oj.uz

Submission #616086

# Submission time Handle Problem Language Result Execution time Memory
616086 2022-07-31T20:23:09 Z Mamedov Simurgh (IOI17_simurgh) C++17
100 / 100
 144 ms 5536 KB 
#pragma GCC optimize ("O3")
#include "simurgh.h"
#include <bits/stdc++.h>
#define pii pair<int, int>
#define piii pair<pii, int>
#define vi vector<int>
#define vvi vector<vi>
#define vpii vector<pii>
#define vvpii vector<vpii>
#define f first
#define s second
#define oo 1000000001
#define eb emplace_back
#define pb push_back
#define mpr make_pair
#define size(v) (int)v.size()
#define ln '\n'
#define ull unsigned long long
#define ll long long
#define all(v) v.begin(), v.end()

using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

struct DSU {
  int n, components;
  vector<int>par;
  DSU(int _n) {
    n = _n;
    components = n;
    par.assign(n, -1);
  }
  int Find(int u) {
    return (par[u] < 0 ? u : (par[u] = Find(par[u])));
  }
  bool Union(int u, int v) {
    u = Find(u);
    v = Find(v);
    if (u != v) {
      if (par[u] > par[v]) {
        swap(u, v);
      }
      par[u] += par[v];
      par[v] = u;
      --components;
      return true;
    } else {
      return false;
    }
  }
};

/// helperTree  (construct any tree and find its edge types (royal or not))
/// findDegree  (find degree for each node)
/// binarySearch (find edges connected to leaf nodes using BS)

bool cmp(array<int, 3>er1, array<int, 3>er2) {
  if (er1[0] * er2[1] == er2[0] * er1[1]) {
    return er1[0] > er2[0];
  } else {
    return er1[0] * er2[1] > er2[0] * er1[1];
  }
}

vpii findHelperTree(int n, int m, vi &u, vi &v, vvi &g, vi &isRoyal) {
  DSU helperTreeDSU(n);
  vector<pii>helperTree;

  vector<array<int, 3>>edgeRatio(n);
  for (int i = 0; i < n; ++i) {
    edgeRatio[i] = {size(g[i]), size(g[i]), i};
  }
  sort(all(edgeRatio), cmp);
  for (int itr = 0; itr < n; ++itr) {
    int i = edgeRatio[0][2];
    DSU dsu(n);
    vi r;
    for (int j = 0; j < m; ++j) {
      if (u[j] != i && v[j] != i && dsu.Union(u[j], v[j])) {
        r.eb(j);
      }
    }
    vi roots;
    for (int j = 0; j < n; ++j) {
      if (j != i && dsu.par[j] < 0) {
        roots.eb(j);
      }
    }
    vvi group(n);
    for (int j : g[i]) {
      int other = u[j] + v[j] - i;
      group[dsu.Find(other)].eb(j);
    }
    for (int j = 0; j < dsu.components - 1; ++j) {
      for (int k = 0; k < dsu.components - 1; ++k) {
        if (k != j) {
          r.eb(group[roots[k]][0]);
        }
      }
      vi royals;
      int maxVal = -1;
      for (int k : group[roots[j]]) {
        if (isRoyal[k] == -1) {
          r.eb(k);
          royals.eb(count_common_roads(r));
          r.pop_back();
        } else if (isRoyal[k] == 1) {
          if (maxVal == -1) {
            r.eb(k);
            royals.eb(count_common_roads(r));
            r.pop_back();
            maxVal = royals.back();
          } else {
            royals.eb(maxVal);
          }
        } else {
          if (maxVal == -1) {
            r.eb(k);
            royals.eb(count_common_roads(r));
            r.pop_back();
            maxVal = royals.back() + 1;
          } else {
            royals.eb(maxVal - 1);
          }
        }
      }
      maxVal = (*max_element(all(royals)));
      for (int k = 0; k < size(group[roots[j]]); ++k) {
        int id = group[roots[j]][k];
        if (royals[k] == maxVal) {
          isRoyal[id] = 1;
        } else {
          isRoyal[id] = 0;
        }
        if (helperTreeDSU.Union(u[id], v[id])) {
          helperTree.eb(mpr(id, isRoyal[id]));
          if (helperTreeDSU.components == 1) return helperTree;
        }
      }
      for (int k = 0; k < dsu.components - 1; ++k) {
        if (k != j) {
          r.pop_back();
        }
      }
    }
    vector<set<int>>subTrees(n);
    for (int j = 0; j < m; ++j) {
      if (helperTreeDSU.Find(u[j]) != helperTreeDSU.Find(v[j])) {
        subTrees[u[j]].insert(helperTreeDSU.Find(v[j]));
        subTrees[v[j]].insert(helperTreeDSU.Find(u[j]));
      }
    }
    for (int j = 0; j < n; ++j) {
      edgeRatio[j] = {size(subTrees[j]), size(g[j]), j};
    }
    sort(all(edgeRatio), cmp);
  }
}

vi findDegrees(int n, int m, vpii &helperTree, vi &u, vi &v, vvi &g) {
  vi degree(n, 0);
  for (int i = 0; i < n; ++i) {
    DSU dsu(n);
    vi r;
    for (int j : g[i]) {
      dsu.Union(u[j], v[j]);
      r.eb(j);
    }
    for (auto [j, isRoyal] : helperTree) {
      if (dsu.Union(u[j], v[j])) {
        r.eb(j);
        degree[i] -= isRoyal;
      }
    }
    degree[i] += count_common_roads(r);
  }
  return degree;
}

int findRoyal(int n, vpii &helperTree, vi &edges, vi &u, vi &v) {
  int low = 0, high = size(edges) - 1;
  int mid;
  while (low < high) {
    mid = (low + high) >> 1;
    DSU dsu(n);
    vi r;
    int royals = 0;
    for (int i = low; i <= mid; ++i) {
      r.eb(edges[i]);
      dsu.Union(u[edges[i]], v[edges[i]]);
    }
    for (auto [i, isRoyal] : helperTree) {
      if (dsu.Union(u[i], v[i])) {
        r.eb(i);
        royals -= isRoyal;
      }
    }
    royals += count_common_roads(r);
    if (royals) {
      high = mid;
    } else {
      low = mid + 1;
    }
  }
  return edges[low];
}
vi find_roads(int n, vi u, vi v) {
  int m = size(u);
  vvi g(n);
  for (int i = 0; i < m; ++i) {
    g[u[i]].eb(i);
    g[v[i]].eb(i);
  }
  vi isRoyal(m, -1);
  vpii helperTree = findHelperTree(n, m, u, v, g, isRoyal);
  vi degree = findDegrees(n, m, helperTree, u, v, g);


  queue<int>q;
  for (int i = 0; i < n; ++i) {
    if (degree[i] == 1) {
      q.push(i);
    }
  }
  vector<int>res;
  for (int i = 1; i < n; ++i) {
    int node = q.front();
    q.pop();
    vi edges;
    int id = -1;
    for (int i : g[node]) {
      if (isRoyal[i] == -1) {
        edges.eb(i);
      } else if (isRoyal[i] == 1) {
        id = i;
        break;
      }
    }
    if (id == -1) {
      id = findRoyal(n, helperTree, edges, u, v);
    }
    for (int i : edges) {
      isRoyal[i] = 0;
    }
    isRoyal[id] = 2;

    res.eb(id);

    int other = (u[id] ^ v[id] ^ node);
    --degree[other];
    if (degree[other] == 1) {
      q.push(other);
    }
  }
  return res;
}

Compilation message

simurgh.cpp: In function 'std::vector<std::pair<int, int> > findHelperTree(int, int, std::vector<int>&, std::vector<int>&, std::vector<std::vector<int> >&, std::vector<int>&)':
simurgh.cpp:67:22: warning: control reaches end of non-void function [-Wreturn-type]
   67 |   DSU helperTreeDSU(n);
      |                      ^

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 304 KB correct
2 Correct 1 ms 212 KB correct
3 Correct 1 ms 212 KB correct
4 Correct 0 ms 212 KB correct
5 Correct 0 ms 212 KB correct
6 Correct 1 ms 212 KB correct
7 Correct 1 ms 212 KB correct
8 Correct 1 ms 212 KB correct
9 Correct 1 ms 212 KB correct
10 Correct 1 ms 212 KB correct
11 Correct 1 ms 304 KB correct
12 Correct 0 ms 212 KB correct
13 Correct 0 ms 212 KB correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 304 KB correct
2 Correct 1 ms 212 KB correct
3 Correct 1 ms 212 KB correct
4 Correct 0 ms 212 KB correct
5 Correct 0 ms 212 KB correct
6 Correct 1 ms 212 KB correct
7 Correct 1 ms 212 KB correct
8 Correct 1 ms 212 KB correct
9 Correct 1 ms 212 KB correct
10 Correct 1 ms 212 KB correct
11 Correct 1 ms 304 KB correct
12 Correct 0 ms 212 KB correct
13 Correct 0 ms 212 KB correct
14 Correct 1 ms 340 KB correct
15 Correct 1 ms 308 KB correct
16 Correct 1 ms 340 KB correct
17 Correct 1 ms 308 KB correct
18 Correct 1 ms 340 KB correct
19 Correct 2 ms 340 KB correct
20 Correct 1 ms 340 KB correct
21 Correct 1 ms 340 KB correct
22 Correct 1 ms 340 KB correct
23 Correct 1 ms 304 KB correct
24 Correct 1 ms 300 KB correct
25 Correct 1 ms 212 KB correct
26 Correct 1 ms 340 KB correct
27 Correct 1 ms 340 KB correct
28 Correct 1 ms 212 KB correct
29 Correct 1 ms 212 KB correct
30 Correct 2 ms 340 KB correct
31 Correct 2 ms 340 KB correct
32 Correct 1 ms 340 KB correct
33 Correct 1 ms 340 KB correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 304 KB correct
2 Correct 1 ms 212 KB correct
3 Correct 1 ms 212 KB correct
4 Correct 0 ms 212 KB correct
5 Correct 0 ms 212 KB correct
6 Correct 1 ms 212 KB correct
7 Correct 1 ms 212 KB correct
8 Correct 1 ms 212 KB correct
9 Correct 1 ms 212 KB correct
10 Correct 1 ms 212 KB correct
11 Correct 1 ms 304 KB correct
12 Correct 0 ms 212 KB correct
13 Correct 0 ms 212 KB correct
14 Correct 1 ms 340 KB correct
15 Correct 1 ms 308 KB correct
16 Correct 1 ms 340 KB correct
17 Correct 1 ms 308 KB correct
18 Correct 1 ms 340 KB correct
19 Correct 2 ms 340 KB correct
20 Correct 1 ms 340 KB correct
21 Correct 1 ms 340 KB correct
22 Correct 1 ms 340 KB correct
23 Correct 1 ms 304 KB correct
24 Correct 1 ms 300 KB correct
25 Correct 1 ms 212 KB correct
26 Correct 1 ms 340 KB correct
27 Correct 1 ms 340 KB correct
28 Correct 1 ms 212 KB correct
29 Correct 1 ms 212 KB correct
30 Correct 2 ms 340 KB correct
31 Correct 2 ms 340 KB correct
32 Correct 1 ms 340 KB correct
33 Correct 1 ms 340 KB correct
34 Correct 25 ms 1332 KB correct
35 Correct 27 ms 1268 KB correct
36 Correct 28 ms 1556 KB correct
37 Correct 12 ms 496 KB correct
38 Correct 27 ms 1372 KB correct
39 Correct 27 ms 1424 KB correct
40 Correct 29 ms 1492 KB correct
41 Correct 26 ms 1364 KB correct
42 Correct 27 ms 1364 KB correct
43 Correct 22 ms 1320 KB correct
44 Correct 21 ms 1236 KB correct
45 Correct 23 ms 1496 KB correct
46 Correct 20 ms 1236 KB correct
47 Correct 17 ms 892 KB correct
48 Correct 7 ms 308 KB correct
49 Correct 11 ms 468 KB correct
50 Correct 17 ms 876 KB correct
51 Correct 23 ms 1436 KB correct
52 Correct 22 ms 1364 KB correct
53 Correct 20 ms 1240 KB correct
54 Correct 22 ms 1236 KB correct
55 Correct 23 ms 1492 KB correct
56 Correct 23 ms 1492 KB correct
57 Correct 25 ms 1468 KB correct

Subtask #4
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 300 KB correct
2 Correct 1 ms 212 KB correct
3 Correct 84 ms 3432 KB correct
4 Correct 123 ms 4812 KB correct
5 Correct 128 ms 4888 KB correct
6 Correct 131 ms 4884 KB correct
7 Correct 140 ms 4980 KB correct
8 Correct 123 ms 4864 KB correct
9 Correct 124 ms 4792 KB correct
10 Correct 126 ms 4884 KB correct
11 Correct 144 ms 4812 KB correct
12 Correct 126 ms 4876 KB correct
13 Correct 0 ms 212 KB correct
14 Correct 134 ms 4852 KB correct
15 Correct 136 ms 4980 KB correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 304 KB correct
2 Correct 1 ms 212 KB correct
3 Correct 1 ms 212 KB correct
4 Correct 0 ms 212 KB correct
5 Correct 0 ms 212 KB correct
6 Correct 1 ms 212 KB correct
7 Correct 1 ms 212 KB correct
8 Correct 1 ms 212 KB correct
9 Correct 1 ms 212 KB correct
10 Correct 1 ms 212 KB correct
11 Correct 1 ms 304 KB correct
12 Correct 0 ms 212 KB correct
13 Correct 0 ms 212 KB correct
14 Correct 1 ms 340 KB correct
15 Correct 1 ms 308 KB correct
16 Correct 1 ms 340 KB correct
17 Correct 1 ms 308 KB correct
18 Correct 1 ms 340 KB correct
19 Correct 2 ms 340 KB correct
20 Correct 1 ms 340 KB correct
21 Correct 1 ms 340 KB correct
22 Correct 1 ms 340 KB correct
23 Correct 1 ms 304 KB correct
24 Correct 1 ms 300 KB correct
25 Correct 1 ms 212 KB correct
26 Correct 1 ms 340 KB correct
27 Correct 1 ms 340 KB correct
28 Correct 1 ms 212 KB correct
29 Correct 1 ms 212 KB correct
30 Correct 2 ms 340 KB correct
31 Correct 2 ms 340 KB correct
32 Correct 1 ms 340 KB correct
33 Correct 1 ms 340 KB correct
34 Correct 25 ms 1332 KB correct
35 Correct 27 ms 1268 KB correct
36 Correct 28 ms 1556 KB correct
37 Correct 12 ms 496 KB correct
38 Correct 27 ms 1372 KB correct
39 Correct 27 ms 1424 KB correct
40 Correct 29 ms 1492 KB correct
41 Correct 26 ms 1364 KB correct
42 Correct 27 ms 1364 KB correct
43 Correct 22 ms 1320 KB correct
44 Correct 21 ms 1236 KB correct
45 Correct 23 ms 1496 KB correct
46 Correct 20 ms 1236 KB correct
47 Correct 17 ms 892 KB correct
48 Correct 7 ms 308 KB correct
49 Correct 11 ms 468 KB correct
50 Correct 17 ms 876 KB correct
51 Correct 23 ms 1436 KB correct
52 Correct 22 ms 1364 KB correct
53 Correct 20 ms 1240 KB correct
54 Correct 22 ms 1236 KB correct
55 Correct 23 ms 1492 KB correct
56 Correct 23 ms 1492 KB correct
57 Correct 25 ms 1468 KB correct
58 Correct 1 ms 300 KB correct
59 Correct 1 ms 212 KB correct
60 Correct 84 ms 3432 KB correct
61 Correct 123 ms 4812 KB correct
62 Correct 128 ms 4888 KB correct
63 Correct 131 ms 4884 KB correct
64 Correct 140 ms 4980 KB correct
65 Correct 123 ms 4864 KB correct
66 Correct 124 ms 4792 KB correct
67 Correct 126 ms 4884 KB correct
68 Correct 144 ms 4812 KB correct
69 Correct 126 ms 4876 KB correct
70 Correct 0 ms 212 KB correct
71 Correct 134 ms 4852 KB correct
72 Correct 136 ms 4980 KB correct
73 Correct 1 ms 212 KB correct
74 Correct 129 ms 4752 KB correct
75 Correct 135 ms 4828 KB correct
76 Correct 87 ms 3680 KB correct
77 Correct 141 ms 4864 KB correct
78 Correct 125 ms 4896 KB correct
79 Correct 131 ms 4896 KB correct
80 Correct 133 ms 4800 KB correct
81 Correct 43 ms 4180 KB correct
82 Correct 139 ms 4852 KB correct
83 Correct 133 ms 5132 KB correct
84 Correct 108 ms 4236 KB correct
85 Correct 115 ms 4832 KB correct
86 Correct 110 ms 4384 KB correct
87 Correct 97 ms 3796 KB correct
88 Correct 91 ms 3148 KB correct
89 Correct 88 ms 2900 KB correct
90 Correct 85 ms 2644 KB correct
91 Correct 41 ms 596 KB correct
92 Correct 29 ms 468 KB correct
93 Correct 120 ms 4780 KB correct
94 Correct 115 ms 4408 KB correct
95 Correct 103 ms 4412 KB correct
96 Correct 87 ms 2756 KB correct
97 Correct 93 ms 3156 KB correct
98 Correct 113 ms 3796 KB correct
99 Correct 107 ms 3140 KB correct
100 Correct 61 ms 1140 KB correct
101 Correct 29 ms 448 KB correct
102 Correct 116 ms 5536 KB correct
103 Correct 125 ms 5536 KB correct
104 Correct 123 ms 5488 KB correct
105 Correct 114 ms 5452 KB correct