  sort(begin(all), end(all), greater<lint>());

  { // Case #1: R is chosen
    lint sum = BaseCost[R]; 
    int cnt = 1;
    Answer[cnt] = max(Answer[cnt], sum);

    for (int i = 0; i < all.size(); i++) {
      sum += all[i], cnt++;
      Answer[cnt] = max(Answer[cnt], sum);
    }
  }

  { // Case #2: R is not chosen, two different subtrees
    pair<lint, lint> mx = {-1, -1};
    for (const auto &i : adj[R]) if (!processed[i.v]) {
      if (optimal[i.v] > mx.first) {
        mx.second = mx.first;
        mx.first = optimal[i.v];
      } else if (optimal[i.v] > mx.second) {
        mx.second = optimal[i.v];
      }
    }
    
    if (mx.first != -1 && mx.second != -1) {
     lint sum = BaseCost[R] + mx.first + mx.second; 
      int cnt = 2;
      Answer[cnt] = max(Answer[cnt], sum);

      for (int i = 0; i < all.size(); i++) {
        if (all[i] == mx.first) {
          mx.first = -1;
        } else if (all[i] == mx.second) {
          mx.second = -1;
        } else {
          sum += all[i], cnt++;
          Answer[cnt] = max(Answer[cnt], sum);
        }
      }
    }
  }
}

void CentroidDecomposition() {
  queue<int> q;
  q.emplace(0);
  while (!q.empty()) {
    int R = Centroid(q.front());
    q.pop();
    Solve(R);
    processed[R] = true;
    for (const auto &i : adj[R]) if (!processed[i.v]) {
      q.emplace(i.v);
    }
  }

  for (int i = 1; i <= N; i++) {
    Answer[i] = max(Answer[i], Answer[i - 1]);
  }
}


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

  cin >> N;

  sz.resize(N);  
  adj.resize(N);
  optimal.resize(N);
  BaseCost.resize(N);
  Answer.resize(N + 1);
  processed.resize(N, false);

  lint sum_all_costs = 0;
  for (int i = 0; i < N - 1; i++) {
    int A, B, C, D;
    cin >> A >> B >> C >> D;
    A--, B--;
    adj[A].emplace_back(B, C, D);
    adj[B].emplace_back(A, D, C);
    sum_all_costs += C + D;
  }

  GenerateBaseCost();
  CentroidDecomposition();

  int Q;
  cin >> Q;
  for (int i = 0; i < Q; i++) {
    int E;
    cin >> E;
    cout << (sum_all_costs - Answer[E]) << "\n";
  }

  return 0;
}

Compilation message

designated_cities.cpp: In function 'void Solve(int)':
designated_cities.cpp:95:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < all.size(); i++) {
                     ~~^~~~~~~~~~~~
designated_cities.cpp:117:25: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
       for (int i = 0; i < all.size(); i++) {
                       ~~^~~~~~~~~~~~

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 881 ms 20732 KB Output is correct
3 Correct 1258 ms 32344 KB Output is correct
4 Correct 824 ms 20956 KB Output is correct
5 Correct 438 ms 20892 KB Output is correct
6 Correct 1006 ms 23000 KB Output is correct
7 Correct 319 ms 21004 KB Output is correct
8 Correct 1272 ms 33544 KB Output is correct
9 Correct 213 ms 23180 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 874 ms 20980 KB Output is correct
3 Correct 1280 ms 35424 KB Output is correct
4 Correct 839 ms 21080 KB Output is correct
5 Correct 417 ms 21012 KB Output is correct
6 Correct 1039 ms 23600 KB Output is correct
7 Correct 261 ms 23308 KB Output is correct
8 Correct 1201 ms 29912 KB Output is correct
9 Correct 211 ms 23564 KB Output is correct

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 4 ms 384 KB Output is correct
13 Correct 7 ms 512 KB Output is correct
14 Correct 9 ms 640 KB Output is correct
15 Correct 7 ms 512 KB Output is correct
16 Correct 8 ms 640 KB Output is correct
17 Correct 8 ms 512 KB Output is correct
18 Correct 7 ms 512 KB Output is correct
19 Correct 7 ms 512 KB Output is correct
20 Correct 7 ms 512 KB Output is correct
21 Correct 8 ms 512 KB Output is correct
22 Correct 9 ms 512 KB Output is correct
23 Correct 7 ms 512 KB Output is correct
24 Correct 7 ms 548 KB Output is correct
25 Correct 8 ms 640 KB Output is correct
26 Correct 7 ms 640 KB Output is correct

Subtask #5
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 881 ms 20732 KB Output is correct
3 Correct 1258 ms 32344 KB Output is correct
4 Correct 824 ms 20956 KB Output is correct
5 Correct 438 ms 20892 KB Output is correct
6 Correct 1006 ms 23000 KB Output is correct
7 Correct 319 ms 21004 KB Output is correct
8 Correct 1272 ms 33544 KB Output is correct
9 Correct 213 ms 23180 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 874 ms 20980 KB Output is correct
12 Correct 1280 ms 35424 KB Output is correct
13 Correct 839 ms 21080 KB Output is correct
14 Correct 417 ms 21012 KB Output is correct
15 Correct 1039 ms 23600 KB Output is correct
16 Correct 261 ms 23308 KB Output is correct
17 Correct 1201 ms 29912 KB Output is correct
18 Correct 211 ms 23564 KB Output is correct
19 Correct 4 ms 384 KB Output is correct
20 Correct 884 ms 21552 KB Output is correct
21 Correct 1266 ms 36056 KB Output is correct
22 Correct 857 ms 21596 KB Output is correct
23 Correct 869 ms 21592 KB Output is correct
24 Correct 883 ms 21464 KB Output is correct
25 Correct 858 ms 21464 KB Output is correct
26 Correct 869 ms 21468 KB Output is correct
27 Correct 440 ms 21268 KB Output is correct
28 Correct 1054 ms 23512 KB Output is correct
29 Correct 867 ms 21448 KB Output is correct
30 Correct 761 ms 21904 KB Output is correct
31 Correct 307 ms 22796 KB Output is correct
32 Correct 1223 ms 30684 KB Output is correct
33 Correct 218 ms 24076 KB Output is correct

Subtask #6
44.0 / 44.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 881 ms 20732 KB Output is correct
14 Correct 1258 ms 32344 KB Output is correct
15 Correct 824 ms 20956 KB Output is correct
16 Correct 438 ms 20892 KB Output is correct
17 Correct 1006 ms 23000 KB Output is correct
18 Correct 319 ms 21004 KB Output is correct
19 Correct 1272 ms 33544 KB Output is correct
20 Correct 213 ms 23180 KB Output is correct
21 Correct 4 ms 384 KB Output is correct
22 Correct 874 ms 20980 KB Output is correct
23 Correct 1280 ms 35424 KB Output is correct
24 Correct 839 ms 21080 KB Output is correct
25 Correct 417 ms 21012 KB Output is correct
26 Correct 1039 ms 23600 KB Output is correct
27 Correct 261 ms 23308 KB Output is correct
28 Correct 1201 ms 29912 KB Output is correct
29 Correct 211 ms 23564 KB Output is correct
30 Correct 4 ms 384 KB Output is correct
31 Correct 7 ms 512 KB Output is correct
32 Correct 9 ms 640 KB Output is correct
33 Correct 7 ms 512 KB Output is correct
34 Correct 8 ms 640 KB Output is correct
35 Correct 8 ms 512 KB Output is correct
36 Correct 7 ms 512 KB Output is correct
37 Correct 7 ms 512 KB Output is correct
38 Correct 7 ms 512 KB Output is correct
39 Correct 8 ms 512 KB Output is correct
40 Correct 9 ms 512 KB Output is correct
41 Correct 7 ms 512 KB Output is correct
42 Correct 7 ms 548 KB Output is correct
43 Correct 8 ms 640 KB Output is correct
44 Correct 7 ms 640 KB Output is correct
45 Correct 4 ms 384 KB Output is correct
46 Correct 884 ms 21552 KB Output is correct
47 Correct 1266 ms 36056 KB Output is correct
48 Correct 857 ms 21596 KB Output is correct
49 Correct 869 ms 21592 KB Output is correct
50 Correct 883 ms 21464 KB Output is correct
51 Correct 858 ms 21464 KB Output is correct
52 Correct 869 ms 21468 KB Output is correct
53 Correct 440 ms 21268 KB Output is correct
54 Correct 1054 ms 23512 KB Output is correct
55 Correct 867 ms 21448 KB Output is correct
56 Correct 761 ms 21904 KB Output is correct
57 Correct 307 ms 22796 KB Output is correct
58 Correct 1223 ms 30684 KB Output is correct
59 Correct 218 ms 24076 KB Output is correct
60 Correct 4 ms 384 KB Output is correct
61 Correct 929 ms 23004 KB Output is correct
62 Correct 1316 ms 33892 KB Output is correct
63 Correct 896 ms 23020 KB Output is correct
64 Correct 883 ms 23120 KB Output is correct
65 Correct 885 ms 22876 KB Output is correct
66 Correct 903 ms 22876 KB Output is correct
67 Correct 904 ms 22872 KB Output is correct
68 Correct 486 ms 22936 KB Output is correct
69 Correct 1063 ms 24664 KB Output is correct
70 Correct 929 ms 22672 KB Output is correct
71 Correct 757 ms 23568 KB Output is correct
72 Correct 362 ms 23944 KB Output is correct
73 Correct 1269 ms 30484 KB Output is correct
74 Correct 258 ms 25328 KB Output is correct