Hashiryo's Library

This documentation is automatically generated by competitive-verifier/competitive-verifier

View the Project on GitHub hashiryo/Library

:warning: test/yosupo/dynamic_tree_vertex_set_path_composite.LCT.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#include "src/DataStructure/LinkCutTree.hpp"
#include "src/Math/ModInt.hpp"
using namespace std;

using Mint= ModInt<998244353>;
struct RcompositeQ {
 using T= pair<Mint, Mint>;
 static T op(const T &l, const T &r) { return make_pair(r.first * l.first, r.first * l.second + r.second); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, Q;
 cin >> N >> Q;
 LinkCutTree<RcompositeQ> lct(N);
 for (int i= 0; i < N; i++) {
  Mint a, b;
  cin >> a >> b;
  lct.set(i, {a, b});
 }
 for (int i= 0; i < N - 1; i++) {
  int u, v;
  cin >> u >> v;
  lct.link(u, v);
 }
 while (Q--) {
  int op;
  cin >> op;
  if (op == 0) {
   int u, v, w, x;
   cin >> u >> v >> w >> x;
   lct.cut(u, v);
   lct.link(w, x);
  } else if (op == 1) {
   int p;
   Mint c, d;
   cin >> p >> c >> d;
   lct.set(p, {c, d});
  } else {
   int u, v;
   Mint x;
   cin >> u >> v >> x;
   auto [c, d]= lct.prod(u, v);
   cout << c * x + d << '\n';
  }
 }
 return 0;
}

#line 1 "test/yosupo/dynamic_tree_vertex_set_path_composite.LCT.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/DataStructure/LinkCutTree.hpp"
#include <algorithm>
#include <vector>
#include <string>
#include <cstddef>
#include <utility>
#include <cassert>
#line 2 "src/Internal/detection_idiom.hpp"
#include <type_traits>
#define _DETECT_BOOL(name, ...) \
 template <class, class= void> struct name: std::false_type {}; \
 template <class T> struct name<T, std::void_t<__VA_ARGS__>>: std::true_type {}; \
 template <class T> static constexpr bool name##_v= name<T>::value
#define _DETECT_TYPE(name, type1, type2, ...) \
 template <class T, class= void> struct name { \
  using type= type2; \
 }; \
 template <class T> struct name<T, std::void_t<__VA_ARGS__>> { \
  using type= type1; \
 }
#line 9 "src/DataStructure/LinkCutTree.hpp"
template <class M= void> class LinkCutTree {
 _DETECT_BOOL(semigroup, typename T::T, decltype(&T::op));
 _DETECT_BOOL(dual, typename T::T, typename T::E, decltype(&T::mp), decltype(&T::cp));
 _DETECT_BOOL(commute, typename T::commute);
 _DETECT_TYPE(myself_or_T, typename T::T, T, typename T::T);
 _DETECT_TYPE(nullptr_or_E, typename T::E, std::nullptr_t, typename T::E);
 using T= std::conditional_t<std::is_void_v<M>, std::nullptr_t, typename myself_or_T<M>::type>;
 using E= typename nullptr_or_E<M>::type;
 struct NodeB {
  int ch[2]= {-1, -1}, par= -1;
  bool revf= 0;
 };
 template <class D, class A> struct NodeV: NodeB {
  T val;
 };
 template <class D> struct NodeV<D, void>: NodeB {};
 template <class D, bool du> struct NodeD: NodeV<D, M> {};
 template <class D> struct NodeD<D, 1>: NodeV<D, M> {
  E laz;
  bool lazf= 0;
 };
 template <class D, bool sg, bool com> struct NodeS: NodeD<D, dual_v<M>> {};
 template <class D> struct NodeS<D, 1, 1>: NodeD<D, dual_v<M>> {
  T sum;
 };
 template <class D> struct NodeS<D, 1, 0>: NodeD<D, dual_v<M>> {
  T sum, rsum;
 };
 using Node= NodeS<void, semigroup_v<M>, commute_v<M>>;
 std::vector<Node> n;
 inline void update(int i) {
  n[i].sum= n[i].val;
  if constexpr (!commute_v<M>) n[i].rsum= n[i].val;
  if (int l= n[i].ch[0]; l != -1) {
   n[i].sum= M::op(n[l].sum, n[i].sum);
   if constexpr (!commute_v<M>) n[i].rsum= M::op(n[i].rsum, n[l].rsum);
  }
  if (int r= n[i].ch[1]; r != -1) {
   n[i].sum= M::op(n[i].sum, n[r].sum);
   if constexpr (!commute_v<M>) n[i].rsum= M::op(n[r].rsum, n[i].rsum);
  }
 }
 inline void propagate(int i, const E &x) {
  if (i == -1) return;
  if (n[i].lazf) M::cp(n[i].laz, x);
  else n[i].laz= x;
  if constexpr (semigroup_v<M>) {
   M::mp(n[i].sum, x);
   if constexpr (!commute_v<M>) M::mp(n[i].rsum, x);
  }
  M::mp(n[i].val, x), n[i].lazf= 1;
 }
 inline void toggle(int i) {
  if (i == -1) return;
  std::swap(n[i].ch[0], n[i].ch[1]);
  if constexpr (semigroup_v<M> && !commute_v<M>) std::swap(n[i].sum, n[i].rsum);
  n[i].revf^= 1;
 }
 inline void push(int i) {
  if (n[i].revf) toggle(n[i].ch[0]), toggle(n[i].ch[1]), n[i].revf= 0;
  if constexpr (dual_v<M>)
   if (n[i].lazf) propagate(n[i].ch[0], n[i].laz), propagate(n[i].ch[1], n[i].laz), n[i].lazf= 0;
 }
 inline int dir(int i) {
  if (int p= n[i].par; p != -1) {
   if (n[p].ch[0] == i) return 0;
   if (n[p].ch[1] == i) return 1;
  }
  return 2;
 }
 inline void rot(int i) {
  int p= n[i].par, d= n[p].ch[1] == i;
  if (int c= n[p].ch[d]= std::exchange(n[i].ch[!d], p); c != -1) n[c].par= p;
  if (d= dir(p); d < 2) n[n[p].par].ch[d]= i;
  n[i].par= std::exchange(n[p].par, i);
  if constexpr (semigroup_v<M>) update(p);
 }
 inline void splay(int i) {
  push(i);
  for (int d; d= dir(i), d < 2; rot(i))
   if (int p= n[i].par, c= dir(p), pp= n[p].par; c < 2) push(pp), push(p), push(i), rot(d == c ? p : i);
   else push(p), push(i);
  if constexpr (semigroup_v<M>) update(i);
 }
 inline int expose(int i) {
  int r= -1;
  for (int p= i; p != -1; r= p, p= n[p].par) {
   splay(p), n[p].ch[1]= r;
   if constexpr (semigroup_v<M>) update(p);
  }
  return splay(i), r;
 }
public:
 LinkCutTree(size_t sz): n(sz) {}
 LinkCutTree(size_t sz, T val): n(sz) {
  for (int i= sz; i--;) n[i].val= val;
 }
 void evert(int k) { expose(k), toggle(k), push(k); }
 void link(int c, int p) {
  evert(c), expose(p), assert(n[c].par == -1), n[p].ch[1]= c, n[c].par= p;
  if constexpr (semigroup_v<M>) update(p);
 }
 void cut(int c, int p) {
  evert(p), expose(c), assert(n[c].ch[0] == p), n[c].ch[0]= n[p].par= -1;
  if constexpr (semigroup_v<M>) update(c);
 }
 int root(int x) {
  for (expose(x);; x= n[x].ch[0])
   if (push(x), n[x].ch[0] == -1) return splay(x), x;
 }
 int parent(int x) {
  if (expose(x), x= n[x].ch[0]; x == -1) return -1;
  for (;; x= n[x].ch[1])
   if (push(x), n[x].ch[1] == -1) return splay(x), x;
 }
 int lca(int x, int y) { return x == y ? x : (expose(x), y= expose(y), n[x].par == -1) ? -1 : y; }
 const T &get(int k) {
  static_assert(!std::is_void_v<M>, "\"get\" is not available\n");
  return expose(k), n[k].val;
 }
 T &at(int k) {
  static_assert(!std::is_void_v<M> && !semigroup_v<M>, "\"at\" is not available\n");
  return expose(k), n[k].val;
 }
 template <class L= M> const std::enable_if_t<semigroup_v<L>, T> &operator[](size_t k) { return get(k); }
 template <class L= M> std::enable_if_t<!semigroup_v<L>, T> &operator[](size_t k) { return at(k); }
 void set(int k, const T &v) {
  static_assert(!std::is_void_v<M>, "\"set\" is not available\n");
  expose(k), n[k].val= v;
  if constexpr (semigroup_v<M>) update(k);
 }
 void mul(int k, const T &v) {
  static_assert(semigroup_v<M> && commute_v<M>, "\"mul\" is not available\n");
  expose(k), n[k].val= M::op(n[k].val, v), update(k);
 }
 // [a,b] closed section
 T prod(int a, int b) {
  static_assert(semigroup_v<M>, "\"prod\" is not available\n");
  return a == b ? get(a) : (evert(a), expose(b), assert(n[a].par != -1), n[b].sum);
 }
 // [a,b] closed section
 void apply(int a, int b, const E &v) {
  static_assert(dual_v<M>, "\"apply\" is not available\n");
  evert(a), expose(b), assert(a == b || n[a].par != -1), propagate(b, v), push(b);
 }
 static std::string which_unavailable() {
  std::string ret= "";
  if constexpr (semigroup_v<M>) ret+= "\"at\" ";
  else ret+= "\"prod\" ";
  if constexpr (!semigroup_v<M> || !commute_v<M>) ret+= "\"mul\" ";
  if constexpr (!dual_v<M>) ret+= "\"apply\" ";
  if constexpr (std::is_void_v<M>) ret+= "\"get\" \"set\" ";
  return ret;
 }
};
#line 5 "src/Math/mod_inv.hpp"
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 7 "test/yosupo/dynamic_tree_vertex_set_path_composite.LCT.test.cpp"
using namespace std;

using Mint= ModInt<998244353>;
struct RcompositeQ {
 using T= pair<Mint, Mint>;
 static T op(const T &l, const T &r) { return make_pair(r.first * l.first, r.first * l.second + r.second); }
};
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, Q;
 cin >> N >> Q;
 LinkCutTree<RcompositeQ> lct(N);
 for (int i= 0; i < N; i++) {
  Mint a, b;
  cin >> a >> b;
  lct.set(i, {a, b});
 }
 for (int i= 0; i < N - 1; i++) {
  int u, v;
  cin >> u >> v;
  lct.link(u, v);
 }
 while (Q--) {
  int op;
  cin >> op;
  if (op == 0) {
   int u, v, w, x;
   cin >> u >> v >> w >> x;
   lct.cut(u, v);
   lct.link(w, x);
  } else if (op == 1) {
   int p;
   Mint c, d;
   cin >> p >> c >> d;
   lct.set(p, {c, d});
  } else {
   int u, v;
   Mint x;
   cin >> u >> v >> x;
   auto [c, d]= lct.prod(u, v);
   cout << c * x + d << '\n';
  }
 }
 return 0;
}
Back to top page