oj.uz

Submission #216479

# Submission time Handle Problem Language Result Execution time Memory
216479 2020-03-27T11:02:59 Z AlexPop28 Capital City (JOI20_capital_city) C++11
100 / 100
 1020 ms 29932 KB 
#include <bits/stdc++.h>
#define dbg() cerr <<
#define name(x) (#x) << ": " << (x) << ' ' <<

using namespace std;

struct DSU {
  vector<int> dad, sz;
  DSU(int n = 0) : dad(n, -1), sz(n, 1) {}

  int Find(int x) {
    if (dad[x] == -1) return x;
    return dad[x] = Find(dad[x]);
  }

  bool Union(int x, int y) {
    x = Find(x), y = Find(y);
    if (x == y) return false;
    if (sz[x] < sz[y]) swap(x, y);
    dad[y] = x;
    sz[x] += sz[y];
    return true;
  }

  void Reset(int node) {
    dad[node] = -1;
    sz[node] = 1;
  }
};


struct Solver {
  int n, k, ans;
  
  DSU dsu;
  vector<bool> vis;
  vector<vector<int>> adj, city;
  vector<int> col, sz, nodes, dad, cnt;

  void Main() {
    cin >> n >> k;
    adj.resize(n);
    for (int i = 0; i < n - 1; ++i) {
      int a, b; cin >> a >> b; --a, --b;
      adj[a].emplace_back(b);
      adj[b].emplace_back(a);
    }
    col.resize(n);
    cnt.resize(k);
    for (int i = 0; i < n; ++i) {
      cin >> col[i]; --col[i];
      ++cnt[col[i]];
    }

    city.resize(k);
    dad.resize(n);
    vis.resize(n);
    dsu = DSU(k);
    sz.resize(n);
  
    ans = n;    
    Centroid(0);

    cout << ans << endl;
  }


  void GetSizes(int node, int par) {
    sz[node] = 1;
    nodes.emplace_back(node);
    for (int &x : adj[node]) {
      if (x == par || vis[x]) continue;
      GetSizes(x, node);
      sz[node] += sz[x];
    }
  }


  int GetCentroid(int node) {
    nodes.clear();
    GetSizes(node, -1);
    while (true) {
      bool br = true;
      for (int &x : adj[node]) {
        if (!vis[x] && sz[x] < sz[node] && 2 * sz[x] > (int)nodes.size()) {
          br = false;
          node = x;
          break;
        }
      }
      if (br) break;
    }
    return node;
  }


  void GetDads(int node, int par) {
    dad[node] = par;
    for (int &x : adj[node]) {
      if (x == par || vis[x]) continue;
      GetDads(x, node);
    }
  }


  void Centroid(int node) {
    node = GetCentroid(node);
    vis[node] = true;
    GetDads(node, -1);

    // dbg() "Begin: " << name(1 + node) endl;

    // dbg() "Nodes: ";
    for (int &x : nodes) {
    //   dbg() x << ' ';
      city[col[x]].emplace_back(x);
    }
    // dbg() endl;

    vector<int> q;
    for (int &x : city[col[node]]) {
      if (x != node)
        q.emplace_back(x);
    }

    int cnt_merges = 0;
    bool all_nodes_of_col = (int)city[col[node]].size() == cnt[col[node]];
    for (int it = 0; it < (int)q.size(); ++it) {
      int x = q[it];
      all_nodes_of_col &= (int)city[col[x]].size() == cnt[col[x]];
      if (dsu.Union(col[x], col[dad[x]])) {
        ++cnt_merges;
        for (int &y : city[col[dad[x]]]) {
          q.emplace_back(y);
        }
      }
    }

    if (all_nodes_of_col) {
      ans = min(ans, cnt_merges);
      // dbg() name(cnt_merges) name(1 + node) name(col[node]) endl;
    }

    for (int &x : nodes) {
      dsu.Reset(col[x]);
      city[col[x]].clear();
    }

    for (int &x : adj[node]) {
      if (!vis[x]) {
        Centroid(x);
      }
    }
    // dbg() "End: " << name(node) endl;
  }
};


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

  Solver solver;
  solver.Main();
}

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 336 KB Output is correct
5 Correct 4 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 4 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 336 KB Output is correct
5 Correct 4 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 4 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 6 ms 512 KB Output is correct
12 Correct 6 ms 512 KB Output is correct
13 Correct 6 ms 512 KB Output is correct
14 Correct 6 ms 512 KB Output is correct
15 Correct 7 ms 512 KB Output is correct
16 Correct 6 ms 512 KB Output is correct
17 Correct 6 ms 512 KB Output is correct
18 Correct 6 ms 512 KB Output is correct
19 Correct 6 ms 512 KB Output is correct
20 Correct 6 ms 512 KB Output is correct
21 Correct 6 ms 512 KB Output is correct
22 Correct 6 ms 640 KB Output is correct
23 Correct 7 ms 640 KB Output is correct
24 Correct 7 ms 768 KB Output is correct
25 Correct 7 ms 640 KB Output is correct
26 Correct 7 ms 640 KB Output is correct
27 Correct 7 ms 640 KB Output is correct
28 Correct 7 ms 640 KB Output is correct
29 Correct 7 ms 512 KB Output is correct
30 Correct 7 ms 512 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 722 ms 29548 KB Output is correct
2 Correct 293 ms 29676 KB Output is correct
3 Correct 992 ms 29388 KB Output is correct
4 Correct 311 ms 29804 KB Output is correct
5 Correct 864 ms 27600 KB Output is correct
6 Correct 294 ms 29676 KB Output is correct
7 Correct 846 ms 27756 KB Output is correct
8 Correct 308 ms 29292 KB Output is correct
9 Correct 1012 ms 26012 KB Output is correct
10 Correct 1000 ms 24684 KB Output is correct
11 Correct 1006 ms 26092 KB Output is correct
12 Correct 1016 ms 27628 KB Output is correct
13 Correct 999 ms 24404 KB Output is correct
14 Correct 1020 ms 27756 KB Output is correct
15 Correct 1004 ms 27884 KB Output is correct
16 Correct 996 ms 25068 KB Output is correct
17 Correct 990 ms 25332 KB Output is correct
18 Correct 992 ms 25428 KB Output is correct
19 Correct 1002 ms 27116 KB Output is correct
20 Correct 1000 ms 28268 KB Output is correct
21 Correct 5 ms 384 KB Output is correct

Subtask #4
59.0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 336 KB Output is correct
5 Correct 4 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 4 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 6 ms 512 KB Output is correct
12 Correct 6 ms 512 KB Output is correct
13 Correct 6 ms 512 KB Output is correct
14 Correct 6 ms 512 KB Output is correct
15 Correct 7 ms 512 KB Output is correct
16 Correct 6 ms 512 KB Output is correct
17 Correct 6 ms 512 KB Output is correct
18 Correct 6 ms 512 KB Output is correct
19 Correct 6 ms 512 KB Output is correct
20 Correct 6 ms 512 KB Output is correct
21 Correct 6 ms 512 KB Output is correct
22 Correct 6 ms 640 KB Output is correct
23 Correct 7 ms 640 KB Output is correct
24 Correct 7 ms 768 KB Output is correct
25 Correct 7 ms 640 KB Output is correct
26 Correct 7 ms 640 KB Output is correct
27 Correct 7 ms 640 KB Output is correct
28 Correct 7 ms 640 KB Output is correct
29 Correct 7 ms 512 KB Output is correct
30 Correct 7 ms 512 KB Output is correct
31 Correct 722 ms 29548 KB Output is correct
32 Correct 293 ms 29676 KB Output is correct
33 Correct 992 ms 29388 KB Output is correct
34 Correct 311 ms 29804 KB Output is correct
35 Correct 864 ms 27600 KB Output is correct
36 Correct 294 ms 29676 KB Output is correct
37 Correct 846 ms 27756 KB Output is correct
38 Correct 308 ms 29292 KB Output is correct
39 Correct 1012 ms 26012 KB Output is correct
40 Correct 1000 ms 24684 KB Output is correct
41 Correct 1006 ms 26092 KB Output is correct
42 Correct 1016 ms 27628 KB Output is correct
43 Correct 999 ms 24404 KB Output is correct
44 Correct 1020 ms 27756 KB Output is correct
45 Correct 1004 ms 27884 KB Output is correct
46 Correct 996 ms 25068 KB Output is correct
47 Correct 990 ms 25332 KB Output is correct
48 Correct 992 ms 25428 KB Output is correct
49 Correct 1002 ms 27116 KB Output is correct
50 Correct 1000 ms 28268 KB Output is correct
51 Correct 5 ms 384 KB Output is correct
52 Correct 599 ms 18668 KB Output is correct
53 Correct 631 ms 18536 KB Output is correct
54 Correct 578 ms 18412 KB Output is correct
55 Correct 580 ms 18800 KB Output is correct
56 Correct 578 ms 18588 KB Output is correct
57 Correct 541 ms 18540 KB Output is correct
58 Correct 626 ms 21612 KB Output is correct
59 Correct 558 ms 21484 KB Output is correct
60 Correct 666 ms 21744 KB Output is correct
61 Correct 707 ms 21872 KB Output is correct
62 Correct 291 ms 29932 KB Output is correct
63 Correct 290 ms 29784 KB Output is correct
64 Correct 301 ms 29420 KB Output is correct
65 Correct 286 ms 29676 KB Output is correct
66 Correct 415 ms 24044 KB Output is correct
67 Correct 417 ms 24520 KB Output is correct
68 Correct 411 ms 24172 KB Output is correct
69 Correct 418 ms 24044 KB Output is correct
70 Correct 423 ms 24172 KB Output is correct
71 Correct 404 ms 24048 KB Output is correct
72 Correct 426 ms 24168 KB Output is correct
73 Correct 422 ms 23656 KB Output is correct
74 Correct 433 ms 24300 KB Output is correct
75 Correct 419 ms 24044 KB Output is correct
76 Correct 682 ms 24812 KB Output is correct
77 Correct 638 ms 24044 KB Output is correct
78 Correct 856 ms 25184 KB Output is correct
79 Correct 852 ms 24172 KB Output is correct
80 Correct 866 ms 28140 KB Output is correct
81 Correct 913 ms 26348 KB Output is correct
82 Correct 846 ms 26220 KB Output is correct
83 Correct 834 ms 24300 KB Output is correct
84 Correct 849 ms 27628 KB Output is correct
85 Correct 849 ms 26604 KB Output is correct
86 Correct 858 ms 24044 KB Output is correct
87 Correct 838 ms 25068 KB Output is correct
88 Correct 717 ms 25456 KB Output is correct
89 Correct 740 ms 23408 KB Output is correct
90 Correct 781 ms 23304 KB Output is correct
91 Correct 811 ms 24592 KB Output is correct
92 Correct 791 ms 23776 KB Output is correct
93 Correct 806 ms 23668 KB Output is correct
94 Correct 780 ms 23284 KB Output is correct
95 Correct 796 ms 24152 KB Output is correct
96 Correct 859 ms 23248 KB Output is correct
97 Correct 823 ms 24520 KB Output is correct