test/yukicoder/1976.test.cpp

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• Last update: 2024-09-01 13:40:30+09:00
• Problem: https://yukicoder.me/problems/no/1976

Depends on

• グラフ (src/Graph/Graph.hpp)
• 重軽分解 (src/Graph/HeavyLightDecomposition.hpp)
• 全方位木DP (src/Graph/Rerooting.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1976
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <array>
#include <algorithm>
#include "src/Graph/Graph.hpp"
#include "src/Graph/Rerooting.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 Graph g(N, N - 1);
 for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
 using Dat= array<int, 2>;
 using Data= array<int, 3>;
 auto put_edge= [&](int, int, const Dat& d) { return Data{d[0] + 1, 0, d[1]}; };
 auto op= [&](const Data& l, const Data& r) {
  int v[]= {l[0], l[1], r[0], r[1]};
  sort(v, v + 4);
  return Data{v[3], v[2], max(l[2], r[2])};
 };
 auto put_vertex= [&](int, const Data& d) { return Dat{d[0], max(d[2], d[0] + d[1])}; };
 Rerooting<Dat> dp(g, put_edge, op, Data{0, 0, 0}, put_vertex);
 int ans= 1 << 30;
 for (auto [u, v]: g) {
  int X= dp(u, v)[1], Y= dp(v, u)[1];
  ans= min(ans, max({X, Y, (X + 1) / 2 + (Y + 1) / 2 + 1}));
 }
 cout << ans << '\n';
 return 0;
}

#line 1 "test/yukicoder/1976.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1976
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <array>
#include <algorithm>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 2 "src/Graph/Rerooting.hpp"
#include <valarray>
#line 3 "src/Graph/HeavyLightDecomposition.hpp"
#include <cassert>
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
 std::vector<int> P, PP, D, I, L, R;
public:
 HeavyLightDecomposition()= default;
 HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
 HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
  const int n= adj.size();
  P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
  auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
   for (P[r]= -1, I[t++]= r; i < t; ++i)
    for (int u: adj[v= I[i]])
     if (P[v] != u) P[I[t++]= u]= v;
  };
  f(root);
  for (int r= 0; r < n; ++r)
   if (P[r] == -2) f(r);
  std::vector<int> Z(n, 1), nx(n, -1);
  for (int i= n, v; i--;) {
   if (P[v= I[i]] == -1) continue;
   if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
   if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
  }
  for (int v= n; v--;) PP[v]= v;
  for (int v: I)
   if (nx[v] != -1) PP[nx[v]]= v;
  for (int v: I)
   if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
  for (int i= n; i--;) L[I[i]]= i;
  for (int v: I) {
   int ir= R[v]= L[v] + Z[v];
   for (int u: adj[v])
    if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
   if (nx[v] != -1) L[nx[v]]= L[v] + 1;
  }
  for (int i= n; i--;) I[L[i]]= i;
 }
 int to_seq(int v) const { return L[v]; }
 int to_vertex(int i) const { return I[i]; }
 size_t size() const { return P.size(); }
 int parent(int v) const { return P[v]; }
 int head(int v) const { return PP[v]; }
 int root(int v) const {
  for (v= PP[v];; v= PP[P[v]])
   if (P[v] == -1) return v;
 }
 bool connected(int u, int v) const { return root(u) == root(v); }
 // u is in v
 bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
 int subtree_size(int v) const { return R[v] - L[v]; }
 int lca(int u, int v) const {
  for (;; v= P[PP[v]]) {
   if (L[u] > L[v]) std::swap(u, v);
   if (PP[u] == PP[v]) return u;
  }
 }
 int la(int v, int k) const {
  assert(k <= D[v]);
  for (int u;; k-= L[v] - L[u] + 1, v= P[u])
   if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
 }
 int jump(int u, int v, int k) const {
  if (!k) return u;
  if (u == v) return -1;
  if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
  int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
  return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
 }
 int depth(int v) const { return D[v]; }
 int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
 // half-open interval [l,r)
 std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
 // sequence of closed intervals [l,r]
 std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
  std::vector<std::pair<int, int>> up, down;
  while (PP[u] != PP[v]) {
   if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
   else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
  }
  if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
  else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
  return up.insert(up.end(), down.rbegin(), down.rend()), up;
 }
};
#line 4 "src/Graph/Rerooting.hpp"
// put_edge(int v, int e, T t) -> U
// op(U l, U r) -> U
// ui(:U) is the identity element of op
// put_vertex(int v, U sum) -> T
template <class T> class Rerooting {
 HeavyLightDecomposition hld;
 std::valarray<T> dp, dp1, dp2;
public:
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex) : hld(hld){
  static_assert(std::is_invocable_r_v<U, F1, int, int, T>, "put_edge(int,int,T) is not invocable");
  static_assert(std::is_invocable_r_v<U, F2, U, U>, "op(U,U) is not invocable");
  static_assert(std::is_invocable_r_v<T, F3, int, U>, "put_vertex(int,U) is not invocable");
  const int n= g.vertex_size();
  dp.resize(n), dp1.resize(n), dp2.resize(n);
  for (int i= n, v; i--;) {
   U sum= ui;
   for (int e: adje[v= hld.to_vertex(i)])
    if (int u= g[e].to(v); u != hld.parent(v)) sum= op(sum, put_edge(v, e, dp1[u]));
   dp1[v]= put_vertex(v, sum);
  }
  for (int i= 0, v; i < n; ++i) {
   auto gv= adje[v= hld.to_vertex(i)];
   int dg= gv.size();
   std::valarray<U> f(dg + 1), b(dg + 1);
   for (int j= 0, e, u; j < dg; ++j) u= g[e= gv[j]].to(v), f[j + 1]= put_edge(v, e, u == hld.parent(v) ? dp2[v] : dp1[u]);
   f[0]= b[dg]= ui;
   for (int j= dg; j--;) b[j]= op(f[j + 1], b[j + 1]);
   for (int j= 0; j < dg; ++j) f[j + 1]= op(f[j], f[j + 1]);
   for (int j= 0; j < dg; ++j)
    if (int u= g[gv[j]].to(v); u != hld.parent(v)) dp2[u]= put_vertex(v, op(f[j], b[j + 1]));
   dp[v]= put_vertex(v, f[dg]);
  }
 }
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, adje, HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), hld, put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 const T &operator[](int v) const { return dp[v]; }
 auto begin() const { return std::cbegin(dp); }
 auto end() const { return std::cend(dp); }
 const T &operator()(int root, int v) const { return root == v ? dp[v] : hld.in_subtree(root, v) ? dp2[hld.jump(v, root, 1)] : dp1[v]; }
};
#line 9 "test/yukicoder/1976.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 Graph g(N, N - 1);
 for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
 using Dat= array<int, 2>;
 using Data= array<int, 3>;
 auto put_edge= [&](int, int, const Dat& d) { return Data{d[0] + 1, 0, d[1]}; };
 auto op= [&](const Data& l, const Data& r) {
  int v[]= {l[0], l[1], r[0], r[1]};
  sort(v, v + 4);
  return Data{v[3], v[2], max(l[2], r[2])};
 };
 auto put_vertex= [&](int, const Data& d) { return Dat{d[0], max(d[2], d[0] + d[1])}; };
 Rerooting<Dat> dp(g, put_edge, op, Data{0, 0, 0}, put_vertex);
 int ans= 1 << 30;
 for (auto [u, v]: g) {
  int X= dp(u, v)[1], Y= dp(v, u)[1];
  ans= min(ans, max({X, Y, (X + 1) / 2 + (Y + 1) / 2 + 1}));
 }
 cout << ans << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	01_sample_1.txt	AC	7 ms	4 MB
g++-13	01_sample_2.txt	AC	5 ms	4 MB
g++-13	02_random_1.txt	AC	47 ms	12 MB
g++-13	02_random_10.txt	AC	48 ms	13 MB
g++-13	02_random_11.txt	AC	7 ms	4 MB
g++-13	02_random_12.txt	AC	36 ms	10 MB
g++-13	02_random_13.txt	AC	35 ms	10 MB
g++-13	02_random_14.txt	AC	33 ms	9 MB
g++-13	02_random_15.txt	AC	44 ms	12 MB
g++-13	02_random_16.txt	AC	20 ms	7 MB
g++-13	02_random_17.txt	AC	8 ms	4 MB
g++-13	02_random_18.txt	AC	36 ms	10 MB
g++-13	02_random_19.txt	AC	49 ms	13 MB
g++-13	02_random_2.txt	AC	30 ms	9 MB
g++-13	02_random_20.txt	AC	32 ms	9 MB
g++-13	02_random_3.txt	AC	14 ms	5 MB
g++-13	02_random_4.txt	AC	26 ms	8 MB
g++-13	02_random_5.txt	AC	38 ms	10 MB
g++-13	02_random_6.txt	AC	27 ms	8 MB
g++-13	02_random_7.txt	AC	48 ms	12 MB
g++-13	02_random_8.txt	AC	44 ms	11 MB
g++-13	02_random_9.txt	AC	16 ms	6 MB
g++-13	03_small_1.txt	AC	6 ms	4 MB
g++-13	03_small_10.txt	AC	5 ms	4 MB
g++-13	03_small_2.txt	AC	5 ms	4 MB
g++-13	03_small_3.txt	AC	5 ms	3 MB
g++-13	03_small_4.txt	AC	5 ms	4 MB
g++-13	03_small_5.txt	AC	5 ms	4 MB
g++-13	03_small_6.txt	AC	5 ms	4 MB
g++-13	03_small_7.txt	AC	5 ms	4 MB
g++-13	03_small_8.txt	AC	5 ms	4 MB
g++-13	03_small_9.txt	AC	5 ms	4 MB
g++-13	99_system_test1.txt	AC	5 ms	3 MB
clang++-18	01_sample_1.txt	AC	6 ms	4 MB
clang++-18	01_sample_2.txt	AC	6 ms	4 MB
clang++-18	02_random_1.txt	AC	46 ms	12 MB
clang++-18	02_random_10.txt	AC	46 ms	12 MB
clang++-18	02_random_11.txt	AC	7 ms	4 MB
clang++-18	02_random_12.txt	AC	35 ms	10 MB
clang++-18	02_random_13.txt	AC	34 ms	10 MB
clang++-18	02_random_14.txt	AC	33 ms	9 MB
clang++-18	02_random_15.txt	AC	44 ms	12 MB
clang++-18	02_random_16.txt	AC	19 ms	6 MB
clang++-18	02_random_17.txt	AC	9 ms	4 MB
clang++-18	02_random_18.txt	AC	36 ms	10 MB
clang++-18	02_random_19.txt	AC	47 ms	13 MB
clang++-18	02_random_2.txt	AC	31 ms	8 MB
clang++-18	02_random_20.txt	AC	30 ms	9 MB
clang++-18	02_random_3.txt	AC	14 ms	5 MB
clang++-18	02_random_4.txt	AC	25 ms	8 MB
clang++-18	02_random_5.txt	AC	37 ms	10 MB
clang++-18	02_random_6.txt	AC	26 ms	8 MB
clang++-18	02_random_7.txt	AC	51 ms	12 MB
clang++-18	02_random_8.txt	AC	41 ms	11 MB
clang++-18	02_random_9.txt	AC	16 ms	6 MB
clang++-18	03_small_1.txt	AC	6 ms	4 MB
clang++-18	03_small_10.txt	AC	5 ms	4 MB
clang++-18	03_small_2.txt	AC	5 ms	4 MB
clang++-18	03_small_3.txt	AC	5 ms	4 MB
clang++-18	03_small_4.txt	AC	6 ms	4 MB
clang++-18	03_small_5.txt	AC	5 ms	4 MB
clang++-18	03_small_6.txt	AC	5 ms	4 MB
clang++-18	03_small_7.txt	AC	5 ms	4 MB
clang++-18	03_small_8.txt	AC	5 ms	4 MB
clang++-18	03_small_9.txt	AC	5 ms	4 MB
clang++-18	99_system_test1.txt	AC	5 ms	4 MB

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