test/atcoder/abc310_g.test.cpp

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• Last update: 2025-08-08 18:52:16+09:00
• Problem: https://atcoder.jp/contests/abc310/tasks/abc310_g

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)
• modintを扱うテンプレート (src/Internal/modint_traits.hpp)
• 剰余の高速化 (src/Internal/Remainder.hpp)
• 逆元 ($\mathbb{Z}/m\mathbb{Z}$) (src/Math/mod_inv.hpp)
• ModInt (src/Math/ModInt.hpp)
• 周期性の利用 (Functionalグラフ) (src/Misc/Period.hpp)

Code

// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc310/tasks/abc310_g
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include "src/Math/ModInt.hpp"
#include "src/Misc/Period.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int N;
 long long K;
 cin >> N >> K;
 vector<int> A(N), B(N);
 for (int i= 0; i < N; ++i) cin >> A[i], --A[i];
 for (int i= 0; i < N; ++i) cin >> B[i];
 Period p(A);
 vector<Mint> sum(N + 1);
 for (int i= N; i--;) {
  auto [p1, p2, c, p3]= p.path(i, K);
  for (auto [l, r]: p1) sum[l]+= B[i], sum[r]-= B[i];
  for (auto [l, r]: p2) sum[l]+= Mint(c) * B[i], sum[r]-= Mint(c) * B[i];
  for (auto [l, r]: p3) sum[l]+= B[i], sum[r]-= B[i];
 }
 for (int i= 0; i < N; ++i) sum[i + 1]+= sum[i];
 for (int i= N; i--;) sum[p(i)]-= B[i];
 Mint iv= Mint(1) / K;
 for (int i= 0; i < N; ++i) cout << sum[p(i)] * iv << " \n"[i + 1 == N];
 return 0;
}

#line 1 "test/atcoder/abc310_g.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc310/tasks/abc310_g
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
 std::make_signed_t<Uint> x= 1, y= 0, z= 0;
 for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
 using Uint= U;
 static constexpr inline auto mod() { return B::md.mod; }
 constexpr MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 constexpr MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
 constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
 constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
 constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
 constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
 constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
 constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
 constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
 constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
 constexpr inline Uint val() const { return B::md.get(x); }
 friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
 friend istream &operator>>(istream &is, MInt &r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 2 "src/Misc/Period.hpp"
#include <map>
#include <unordered_map>
#line 2 "src/Graph/HeavyLightDecomposition.hpp"
#include <array>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#line 6 "src/Internal/ListRange.hpp"
#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 9 "test/atcoder/abc310_g.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int N;
 long long K;
 cin >> N >> K;
 vector<int> A(N), B(N);
 for (int i= 0; i < N; ++i) cin >> A[i], --A[i];
 for (int i= 0; i < N; ++i) cin >> B[i];
 Period p(A);
 vector<Mint> sum(N + 1);
 for (int i= N; i--;) {
  auto [p1, p2, c, p3]= p.path(i, K);
  for (auto [l, r]: p1) sum[l]+= B[i], sum[r]-= B[i];
  for (auto [l, r]: p2) sum[l]+= Mint(c) * B[i], sum[r]-= Mint(c) * B[i];
  for (auto [l, r]: p3) sum[l]+= B[i], sum[r]-= B[i];
 }
 for (int i= 0; i < N; ++i) sum[i + 1]+= sum[i];
 for (int i= N; i--;) sum[p(i)]-= B[i];
 Mint iv= Mint(1) / K;
 for (int i= 0; i < N; ++i) cout << sum[p(i)] * iv << " \n"[i + 1 == N];
 return 0;
}

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