oj.uz

Submission #216483

# Submission time Handle Problem Language Result Execution time Memory
216483 2020-03-27T11:06:15 Z AlexPop28 Capital City (JOI20_capital_city) C++11
100 / 100
 1083 ms 29932 KB 
#include <bits/stdc++.h>
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);

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

    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);
    }

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

    for (int &x : adj[node]) {
      if (!vis[x]) {
        Centroid(x);
      }
    }
  }
};


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 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

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 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 6 ms 512 KB Output is correct
12 Correct 7 ms 512 KB Output is correct
13 Correct 7 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 7 ms 512 KB Output is correct
17 Correct 6 ms 512 KB Output is correct
18 Correct 7 ms 512 KB Output is correct
19 Correct 6 ms 512 KB Output is correct
20 Correct 7 ms 512 KB Output is correct
21 Correct 6 ms 512 KB Output is correct
22 Correct 7 ms 640 KB Output is correct
23 Correct 7 ms 640 KB Output is correct
24 Correct 7 ms 512 KB Output is correct
25 Correct 8 ms 640 KB Output is correct
26 Correct 7 ms 640 KB Output is correct
27 Correct 9 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 854 ms 29548 KB Output is correct
2 Correct 286 ms 29804 KB Output is correct
3 Correct 866 ms 29516 KB Output is correct
4 Correct 298 ms 29932 KB Output is correct
5 Correct 818 ms 27628 KB Output is correct
6 Correct 292 ms 29676 KB Output is correct
7 Correct 820 ms 27756 KB Output is correct
8 Correct 296 ms 29292 KB Output is correct
9 Correct 1022 ms 26064 KB Output is correct
10 Correct 971 ms 24556 KB Output is correct
11 Correct 998 ms 26220 KB Output is correct
12 Correct 1047 ms 27652 KB Output is correct
13 Correct 992 ms 24428 KB Output is correct
14 Correct 973 ms 27884 KB Output is correct
15 Correct 1083 ms 27756 KB Output is correct
16 Correct 989 ms 24876 KB Output is correct
17 Correct 988 ms 25196 KB Output is correct
18 Correct 983 ms 25268 KB Output is correct
19 Correct 1042 ms 27224 KB Output is correct
20 Correct 1020 ms 28396 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 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 6 ms 512 KB Output is correct
12 Correct 7 ms 512 KB Output is correct
13 Correct 7 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 7 ms 512 KB Output is correct
17 Correct 6 ms 512 KB Output is correct
18 Correct 7 ms 512 KB Output is correct
19 Correct 6 ms 512 KB Output is correct
20 Correct 7 ms 512 KB Output is correct
21 Correct 6 ms 512 KB Output is correct
22 Correct 7 ms 640 KB Output is correct
23 Correct 7 ms 640 KB Output is correct
24 Correct 7 ms 512 KB Output is correct
25 Correct 8 ms 640 KB Output is correct
26 Correct 7 ms 640 KB Output is correct
27 Correct 9 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 854 ms 29548 KB Output is correct
32 Correct 286 ms 29804 KB Output is correct
33 Correct 866 ms 29516 KB Output is correct
34 Correct 298 ms 29932 KB Output is correct
35 Correct 818 ms 27628 KB Output is correct
36 Correct 292 ms 29676 KB Output is correct
37 Correct 820 ms 27756 KB Output is correct
38 Correct 296 ms 29292 KB Output is correct
39 Correct 1022 ms 26064 KB Output is correct
40 Correct 971 ms 24556 KB Output is correct
41 Correct 998 ms 26220 KB Output is correct
42 Correct 1047 ms 27652 KB Output is correct
43 Correct 992 ms 24428 KB Output is correct
44 Correct 973 ms 27884 KB Output is correct
45 Correct 1083 ms 27756 KB Output is correct
46 Correct 989 ms 24876 KB Output is correct
47 Correct 988 ms 25196 KB Output is correct
48 Correct 983 ms 25268 KB Output is correct
49 Correct 1042 ms 27224 KB Output is correct
50 Correct 1020 ms 28396 KB Output is correct
51 Correct 5 ms 384 KB Output is correct
52 Correct 560 ms 18536 KB Output is correct
53 Correct 623 ms 18564 KB Output is correct
54 Correct 627 ms 18512 KB Output is correct
55 Correct 664 ms 18672 KB Output is correct
56 Correct 632 ms 18716 KB Output is correct
57 Correct 624 ms 18540 KB Output is correct
58 Correct 688 ms 21740 KB Output is correct
59 Correct 647 ms 21484 KB Output is correct
60 Correct 784 ms 21872 KB Output is correct
61 Correct 831 ms 21872 KB Output is correct
62 Correct 286 ms 29676 KB Output is correct
63 Correct 285 ms 29804 KB Output is correct
64 Correct 302 ms 29420 KB Output is correct
65 Correct 291 ms 29676 KB Output is correct
66 Correct 489 ms 24212 KB Output is correct
67 Correct 487 ms 24296 KB Output is correct
68 Correct 487 ms 24044 KB Output is correct
69 Correct 507 ms 24168 KB Output is correct
70 Correct 489 ms 24040 KB Output is correct
71 Correct 491 ms 24232 KB Output is correct
72 Correct 484 ms 24172 KB Output is correct
73 Correct 488 ms 23532 KB Output is correct
74 Correct 494 ms 24176 KB Output is correct
75 Correct 491 ms 24044 KB Output is correct
76 Correct 743 ms 24860 KB Output is correct
77 Correct 707 ms 24044 KB Output is correct
78 Correct 1000 ms 25196 KB Output is correct
79 Correct 1006 ms 24172 KB Output is correct
80 Correct 1029 ms 27948 KB Output is correct
81 Correct 1027 ms 26092 KB Output is correct
82 Correct 1041 ms 26224 KB Output is correct
83 Correct 1053 ms 24428 KB Output is correct
84 Correct 1066 ms 27628 KB Output is correct
85 Correct 1044 ms 26804 KB Output is correct
86 Correct 1008 ms 24172 KB Output is correct
87 Correct 1000 ms 25324 KB Output is correct
88 Correct 851 ms 25564 KB Output is correct
89 Correct 855 ms 23284 KB Output is correct
90 Correct 860 ms 23156 KB Output is correct
91 Correct 885 ms 24560 KB Output is correct
92 Correct 859 ms 23792 KB Output is correct
93 Correct 857 ms 23788 KB Output is correct
94 Correct 862 ms 23280 KB Output is correct
95 Correct 862 ms 24228 KB Output is correct
96 Correct 863 ms 23520 KB Output is correct
97 Correct 874 ms 24560 KB Output is correct