test/yukicoder/1097.test.cpp

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• Last update: 2024-09-01 13:40:30+09:00
• Problem: https://yukicoder.me/problems/no/1097

Depends on

• グラフ (src/Graph/Graph.hpp)
• 重軽分解 (src/Graph/HeavyLightDecomposition.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• 周期性の利用 (Functionalグラフ) (src/Misc/Period.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1097
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include "src/Misc/Period.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 vector<int> A(N), to(N);
 for (int i= 0; i < N; ++i) cin >> A[i], to[i]= (i + A[i]) % N;
 Period p(to);
 vector<long long> sum(N + 1);
 for (int i= N; i--;) sum[p(i) + 1]= A[i];
 for (int i= 0; i < N; ++i) sum[i + 1]+= sum[i];
 int Q;
 cin >> Q;
 while (Q--) {
  long long K;
  cin >> K;
  long long ans= 0;
  auto [p1, p2, c, p3]= p.path(0, K - 1);
  for (auto [l, r]: p1) ans+= sum[r] - sum[l];
  for (auto [l, r]: p2) ans+= c * (sum[r] - sum[l]);
  for (auto [l, r]: p3) ans+= sum[r] - sum[l];
  cout << ans << '\n';
 }
 return 0;
}

#line 1 "test/yukicoder/1097.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1097
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#line 2 "src/Misc/Period.hpp"
#include <map>
#include <unordered_map>
#line 2 "src/Graph/HeavyLightDecomposition.hpp"
#include <array>
#include <cassert>
#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 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 5 "src/Misc/Period.hpp"
namespace period_internal {
template <class Map> struct PeriodB {
 using Iter= typename Map::const_iterator;
 Map mp;
};
template <class T> using PerB= std::conditional_t<std::is_integral_v<T>, PeriodB<std::unordered_map<T, int>>, PeriodB<std::map<T, int>>>;
}
template <class T= int> class Period: period_internal::PerB<T> {
 using typename period_internal::PerB<T>::Iter;
 using Path= std::vector<std::pair<int, int>>;
 std::vector<int> t, rt;
 std::vector<T> dc;
 HeavyLightDecomposition hld;
 static std::vector<int> iota(int n) {
  std::vector<int> v(n);
  for (int i= n; i--;) v[i]= i;
  return v;
 }
public:
 Period()= default;
 template <class F> Period(const F &f, const std::vector<T> &inits) {
  int n= 0;
  auto id= [&](const T &x) {
   if (auto it= this->mp.find(x); it != this->mp.end()) return it->second;
   return dc.emplace_back(x), t.push_back(-1), rt.push_back(-1), this->mp[x]= n++;
  };
  for (const T &s: inits)
   if (int v= id(s), w; rt[v] == -1) {
    for (w= v;; rt[w]= -2, w= t[w]= id(f(dc[w])))
     if (rt[w] != -1) {
      if (rt[w] != -2) w= rt[w];
      break;
     }
    for (int u= v; rt[u] == -2; u= t[u]) rt[u]= w;
   }
  Graph g(n + 1, n);
  for (int v= n; v--;) g[v]= {(rt[v] == v ? n : t[v]), v};
  hld= HeavyLightDecomposition(g.adjacency_vertex(1), n);
 }
 Period(const std::vector<int> &functional): Period([&](int x) { return functional[x]; }, iota(functional.size())) { static_assert(std::is_same_v<T, int>); }
 int operator()(const T &x) const {
  Iter it= this->mp.find(x);
  assert(it != this->mp.end());
  return t.size() - hld.to_seq(it->second);
 }
 size_t size() const { return t.size(); }
 // f^k(x)
 template <class Int, class= std::void_t<decltype(std::declval<Int>() % std::declval<int>())>> T jump(const T &x, Int k) const {
  Iter it= this->mp.find(x);
  assert(it != this->mp.end());
  int v= it->second, d= hld.depth(v) - 1;
  if (k <= d) return dc[hld.la(v, (int)k)];
  int b= t[v= rt[v]], l= (k-= d) % hld.depth(b);
  if (l == 0) return dc[v];
  return dc[hld.la(b, l - 1)];
 }
 // x, f(x), f(f(x)), ... f^k(x)
 // (x,...,f^i(x)), (f^(i+1)(x),...,f^(j-1)(x)) x cycle, (f^j(x),...,f^k(x))
 // sequence of half-open intervals [l,r)
 template <class Int, class= std::void_t<decltype(std::declval<Int>() % std::declval<int>())>> std::tuple<Path, Path, Int, Path> path(const T &x, Int k) const {
  Iter it= this->mp.find(x);
  assert(it != this->mp.end());
  int v= it->second, n= t.size(), d= hld.depth(v) - 1;
  std::array<Path, 3> pth;
  Int cnt= 0;
  if (k > d) {
   int r= rt[v], b= t[r], c= hld.depth(b), l= (k-= d) % c;
   if (pth[0]= hld.path(v, r), pth[1]= hld.path(b, r), cnt= k / c; l) pth[2]= hld.path(b, hld.la(b, l - 1));
  } else pth[0]= hld.path(v, hld.la(v, (int)k));
  for (int s= 3; s--;)
   for (auto &[l, r]: pth[s]) l= n - l, r= n - r + 1;
  return {pth[0], pth[1], cnt, pth[2]};
 }
 Path path_upto_cycle(const T &x) const {
  Iter it= this->mp.find(x);
  assert(it != this->mp.end());
  int v= it->second, n= t.size(), r= rt[v], b= t[r], w= hld.lca(b, v);
  auto p1= hld.path(v, r);
  if (b != w) {
   auto p2= hld.path(b, hld.jump(w, b, 1));
   p1.insert(p1.end(), p2.begin(), p2.end());
  }
  for (auto &[l, r]: p1) l= n - l, r= n - r + 1;
  return p1;
 }
};
#line 7 "test/yukicoder/1097.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 vector<int> A(N), to(N);
 for (int i= 0; i < N; ++i) cin >> A[i], to[i]= (i + A[i]) % N;
 Period p(to);
 vector<long long> sum(N + 1);
 for (int i= N; i--;) sum[p(i) + 1]= A[i];
 for (int i= 0; i < N; ++i) sum[i + 1]+= sum[i];
 int Q;
 cin >> Q;
 while (Q--) {
  long long K;
  cin >> K;
  long long ans= 0;
  auto [p1, p2, c, p3]= p.path(0, K - 1);
  for (auto [l, r]: p1) ans+= sum[r] - sum[l];
  for (auto [l, r]: p2) ans+= c * (sum[r] - sum[l]);
  for (auto [l, r]: p3) ans+= sum[r] - sum[l];
  cout << ans << '\n';
 }
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_sample_01.txt	AC	6 ms	4 MB
g++-13	00_sample_02.txt	AC	5 ms	4 MB
g++-13	01_small_01.txt	AC	5 ms	4 MB
g++-13	01_small_02.txt	AC	5 ms	4 MB
g++-13	01_small_03.txt	AC	5 ms	3 MB
g++-13	01_small_04.txt	AC	5 ms	4 MB
g++-13	01_small_05.txt	AC	5 ms	4 MB
g++-13	02_mid_01.txt	AC	12 ms	5 MB
g++-13	02_mid_02.txt	AC	12 ms	5 MB
g++-13	02_mid_03.txt	AC	12 ms	5 MB
g++-13	02_mid_04.txt	AC	12 ms	5 MB
g++-13	02_mid_05.txt	AC	12 ms	5 MB
g++-13	03_large_01.txt	AC	83 ms	15 MB
g++-13	03_large_02.txt	AC	92 ms	15 MB
g++-13	03_large_03.txt	AC	84 ms	15 MB
g++-13	03_large_04.txt	AC	86 ms	15 MB
g++-13	03_large_05.txt	AC	76 ms	15 MB
g++-13	04_max_01.txt	AC	54 ms	15 MB
g++-13	04_max_02.txt	AC	55 ms	15 MB
g++-13	04_max_03.txt	AC	58 ms	15 MB
g++-13	04_max_04.txt	AC	58 ms	15 MB
g++-13	04_max_05.txt	AC	61 ms	15 MB
g++-13	04_max_06.txt	AC	61 ms	15 MB
clang++-18	00_sample_01.txt	AC	5 ms	4 MB
clang++-18	00_sample_02.txt	AC	5 ms	4 MB
clang++-18	01_small_01.txt	AC	5 ms	4 MB
clang++-18	01_small_02.txt	AC	5 ms	4 MB
clang++-18	01_small_03.txt	AC	5 ms	4 MB
clang++-18	01_small_04.txt	AC	5 ms	4 MB
clang++-18	01_small_05.txt	AC	5 ms	4 MB
clang++-18	02_mid_01.txt	AC	12 ms	5 MB
clang++-18	02_mid_02.txt	AC	12 ms	5 MB
clang++-18	02_mid_03.txt	AC	12 ms	5 MB
clang++-18	02_mid_04.txt	AC	12 ms	5 MB
clang++-18	02_mid_05.txt	AC	12 ms	5 MB
clang++-18	03_large_01.txt	AC	81 ms	15 MB
clang++-18	03_large_02.txt	AC	84 ms	15 MB
clang++-18	03_large_03.txt	AC	83 ms	15 MB
clang++-18	03_large_04.txt	AC	83 ms	15 MB
clang++-18	03_large_05.txt	AC	76 ms	15 MB
clang++-18	04_max_01.txt	AC	50 ms	15 MB
clang++-18	04_max_02.txt	AC	52 ms	15 MB
clang++-18	04_max_03.txt	AC	53 ms	15 MB
clang++-18	04_max_04.txt	AC	53 ms	15 MB
clang++-18	04_max_05.txt	AC	58 ms	15 MB
clang++-18	04_max_06.txt	AC	61 ms	15 MB

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