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Submission #224463

# Submission time Handle Problem Language Result Execution time Memory
224463 2020-04-18T00:25:38 Z rama_pang Simurgh (IOI17_simurgh) C++14
100 / 100
 228 ms 4856 KB 
#include "simurgh.h"
#include <bits/stdc++.h>
using namespace std;

class DisjointSet {
 private:
  vector<int> p;
  vector<int> sz;

 public:
  DisjointSet() {}
  DisjointSet(int n) {
    p.assign(n, 0);
    iota(begin(p), end(p), 0);
    sz.assign(n, 1);
  }

  int Find(int x) {
    return p[x] == x ? x : p[x] = Find(p[x]);
  }

  bool Unite(int x, int y) {
    x = Find(x), y = Find(y);
    if (x == y) return false;
    if (sz[x] > sz[y]) swap(x, y);
    p[x] = y;
    sz[y] += sz[x];
    return true;
  }

  bool SameSet(int x, int y) {
    return Find(x) == Find(y);
  }
};

vector<int> find_roads(int n, vector<int> u, vector<int> v) {
  int m = u.size();
  DisjointSet dsu(n);

  vector<int> T; // Spanning Tree of G
  vector<vector<int>> Tadj(n);
  vector<int> Tpar(n, -1);
  vector<int> Tdepth(n, 0);

  vector<bool> inT(m, false);
  vector<int> is_royal(m, -1); // undetermined: -1, not royal: 0, royal: 1

  for (int i = 0; i < m; i++) {
    if (dsu.Unite(u[i], v[i])) {
      inT[i] = true;
      T.emplace_back(i);
      Tadj[u[i]].emplace_back(i);
      Tadj[v[i]].emplace_back(i);
    }
  }

  int Troyal = count_common_roads(T);

  function<void(int, int)> dfs = [&](int cur, int p) {
    for (auto e : Tadj[cur]) {
      int nxt = (u[e] == cur ? v[e] : u[e]);
      if (nxt != p) {
        Tpar[nxt] = e;
        Tdepth[nxt] = Tdepth[cur] + 1;
        dfs(nxt, cur);
      }
    }
  };

  function<void(int)> determine = [&](int edge) {
    function<int(vector<int> T_, int, int)> Query = 
        [&](vector<int> T_, int remove, int add) {
      replace(begin(T_), end(T_), remove, add);
      return count_common_roads(T_);
    };

    vector<int> C; // Cycle
    int a = u[edge], b = v[edge];

    // Get edges of T in the cycle 
    if (Tdepth[a] > Tdepth[b]) swap(a, b);
    while (Tdepth[b] > Tdepth[a]) {
      C.emplace_back(Tpar[b]);
      b = (u[Tpar[b]] == b ? v[Tpar[b]] : u[Tpar[b]]);
    }
    while (a != b) {
      C.emplace_back(Tpar[a]);
      C.emplace_back(Tpar[b]);
      a = (u[Tpar[a]] == a ? v[Tpar[a]] : u[Tpar[a]]);
      b = (u[Tpar[b]] == b ? v[Tpar[b]] : u[Tpar[b]]);
    }

    // check if there is an already determined edge
    for (auto e : C) {
      if (is_royal[edge] == -1 && is_royal[e] != -1) { // there is an already determined edge
        int Nroyal = Query(T, e, edge);
        if (Nroyal == Troyal) {
          is_royal[edge] = is_royal[e];
        } else {
          is_royal[edge] = is_royal[e] ? 0 : 1;
        }
      }
    }

    // all edges are undetermined, check each of them
    if (is_royal[edge] == -1) {
      vector<int> same;
      for (auto e : C) {
        int Nroyal = Query(T, e, edge);
        if (Nroyal == Troyal) {
          same.emplace_back(e); 
        } else if (Nroyal < Troyal) { // e is a royal road while edge isn't
          is_royal[e] = 1;
          is_royal[edge] = 0;
          break;
        } else if (Nroyal > Troyal) { // e isn't a royal road while edge is
          is_royal[e] = 0;
          is_royal[edge] = 1;
          break;
        }
      } 

      if (is_royal[edge] == -1) { // royal roads will never form a cycle
        is_royal[edge] = 0;
      }

      // update edges which have the same royality as edge
      for (auto e : same) {
        is_royal[e] = is_royal[edge];
      }
    }

    // we have determined edge, now to determine other edges in the cycle
    for (auto e : C) {
      if (is_royal[e] == -1) {
        int Nroyal = Query(T, e, edge);
        if (Nroyal == Troyal) {
          is_royal[e] = is_royal[edge];
        } else {
          is_royal[e] = is_royal[edge] ? 0 : 1; 
        }
      }
    }

    for (auto e : C) { // create connected component with determined edges
      dsu.Unite(u[e], v[e]);
    }
  };

  function<void(int, vector<int>)> find_royal = [&](int vertex, vector<int> adjacent) {
    function<int(vector<int>, vector<int>)> Query = 
        [&](vector<int> T_, vector<int> E) { // complete the golden set E with edges from T_
      DisjointSet d(n);
      for (auto e : E) {
        d.Unite(u[e], v[e]);
      }

      int royals_from_T = 0;
      for (auto e : T_) {
        if (d.Unite(u[e], v[e])) {
          royals_from_T += is_royal[e];
          E.emplace_back(e);
        }
      }

      return count_common_roads(E) - royals_from_T;
    };

    int count_royals = Query(T, adjacent);
    for (int L = 0; count_royals > 0; count_royals--) {
      int lo = L;
      int hi = (int) adjacent.size() - 1;

      while (lo < hi) {
        int mid = (lo + hi) / 2;
        vector<int> E(begin(adjacent) + L, begin(adjacent) + mid + 1);
        if (Query(T, E) > 0) {
          hi = mid;
        } else {
          lo = mid + 1;
        }
      }

      is_royal[adjacent[lo]] = 1;
      L = lo + 1;
    }

    for (auto e : adjacent) {
      if (is_royal[e] == -1) {
        is_royal[e] = 0;
      }
    }
  };


  dfs(0, -1);
  dsu = DisjointSet(n); // determine whether edges from u[i] and v[i] are all determined

  for (int i = 0; i < m; i++) {
    if (inT[i]) continue; // edge is in T
    if (dsu.SameSet(u[i], v[i])) continue; // all edges from u to v is already determined
    determine(i); // determine royalities of cycle from u[i] to v[i]
  }

  for (auto e : T) {
    if (is_royal[e] == -1) { // if an edge in T is undetermined, that means it is a bridge
      is_royal[e] = 1;
    }
  }

  vector<vector<int>> adj(n);
  for (int i = 0; i < m; i++) {
    if (inT[i]) continue;
    adj[u[i]].emplace_back(i);
  }

  // we have determined all roads in T, determine the remaining royal roads with binary search
  for (int i = 0; i < n; i++) {
    find_royal(i, adj[i]);
  }

  vector<int> royal_roads;
  for (int i = 0; i < m; i++) {
    if (is_royal[i] == 1) {
      royal_roads.emplace_back(i);
    }
  }
  
  return royal_roads;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB correct
2 Correct 4 ms 256 KB correct
3 Correct 4 ms 256 KB correct
4 Correct 5 ms 256 KB correct
5 Correct 5 ms 256 KB correct
6 Correct 4 ms 256 KB correct
7 Correct 4 ms 256 KB correct
8 Correct 5 ms 256 KB correct
9 Correct 4 ms 256 KB correct
10 Correct 5 ms 256 KB correct
11 Correct 5 ms 384 KB correct
12 Correct 5 ms 384 KB correct
13 Correct 4 ms 256 KB correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB correct
2 Correct 4 ms 256 KB correct
3 Correct 4 ms 256 KB correct
4 Correct 5 ms 256 KB correct
5 Correct 5 ms 256 KB correct
6 Correct 4 ms 256 KB correct
7 Correct 4 ms 256 KB correct
8 Correct 5 ms 256 KB correct
9 Correct 4 ms 256 KB correct
10 Correct 5 ms 256 KB correct
11 Correct 5 ms 384 KB correct
12 Correct 5 ms 384 KB correct
13 Correct 4 ms 256 KB correct
14 Correct 6 ms 384 KB correct
15 Correct 6 ms 384 KB correct
16 Correct 6 ms 384 KB correct
17 Correct 6 ms 384 KB correct
18 Correct 6 ms 384 KB correct
19 Correct 6 ms 384 KB correct
20 Correct 6 ms 384 KB correct
21 Correct 6 ms 384 KB correct
22 Correct 5 ms 384 KB correct
23 Correct 5 ms 384 KB correct
24 Correct 5 ms 384 KB correct
25 Correct 5 ms 256 KB correct
26 Correct 5 ms 384 KB correct
27 Correct 5 ms 384 KB correct
28 Correct 5 ms 384 KB correct
29 Correct 5 ms 256 KB correct
30 Correct 5 ms 384 KB correct
31 Correct 5 ms 384 KB correct
32 Correct 5 ms 384 KB correct
33 Correct 5 ms 384 KB correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB correct
2 Correct 4 ms 256 KB correct
3 Correct 4 ms 256 KB correct
4 Correct 5 ms 256 KB correct
5 Correct 5 ms 256 KB correct
6 Correct 4 ms 256 KB correct
7 Correct 4 ms 256 KB correct
8 Correct 5 ms 256 KB correct
9 Correct 4 ms 256 KB correct
10 Correct 5 ms 256 KB correct
11 Correct 5 ms 384 KB correct
12 Correct 5 ms 384 KB correct
13 Correct 4 ms 256 KB correct
14 Correct 6 ms 384 KB correct
15 Correct 6 ms 384 KB correct
16 Correct 6 ms 384 KB correct
17 Correct 6 ms 384 KB correct
18 Correct 6 ms 384 KB correct
19 Correct 6 ms 384 KB correct
20 Correct 6 ms 384 KB correct
21 Correct 6 ms 384 KB correct
22 Correct 5 ms 384 KB correct
23 Correct 5 ms 384 KB correct
24 Correct 5 ms 384 KB correct
25 Correct 5 ms 256 KB correct
26 Correct 5 ms 384 KB correct
27 Correct 5 ms 384 KB correct
28 Correct 5 ms 384 KB correct
29 Correct 5 ms 256 KB correct
30 Correct 5 ms 384 KB correct
31 Correct 5 ms 384 KB correct
32 Correct 5 ms 384 KB correct
33 Correct 5 ms 384 KB correct
34 Correct 45 ms 1280 KB correct
35 Correct 47 ms 1280 KB correct
36 Correct 42 ms 1024 KB correct
37 Correct 16 ms 384 KB correct
38 Correct 46 ms 1372 KB correct
39 Correct 43 ms 1152 KB correct
40 Correct 39 ms 1024 KB correct
41 Correct 44 ms 1400 KB correct
42 Correct 43 ms 1280 KB correct
43 Correct 15 ms 896 KB correct
44 Correct 15 ms 768 KB correct
45 Correct 15 ms 896 KB correct
46 Correct 14 ms 768 KB correct
47 Correct 12 ms 512 KB correct
48 Correct 9 ms 384 KB correct
49 Correct 10 ms 384 KB correct
50 Correct 12 ms 512 KB correct
51 Correct 16 ms 768 KB correct
52 Correct 14 ms 768 KB correct
53 Correct 14 ms 768 KB correct
54 Correct 15 ms 896 KB correct
55 Correct 15 ms 768 KB correct
56 Correct 15 ms 768 KB correct
57 Correct 15 ms 768 KB correct

Subtask #4
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 256 KB correct
2 Correct 4 ms 384 KB correct
3 Correct 132 ms 2680 KB correct
4 Correct 210 ms 4856 KB correct
5 Correct 205 ms 4472 KB correct
6 Correct 197 ms 4472 KB correct
7 Correct 198 ms 4728 KB correct
8 Correct 194 ms 4540 KB correct
9 Correct 204 ms 4600 KB correct
10 Correct 209 ms 4600 KB correct
11 Correct 207 ms 4472 KB correct
12 Correct 216 ms 4728 KB correct
13 Correct 5 ms 256 KB correct
14 Correct 198 ms 4600 KB correct
15 Correct 228 ms 4604 KB correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB correct
2 Correct 4 ms 256 KB correct
3 Correct 4 ms 256 KB correct
4 Correct 5 ms 256 KB correct
5 Correct 5 ms 256 KB correct
6 Correct 4 ms 256 KB correct
7 Correct 4 ms 256 KB correct
8 Correct 5 ms 256 KB correct
9 Correct 4 ms 256 KB correct
10 Correct 5 ms 256 KB correct
11 Correct 5 ms 384 KB correct
12 Correct 5 ms 384 KB correct
13 Correct 4 ms 256 KB correct
14 Correct 6 ms 384 KB correct
15 Correct 6 ms 384 KB correct
16 Correct 6 ms 384 KB correct
17 Correct 6 ms 384 KB correct
18 Correct 6 ms 384 KB correct
19 Correct 6 ms 384 KB correct
20 Correct 6 ms 384 KB correct
21 Correct 6 ms 384 KB correct
22 Correct 5 ms 384 KB correct
23 Correct 5 ms 384 KB correct
24 Correct 5 ms 384 KB correct
25 Correct 5 ms 256 KB correct
26 Correct 5 ms 384 KB correct
27 Correct 5 ms 384 KB correct
28 Correct 5 ms 384 KB correct
29 Correct 5 ms 256 KB correct
30 Correct 5 ms 384 KB correct
31 Correct 5 ms 384 KB correct
32 Correct 5 ms 384 KB correct
33 Correct 5 ms 384 KB correct
34 Correct 45 ms 1280 KB correct
35 Correct 47 ms 1280 KB correct
36 Correct 42 ms 1024 KB correct
37 Correct 16 ms 384 KB correct
38 Correct 46 ms 1372 KB correct
39 Correct 43 ms 1152 KB correct
40 Correct 39 ms 1024 KB correct
41 Correct 44 ms 1400 KB correct
42 Correct 43 ms 1280 KB correct
43 Correct 15 ms 896 KB correct
44 Correct 15 ms 768 KB correct
45 Correct 15 ms 896 KB correct
46 Correct 14 ms 768 KB correct
47 Correct 12 ms 512 KB correct
48 Correct 9 ms 384 KB correct
49 Correct 10 ms 384 KB correct
50 Correct 12 ms 512 KB correct
51 Correct 16 ms 768 KB correct
52 Correct 14 ms 768 KB correct
53 Correct 14 ms 768 KB correct
54 Correct 15 ms 896 KB correct
55 Correct 15 ms 768 KB correct
56 Correct 15 ms 768 KB correct
57 Correct 15 ms 768 KB correct
58 Correct 4 ms 256 KB correct
59 Correct 4 ms 384 KB correct
60 Correct 132 ms 2680 KB correct
61 Correct 210 ms 4856 KB correct
62 Correct 205 ms 4472 KB correct
63 Correct 197 ms 4472 KB correct
64 Correct 198 ms 4728 KB correct
65 Correct 194 ms 4540 KB correct
66 Correct 204 ms 4600 KB correct
67 Correct 209 ms 4600 KB correct
68 Correct 207 ms 4472 KB correct
69 Correct 216 ms 4728 KB correct
70 Correct 5 ms 256 KB correct
71 Correct 198 ms 4600 KB correct
72 Correct 228 ms 4604 KB correct
73 Correct 4 ms 384 KB correct
74 Correct 209 ms 4704 KB correct
75 Correct 217 ms 4344 KB correct
76 Correct 110 ms 1792 KB correct
77 Correct 212 ms 4728 KB correct
78 Correct 220 ms 4600 KB correct
79 Correct 206 ms 4472 KB correct
80 Correct 203 ms 4472 KB correct
81 Correct 183 ms 3704 KB correct
82 Correct 207 ms 4344 KB correct
83 Correct 175 ms 2552 KB correct
84 Correct 54 ms 2808 KB correct
85 Correct 55 ms 2688 KB correct
86 Correct 44 ms 1920 KB correct
87 Correct 40 ms 1400 KB correct
88 Correct 37 ms 1152 KB correct
89 Correct 37 ms 1152 KB correct
90 Correct 35 ms 1024 KB correct
91 Correct 24 ms 512 KB correct
92 Correct 21 ms 384 KB correct
93 Correct 52 ms 2688 KB correct
94 Correct 47 ms 1920 KB correct
95 Correct 44 ms 1792 KB correct
96 Correct 35 ms 1104 KB correct
97 Correct 37 ms 1152 KB correct
98 Correct 39 ms 1408 KB correct
99 Correct 36 ms 1280 KB correct
100 Correct 28 ms 640 KB correct
101 Correct 23 ms 512 KB correct
102 Correct 49 ms 2560 KB correct
103 Correct 48 ms 2424 KB correct
104 Correct 48 ms 2560 KB correct
105 Correct 49 ms 2432 KB correct