Submission #559264

#	Time	Username	Problem	Language	Result	Execution time	Memory
559264		Sweezy	Cat in a tree (BOI17_catinatree)	C++17	51 / 100	1089 ms	38588 KiB

catinatree

#include <bits/stdc++.h>
 
using namespace std;
#define int long long

#ifdef LOCAL
#include "algo/debug.h"
#else
#define debug(...) 42
#endif

#define all(a) (a).begin(), (a).end()
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define reps(i, s, n) for (int i = s; i < (n); ++i)
#define pb push_back
#define sz(a) (int) (a.size())

const int N = 2e5 + 5;
const int inf = 1e9;

vector<int> g[N];
int s[N], mdist[N], used[N], res, d;
vector<pair<int, int>> centroids[N], vs;

void sizes(int v, int p) {
  s[v] = 1;
  for (auto &u : g[v]) {
    if (u != p && !used[u]) {
      sizes(u, v);
      s[v] += s[u];
    }
  }
}

int centroid(int v, int p, int n) {
  for (auto &u : g[v]) {
    if (u != p && !used[u] && s[u] > n / 2) {
      return centroid(u, v, n);
    } 
  }
  return v;
}

void add_centroid(int v, int p, int centroid, int dist) {
  centroids[v].emplace_back(centroid, dist);
  for (auto &u : g[v]) {
    if (u != p && !used[u]) {
      add_centroid(u, v, centroid, dist + 1);
    }
  }
}

void decomposition1(int v) {
  used[v] = 1;
  sizes(v, -1);

  add_centroid(v, -1, v, 0);

  for (auto &u : g[v]) {
    if (!used[u]) {
      decomposition1(centroid(u, v, s[u]));
    }
  }
}

void dfs(int v, int p, int dst) {
  vs.emplace_back(dst, v);
  for (auto &u : g[v]) {
    if (u != p) {
      dfs(u, v, dst + 1);
    }
  }
}

void decomposition2(int v) {
  used[v] = 1;
  sizes(v, -1);

  vs.clear();
  dfs(v, -1, 0);
  sort(vs.begin(), vs.end());

  auto can = [&] (int ver, int dst) -> bool {
    for (auto &[centroid, dist_to_centroid] : centroids[ver]) {
      if (dist_to_centroid + mdist[centroid] < d) {
        return false;
      }
    }
    return true;
  };

  int m = sz(vs), r = m, cnt = 0;
  rep(l, m) {
    while (r - 1 >= l && vs[r - 1].first >= max(vs[l].first, d - vs[l].first)) {
      r--;
      int ver = vs[r].second;
      int dst = vs[r].first;
      if (can(ver, dst)) {
        cnt++;
        for (auto &[centroid, dist_to_centroid] : centroids[ver]) {
          mdist[centroid] = min(mdist[centroid], dist_to_centroid);
        }
      }
    }
    if (l == r) {
      res = max(res, cnt);
      break;
    } else {
      res = max(res, cnt + can(vs[l].second, vs[l].first));
    }
  }

  for (auto &[vd, ver] : vs) {
    for (auto &[centroid, dist_to_centroid] : centroids[ver]) {
      mdist[centroid] = inf;
    }
  }

  for (auto &u : g[v]) {
    if (!used[u]) {
      decomposition2(centroid(u, v, s[u]));
    }
  }
}

void solve() {
  fill(mdist, mdist + N, inf);

  int n;
  cin >> n >> d;
 
  if (d > n - 1) {
    cout << 1;
    return;
  }
 
  if (d == 0) {
    cout << n;
    return;
  }
 
  reps(i, 1, n) {
    int p;
    cin >> p;
    g[p].push_back(i);
    g[i].push_back(p);
  }
  
  decomposition1(0);
  fill(used, used + N, 0);
  decomposition2(0);

  cout << res;
}
 
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
  return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 40 / 40
• Subtask 3: 0 / 49