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Submission #1037450

# Submission time Handle Problem Language Result Execution time Memory
1037450 2024-07-28T22:29:21 Z spacewalker Parachute rings (IOI12_rings) C++17
100 / 100
 299 ms 90124 KB 
#include <bits/stdc++.h>

using namespace std;

struct ComponentUnionFind {
  bool is_chains = true;
  vector<int> par;
  vector<int> _degree;
  int extra_edges = 0;
  ComponentUnionFind(int n) : par(n, -1), _degree(n, 0) {}
  int find(int i) {
    return par[i] < 0 ? i : (par[i] = find(par[i])); 
  }
  int csize(int i) {
    return -par[find(i)];
  }
  int degree(int i) {
    return _degree[i];
  }
  bool join(int i, int j) {
    ++_degree[i]; ++_degree[j];
    if (_degree[i] > 2 || _degree[j] > 2) is_chains = false;
    int ir = find(i), jr = find(j);
    if (ir == jr) {
      ++extra_edges;
      is_chains = false;
      return false;
    }
    if (par[ir] > par[jr]) {
      swap(i, j); swap(ir, jr);
    }
    par[ir] += par[jr]; par[jr] = ir;
    return true;
  }
};

ComponentUnionFind create_from_ban(const vector<pair<int, int>> &edge_list, int n, int banned) {
  ComponentUnionFind cuf(n);
  for (auto [u, v] : edge_list) {
    if (u != banned && v != banned) cuf.join(u, v);
  }
  return cuf;
}

struct ParachuteRings {
  int n;
  vector<pair<ComponentUnionFind, int>> cufs;
  vector<pair<int, int>> edge_list;
  // size of the first cycle formed
  optional<int> critical_cycle_size;
  bool spoiled;
  ParachuteRings(int n) : n(n), cufs{{ComponentUnionFind(n), -1}}, spoiled(false) {}
  ParachuteRings() {} 
  int count_critical() {
    if (spoiled) return 0;
    // here, we know the graph is NOT spoiled
    else if (cufs.size() > 1) {
      int ans = 0;
      for (auto &[cuf, _] : cufs) if (cuf.is_chains) ++ans;
      return ans;
    } else {
      // if we have no critical cycle, everything must still be chains
      return critical_cycle_size.value_or(n);
    }
  }
  
  void reset_cufs(int i) {
    vector<pair<ComponentUnionFind, int>> new_cufs;
    vector<int> bans;
    for (auto [u, v] : edge_list) {
      if (u == i) bans.push_back(v);
      if (v == i) bans.push_back(u);
    }
    bans.push_back(i);
    for (int v : bans) new_cufs.emplace_back(create_from_ban(edge_list, n, v), v);
    cufs = new_cufs;
  }

  void link(int i, int j) {
    edge_list.emplace_back(i, j);
    if (spoiled) return;
    if (cufs.size() > 1) {
      for (auto &[cuf, banned] : cufs) {
        if (!(i == banned || j == banned)) cuf.join(i, j);
      }
    } else {
      auto &cuf = cufs[0].first;
      bool cycle_created = !cuf.join(i, j);
      if (cuf.degree(i) > 2 || cuf.degree(j) > 2) {
        if (cuf.degree(i) > 2) reset_cufs(i);
        else reset_cufs(j);
      } else {
        // all nodes still have degree <= 2
        // now, we must check for cycles
        // here, i guarantee cuf is still valid
        if (cycle_created) {
          if (cuf.extra_edges >= 2) {
            // we have two disjoint cycles, spoil the graph now
            spoiled = true;
          } else {
            critical_cycle_size = cuf.csize(i);
          }
        }
      }
      // if i fuck up here because i access cuf when i invalidated it that is
      // unironically a "muh memory safety!!!!!" moment
    }
  }
  void dump_state() {
    return;
    cerr << "!!! STATE DUMP " << endl;
    if (spoiled) cerr << "spoiled" << endl;
    else {
      cerr << "crit cycle " << critical_cycle_size.value_or(-1) << endl;
      cerr << cufs.size() << "simulations" << endl;
      for (auto &[cuf, banned] : cufs) {
        cerr << "cuf with ban" << banned << " = " << cuf.is_chains << endl;
      }
    }
  }
};

ParachuteRings pr;

void Init(int N) {
  pr = ParachuteRings(N);
  pr.dump_state();
}

void Link(int A, int B) {
  pr.link(A, B);
  pr.dump_state();
}

int CountCritical() {
  return pr.count_critical();
  pr.dump_state();
}

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 860 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 860 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 100 ms 17284 KB Output is correct
2 Correct 233 ms 62580 KB Output is correct
3 Correct 292 ms 75812 KB Output is correct
4 Correct 185 ms 33460 KB Output is correct
5 Correct 199 ms 33508 KB Output is correct
6 Correct 192 ms 32892 KB Output is correct
7 Correct 299 ms 75300 KB Output is correct
8 Correct 240 ms 80744 KB Output is correct
9 Correct 285 ms 90124 KB Output is correct
10 Correct 195 ms 32952 KB Output is correct

Subtask #3
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 860 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 860 KB Output is correct
11 Correct 1 ms 856 KB Output is correct
12 Correct 3 ms 1372 KB Output is correct
13 Correct 3 ms 1372 KB Output is correct
14 Correct 3 ms 1116 KB Output is correct
15 Correct 2 ms 1884 KB Output is correct
16 Correct 2 ms 860 KB Output is correct
17 Correct 2 ms 1120 KB Output is correct
18 Correct 3 ms 1884 KB Output is correct
19 Correct 2 ms 860 KB Output is correct
20 Correct 2 ms 1372 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 860 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 860 KB Output is correct
11 Correct 1 ms 856 KB Output is correct
12 Correct 3 ms 1372 KB Output is correct
13 Correct 3 ms 1372 KB Output is correct
14 Correct 3 ms 1116 KB Output is correct
15 Correct 2 ms 1884 KB Output is correct
16 Correct 2 ms 860 KB Output is correct
17 Correct 2 ms 1120 KB Output is correct
18 Correct 3 ms 1884 KB Output is correct
19 Correct 2 ms 860 KB Output is correct
20 Correct 2 ms 1372 KB Output is correct
21 Correct 7 ms 1816 KB Output is correct
22 Correct 12 ms 2532 KB Output is correct
23 Correct 18 ms 3228 KB Output is correct
24 Correct 18 ms 7080 KB Output is correct
25 Correct 8 ms 7504 KB Output is correct
26 Correct 18 ms 7308 KB Output is correct
27 Correct 16 ms 3788 KB Output is correct
28 Correct 21 ms 7016 KB Output is correct
29 Correct 16 ms 7500 KB Output is correct
30 Correct 20 ms 3724 KB Output is correct

Subtask #5
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 860 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 860 KB Output is correct
11 Correct 100 ms 17284 KB Output is correct
12 Correct 233 ms 62580 KB Output is correct
13 Correct 292 ms 75812 KB Output is correct
14 Correct 185 ms 33460 KB Output is correct
15 Correct 199 ms 33508 KB Output is correct
16 Correct 192 ms 32892 KB Output is correct
17 Correct 299 ms 75300 KB Output is correct
18 Correct 240 ms 80744 KB Output is correct
19 Correct 285 ms 90124 KB Output is correct
20 Correct 195 ms 32952 KB Output is correct
21 Correct 1 ms 856 KB Output is correct
22 Correct 3 ms 1372 KB Output is correct
23 Correct 3 ms 1372 KB Output is correct
24 Correct 3 ms 1116 KB Output is correct
25 Correct 2 ms 1884 KB Output is correct
26 Correct 2 ms 860 KB Output is correct
27 Correct 2 ms 1120 KB Output is correct
28 Correct 3 ms 1884 KB Output is correct
29 Correct 2 ms 860 KB Output is correct
30 Correct 2 ms 1372 KB Output is correct
31 Correct 7 ms 1816 KB Output is correct
32 Correct 12 ms 2532 KB Output is correct
33 Correct 18 ms 3228 KB Output is correct
34 Correct 18 ms 7080 KB Output is correct
35 Correct 8 ms 7504 KB Output is correct
36 Correct 18 ms 7308 KB Output is correct
37 Correct 16 ms 3788 KB Output is correct
38 Correct 21 ms 7016 KB Output is correct
39 Correct 16 ms 7500 KB Output is correct
40 Correct 20 ms 3724 KB Output is correct
41 Correct 70 ms 13572 KB Output is correct
42 Correct 166 ms 69304 KB Output is correct
43 Correct 119 ms 65572 KB Output is correct
44 Correct 264 ms 70556 KB Output is correct
45 Correct 236 ms 72392 KB Output is correct
46 Correct 161 ms 31600 KB Output is correct
47 Correct 179 ms 31728 KB Output is correct
48 Correct 229 ms 71632 KB Output is correct
49 Correct 156 ms 32024 KB Output is correct
50 Correct 155 ms 30772 KB Output is correct
51 Correct 167 ms 56136 KB Output is correct
52 Correct 232 ms 57252 KB Output is correct
53 Correct 169 ms 70876 KB Output is correct
54 Correct 243 ms 66264 KB Output is correct
55 Correct 278 ms 67808 KB Output is correct