matsutaku-library
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test/yosupo/range_affine_range_sum-splay_tree.test.cpp
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- Last update: 2024-07-11 22:21:57+09:00
- Problem: https://judge.yosupo.jp/problem/range_affine_range_sum
Code
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include "include/mtl/splay_tree_list.hpp"
#include "include/mtl/modular.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll MOD = 998244353;
using mint = Modular<MOD>;
struct Sum {
mint a=0;
int sz=0;
Sum operator*(const Sum& r) const {
return {a+r.a, sz+r.sz};
}
};
struct Affine {
mint b=1, c=0;
Affine& operator*=(const Affine& r) {
b *= r.b;
c = c*r.b + r.c;
return *this;
}
Sum act(const Sum& a) const {
return {b*a.a + c*a.sz, a.sz};
}
};
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
int N,Q; cin>>N>>Q;
vector<Sum> A(N);
for (auto& a : A) {
cin>>a.a;
a.sz = 1;
}
SplayTreeList<Sum, Affine> rsq(A.begin(), A.end());
for (int q = 0; q < Q; q++) {
int t; cin>>t;
if (t == 0) {
int l,r,b,c; cin>>l>>r>>b>>c;
rsq.update(l,r, {b,c});
} else if (t == 1) {
int l,r; cin>>l>>r;
auto ans = rsq.prod(l,r);
cout << ans.a << endl;
}
}
return 0;
}
#line 1 "test/yosupo/range_affine_range_sum-splay_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#line 2 "include/mtl/splay_tree.hpp"
#include <memory>
#include <cassert>
template<class NodeType>
struct SplayTreeNodeBase {
using node_type = NodeType;
using node_shared = std::shared_ptr<node_type>;
using node_weak = std::weak_ptr<node_type>;
node_shared l,r;
node_weak p;
bool rev;
bool is_root() const {
return p.expired() || (p.lock()->l.get() != this && p.lock()->r.get() != this);
}
};
template<class T>
struct SplayTreeNodeTraits {
using node_type = typename T::node_type;
using node_shared = typename T::node_shared;
using node_weak = typename T::node_weak;
};
template<class Node>
struct SplayTreeBase {
using node_traits = SplayTreeNodeTraits<Node>;
using node_type = typename node_traits::node_type;
using node_shared = typename node_traits::node_shared;
using node_weak = typename node_traits::node_weak;
SplayTreeBase() = default;
void rotate_left(const node_shared& u) const {
auto p = u->p.lock(), q = p->p.lock();
p->r = u->l;
if (p->r)
p->r->p = p;
u->l = p;
p->p = u;
u->p = q;
if (q) {
if (q->l == p)
q->l = u;
else if (q->r == p)
q->r = u;
}
}
void rotate_right(const node_shared& u) const {
auto p = u->p.lock(), q = p->p.lock();
p->l = u->r;
if (p->l)
p->l->p = p;
u->r = p;
p->p = u;
u->p = q;
if (q) {
if (q->l == p)
q->l = u;
else if (q->r == p)
q->r = u;
}
}
virtual void reverse_prod(const node_shared& u) const {}
virtual void propagate(const node_shared& u) const {}
virtual void aggregate(const node_shared& u) const {}
void splay(const node_shared& u) const {
if (u->is_root()) {
this->propagate(u);
this->aggregate(u);
return;
}
do {
assert(u);
auto p = u->p.lock();
assert(p);
if (p->is_root()) {
this->propagate(p);
this->propagate(u);
if (p->l == u)
rotate_right(u);
else if (p->r == u)
rotate_left(u);
else throw "invalid tree";
this->aggregate(p);
this->aggregate(u);
} else {
auto q = p->p.lock();
this->propagate(q);
this->propagate(p);
this->propagate(u);
if (q->l == p) {
if (p->l == u) { // zig-zig
rotate_right(p);
rotate_right(u);
this->aggregate(q);
this->aggregate(p);
} else if (p->r == u) { // zig-zag
rotate_left(u);
rotate_right(u);
this->aggregate(p);
this->aggregate(q);
} else throw "invalid tree";
} else if (q->r == p) {
if (p->r == u) { // zig-zig
rotate_left(p);
rotate_left(u);
this->aggregate(q);
this->aggregate(p);
} else if (p->l == u) { // zig-zag
rotate_right(u);
rotate_left(u);
this->aggregate(p);
this->aggregate(q);
} else throw "invalid tree";
}
this->aggregate(u);
}
} while (!u->is_root());
}
};
#line 2 "include/mtl/monoid.hpp"
#include <utility>
#if __cpp_concepts >= 202002L
#include <concepts>
#endif
template<class T, T (*op)(T, T), T (*e)()>
struct Monoid {
T x;
Monoid() : x(e()) {}
template<class... Args>
Monoid(Args&&... args) : x(std::forward<Args>(args)...) {}
Monoid operator*(const Monoid& rhs) const {
return Monoid(op(x, rhs.x));
}
const T& val() const {
return x;
}
};
struct VoidMonoid {
VoidMonoid() {}
VoidMonoid operator*(const VoidMonoid& rhs) const {
return VoidMonoid();
}
};
#if __cpp_concepts >= 202002L
template<class T>
concept IsMonoid = requires (T m) {
{ m * m } -> std::same_as<T>;
};
#endif
template<class T, T (*op)(T, T), T (*e)()>
struct CommutativeMonoid : public Monoid<T, op, e> {
using Base = Monoid<T, op, e>;
CommutativeMonoid(T x=e()) : Base(x) {}
CommutativeMonoid operator+(const CommutativeMonoid& rhs) const {
return CommutativeMonoid(*this * rhs);
}
};
#if __cpp_concepts >= 202002L
template<class T>
concept IsCommutativeMonoid = requires (T m) {
{ m + m } -> std::same_as<T>;
};
#endif
template<class S, class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
struct OperatorMonoid {
F f;
OperatorMonoid() : f(id()) {}
template<class... Args>
OperatorMonoid(Args&&... args) : f(std::forward<Args>(args)...) {}
OperatorMonoid& operator*=(const OperatorMonoid& rhs) {
f = composition(rhs.f, f);
return *this;
}
S act(const S& s) const {
return mapping(f, s);
}
};
struct VoidOperatorMonoid {
VoidOperatorMonoid() {}
VoidOperatorMonoid& operator*=(const VoidOperatorMonoid& rhs) {
return *this;
}
template<class T>
T act(const T& s) const {
return s;
}
};
#if __cpp_concepts >= 202002L
template<class F, class S>
concept IsOperatorMonoid = requires (F f, S s) {
{ f *= f } -> std::same_as<F&>;
{ f.act(s) } -> std::same_as<S>;
};
#endif
#line 4 "include/mtl/splay_tree_list.hpp"
template<class M, class O>
struct SplayTreeListNode : SplayTreeNodeBase<SplayTreeListNode<M,O>> {
size_t sum;
M m, prod, rprod;
O f;
using Base = SplayTreeNodeBase<SplayTreeListNode<M,O>>;
template<class... Args>
SplayTreeListNode(Args&&... args)
: Base(), sum(1), m(std::forward<Args>(args)...), prod(m), rprod(m), f() {}
};
template<class M, class O=VoidOperatorMonoid>
#if __cpp_concepts >= 202002L
requires IsMonoid<M> && IsOperatorMonoid<O, M>
#endif
struct SplayTreeList : SplayTreeBase<SplayTreeListNode<M, O>> {
using node_type = SplayTreeListNode<M, O>;
using base = SplayTreeBase<node_type>;
using monoid_type = M;
using operator_monoid_type = O;
using node_shared = typename SplayTreeNodeTraits<node_type>::node_shared;
node_shared root;
SplayTreeList() : base(), root(nullptr) {}
template<class InputIt>
node_shared _dfs_init(InputIt first, InputIt last) {
if (first == last) return nullptr;
auto n = std::distance(first, last);
auto mid = std::next(first, n / 2);
auto u = std::make_shared<node_type>(*mid);
u->l = _dfs_init(first, mid);
if (u->l) u->l->p = u;
u->r = _dfs_init(std::next(mid), last);
if (u->r) u->r->p = u;
this->aggregate(u);
return u;
}
template<class InputIt>
SplayTreeList(InputIt first, InputIt last) : SplayTreeList() {
if (first == last) return;
using iterator_category = typename std::iterator_traits<InputIt>::iterator_category;
if constexpr (std::is_base_of<iterator_category, std::random_access_iterator_tag>::value) {
root = _dfs_init(first, last);
} else {
auto it = first;
root = std::make_shared<node_type>(*it);
++it;
for (; it != last; ++it) {
auto u = std::make_shared<node_type>(*it);
u->l = root;
root->p = u;
root = u;
this->aggregate(u);
}
}
}
void reverse_prod(const node_shared& u) const override {
std::swap(u->prod, u->rprod);
}
void propagate(const node_shared& u) const override {
if (u->l) {
u->l->m = u->f.act(u->l->m);
u->l->prod = u->f.act(u->l->prod);
u->l->rprod = u->f.act(u->l->rprod);
u->l->f *= u->f;
}
if (u->r) {
u->r->m = u->f.act(u->r->m);
u->r->prod = u->f.act(u->r->prod);
u->r->rprod = u->f.act(u->r->rprod);
u->r->f *= u->f;
}
if (u->rev) {
std::swap(u->l, u->r);
if (u->l) {
u->l->rev ^= true;
reverse_prod(u->l);
}
if (u->r) {
u->r->rev ^= true;
reverse_prod(u->r);
}
u->rev = false;
}
u->f = operator_monoid_type();
}
void aggregate(const node_shared& u) const override {
u->sum = 1;
u->prod = u->m;
u->rprod = u->m;
if (u->l) {
u->sum += u->l->sum;
u->prod = u->l->prod * u->prod;
u->rprod = u->rprod * u->l->rprod;
}
if (u->r) {
u->sum += u->r->sum;
u->prod = u->prod * u->r->prod;
u->rprod = u->r->rprod * u->rprod;
}
}
node_shared kth_element(size_t k) {
assert(k < root->sum);
auto u = root;
while (true) {
assert(u);
auto lp = u->l ? u->l->sum : 0;
auto rp = u->r ? u->r->sum : 0;
// cerr<<u->m.first<<' '<<u->sum<<' '<<lp<<' '<<rp<<endl;
assert(u->sum == lp+rp+1);
propagate(u);
if (!u->l) {
if (k == 0)
break;
k--;
u = u->r;
} else if (u->l->sum == k) {
break;
} else if (u->l->sum > k) {
u = u->l;
} else {
k -= u->l->sum + 1;
u = u->r;
}
}
assert(u);
base::splay(u);
root = u;
return u;
}
template<class... Args>
void insert(size_t i, Args&&... args) {
auto u = std::make_shared<node_type>(std::forward<Args>(args)...);
if (i == 0) {
u->r = root;
if (root) root->p = u;
root = u;
aggregate(u);
return;
}
if (i == root->sum) {
u->l = root;
if (root) root->p = u;
root = u;
aggregate(u);
return;
}
auto p = kth_element(i);
u->l = p->l;
u->r = p;
if (u->l)
u->l->p = u;
u->r->p = u;
p->l = nullptr;
root = u;
aggregate(p);
aggregate(u);
}
void erase(size_t i) {
assert(i < root->sum);
auto p = kth_element(i);
if (i == 0) {
root = p->r;
if (root)
root->p.reset();
return;
}
if (i == root->sum-1) {
root = p->l;
if (root)
root->p.reset();
return;
}
auto r = p->r;
auto l = p->l;
root = r;
root->p.reset();
r = kth_element(0);
r->l = l;
l->p = r;
aggregate(r);
// p has no referry so p is deleted outomatically.
}
node_shared between(size_t l, size_t r) {
assert(r <= root->sum);
if (l == 0) {
if (r == root->sum)
return root;
else
return kth_element(r)->l;
}
if (r == root->sum) {
return kth_element(l-1)->r;
}
auto rp = kth_element(r);
root = rp->l;
root->p.reset();
auto lp = kth_element(l-1);
rp->l = lp;
lp->p = rp;
root = rp;
aggregate(rp);
return lp->r;
}
monoid_type prod(size_t l, size_t r) {
return between(l, r)->prod;
}
void reverse(size_t l, size_t r) {
if (l == r) return;
auto u = between(l, r);
u->rev ^= true;
reverse_prod(u);
base::splay(u);
root = u;
}
template<class... Args>
void set(size_t i, Args&&... args) {
auto u = kth_element(i);
u->m = monoid_type(std::forward<Args>(args)...);
this->aggregate(u);
}
void update(size_t i, const operator_monoid_type& f) {
auto u = kth_element(i);
u->m = f.act(u->m);
this->aggregate(u);
}
void update(size_t l, size_t r, const operator_monoid_type& f) {
assert(l < r);
auto u = between(l, r);
u->m = f.act(u->m);
u->prod = f.act(u->prod);
u->rprod = f.act(u->rprod);
u->f *= f;
base::splay(u);
root = u;
}
};
#line 2 "include/mtl/bit_manip.hpp"
#include <cstdint>
#line 4 "include/mtl/bit_manip.hpp"
#if __cplusplus >= 202002L
#ifndef MTL_CPP20
#define MTL_CPP20
#endif
#include <bit>
#endif
namespace bm {
/// Count 1s for each 8 bits
inline constexpr uint64_t popcnt_e8(uint64_t x) {
x = (x & 0x5555555555555555) + ((x>>1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x>>2) & 0x3333333333333333);
x = (x & 0x0F0F0F0F0F0F0F0F) + ((x>>4) & 0x0F0F0F0F0F0F0F0F);
return x;
}
/// Count 1s
inline constexpr unsigned popcnt(uint64_t x) {
#ifdef MTL_CPP20
return std::popcount(x);
#else
return (popcnt_e8(x) * 0x0101010101010101) >> 56;
#endif
}
/// Alias to mtl::popcnt(x)
constexpr unsigned popcount(uint64_t x) {
return popcnt(x);
}
/// Count trailing 0s. s.t. *11011000 -> 3
inline constexpr unsigned ctz(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_zero(x);
#else
return popcnt((x & (-x)) - 1);
#endif
}
/// Alias to mtl::ctz(x)
constexpr unsigned countr_zero(uint64_t x) {
return ctz(x);
}
/// Count trailing 1s. s.t. *11011011 -> 2
inline constexpr unsigned cto(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_one(x);
#else
return ctz(~x);
#endif
}
/// Alias to mtl::cto(x)
constexpr unsigned countr_one(uint64_t x) {
return cto(x);
}
inline constexpr unsigned ctz8(uint8_t x) {
return x == 0 ? 8 : popcnt_e8((x & (-x)) - 1);
}
/// [00..0](8bit) -> 0, [**..*](not only 0) -> 1
inline constexpr uint8_t summary(uint64_t x) {
constexpr uint64_t hmask = 0x8080808080808080ull;
constexpr uint64_t lmask = 0x7F7F7F7F7F7F7F7Full;
auto a = x & hmask;
auto b = x & lmask;
b = hmask - b;
b = ~b;
auto c = (a | b) & hmask;
c *= 0x0002040810204081ull;
return uint8_t(c >> 56);
}
/// Extract target area of bits
inline constexpr uint64_t bextr(uint64_t x, unsigned start, unsigned len) {
uint64_t mask = len < 64 ? (1ull<<len)-1 : 0xFFFFFFFFFFFFFFFFull;
return (x >> start) & mask;
}
/// 00101101 -> 00111111 -count_1s-> 6
inline constexpr unsigned log2p1(uint8_t x) {
if (x & 0x80)
return 8;
uint64_t p = uint64_t(x) * 0x0101010101010101ull;
p -= 0x8040201008040201ull;
p = ~p & 0x8080808080808080ull;
p = (p >> 7) * 0x0101010101010101ull;
p >>= 56;
return p;
}
/// 00101100 -mask_mssb-> 00100000 -to_index-> 5
inline constexpr unsigned mssb8(uint8_t x) {
assert(x != 0);
return log2p1(x) - 1;
}
/// 00101100 -mask_lssb-> 00000100 -to_index-> 2
inline constexpr unsigned lssb8(uint8_t x) {
assert(x != 0);
return popcnt_e8((x & -x) - 1);
}
/// Count leading 0s. 00001011... -> 4
inline constexpr unsigned clz(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_zero(x);
#else
if (x == 0)
return 64;
auto i = mssb8(summary(x));
auto j = mssb8(bextr(x, 8 * i, 8));
return 63 - (8 * i + j);
#endif
}
/// Alias to mtl::clz(x)
constexpr unsigned countl_zero(uint64_t x) {
return clz(x);
}
/// Count leading 1s. 11110100... -> 4
inline constexpr unsigned clo(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_one(x);
#else
return clz(~x);
#endif
}
/// Alias to mtl::clo(x)
constexpr unsigned countl_one(uint64_t x) {
return clo(x);
}
inline constexpr unsigned clz8(uint8_t x) {
return x == 0 ? 8 : 7 - mssb8(x);
}
inline constexpr uint64_t bit_reverse(uint64_t x) {
x = ((x & 0x00000000FFFFFFFF) << 32) | ((x & 0xFFFFFFFF00000000) >> 32);
x = ((x & 0x0000FFFF0000FFFF) << 16) | ((x & 0xFFFF0000FFFF0000) >> 16);
x = ((x & 0x00FF00FF00FF00FF) << 8) | ((x & 0xFF00FF00FF00FF00) >> 8);
x = ((x & 0x0F0F0F0F0F0F0F0F) << 4) | ((x & 0xF0F0F0F0F0F0F0F0) >> 4);
x = ((x & 0x3333333333333333) << 2) | ((x & 0xCCCCCCCCCCCCCCCC) >> 2);
x = ((x & 0x5555555555555555) << 1) | ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
return x;
}
/// Check if x is power of 2. 00100000 -> true, 00100001 -> false
constexpr bool has_single_bit(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::has_single_bit(x);
#else
return x != 0 && (x & (x - 1)) == 0;
#endif
}
/// Bit width needs to represent x. 00110110 -> 6
constexpr int bit_width(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::bit_width(x);
#else
return 64 - clz(x);
#endif
}
/// Ceil power of 2. 00110110 -> 01000000
constexpr uint64_t bit_ceil(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_ceil(x);
#else
if (x == 0) return 1;
return 1ull << bit_width(x - 1);
#endif
}
/// Floor power of 2. 00110110 -> 00100000
constexpr uint64_t bit_floor(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_floor(x);
#else
if (x == 0) return 0;
return 1ull << (bit_width(x) - 1);
#endif
}
} // namespace bm
#line 3 "include/mtl/modular.hpp"
#include <iostream>
#line 5 "include/mtl/modular.hpp"
template <int MOD>
class Modular {
private:
unsigned int val_;
public:
static constexpr unsigned int mod() { return MOD; }
template<class T>
static constexpr unsigned int safe_mod(T v) {
auto x = (long long)(v%(long long)mod());
if (x < 0) x += mod();
return (unsigned int) x;
}
constexpr Modular() : val_(0) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && std::is_unsigned<T>::value
> * = nullptr>
constexpr Modular(T v) : val_(v%mod()) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && !std::is_unsigned<T>::value
> * = nullptr>
constexpr Modular(T v) : val_(safe_mod(v)) {}
constexpr unsigned int val() const { return val_; }
constexpr Modular& operator+=(Modular x) {
val_ += x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr Modular operator-() const { return {mod() - val_}; }
constexpr Modular& operator-=(Modular x) {
val_ += mod() - x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr Modular& operator*=(Modular x) {
auto v = (long long) val_ * x.val();
if (v >= mod()) v %= mod();
val_ = v;
return *this;
}
constexpr Modular pow(long long p) const {
assert(p >= 0);
Modular t = 1;
Modular u = *this;
while (p) {
if (p & 1)
t *= u;
u *= u;
p >>= 1;
}
return t;
}
friend constexpr Modular pow(Modular x, long long p) {
return x.pow(p);
}
constexpr Modular inv() const { return pow(mod()-2); }
constexpr Modular& operator/=(Modular x) { return *this *= x.inv(); }
constexpr Modular operator+(Modular x) const { return Modular(*this) += x; }
constexpr Modular operator-(Modular x) const { return Modular(*this) -= x; }
constexpr Modular operator*(Modular x) const { return Modular(*this) *= x; }
constexpr Modular operator/(Modular x) const { return Modular(*this) /= x; }
constexpr Modular& operator++() { return *this += 1; }
constexpr Modular operator++(int) { Modular c = *this; ++(*this); return c; }
constexpr Modular& operator--() { return *this -= 1; }
constexpr Modular operator--(int) { Modular c = *this; --(*this); return c; }
constexpr bool operator==(Modular x) const { return val() == x.val(); }
constexpr bool operator!=(Modular x) const { return val() != x.val(); }
constexpr bool is_square() const {
return pow((mod()-1)/2) == 1;
}
/**
* Return x s.t. x * x = a mod p
* reference: https://zenn.dev/peria/articles/c6afc72b6b003c
*/
constexpr Modular sqrt() const {
if (!is_square())
throw std::runtime_error("not square");
auto mod_eight = mod() % 8;
if (mod_eight == 3 || mod_eight == 7) {
return pow((mod()+1)/4);
} else if (mod_eight == 5) {
auto x = pow((mod()+3)/8);
if (x * x != *this)
x *= Modular(2).pow((mod()-1)/4);
return x;
} else {
Modular d = 2;
while (d.is_square())
d += 1;
auto t = mod()-1;
int s = bm::ctz(t);
t >>= s;
auto a = pow(t);
auto D = d.pow(t);
int m = 0;
Modular dt = 1;
Modular du = D;
for (int i = 0; i < s; i++) {
if ((a*dt).pow(1u<<(s-1-i)) == -1) {
m |= 1u << i;
dt *= du;
}
du *= du;
}
return pow((t+1)/2) * D.pow(m/2);
}
}
friend std::ostream& operator<<(std::ostream& os, const Modular& x) {
return os << x.val();
}
friend std::istream& operator>>(std::istream& is, Modular& x) {
return is >> x.val_;
}
};
using Modular998244353 = Modular<998244353>;
using Modular1000000007 = Modular<(int)1e9+7>;
template<int Id=0>
class DynamicModular {
private:
static unsigned int mod_;
unsigned int val_;
public:
static unsigned int mod() { return mod_; }
static void set_mod(unsigned int m) { mod_ = m; }
template<class T>
static constexpr unsigned int safe_mod(T v) {
auto x = (long long)(v%(long long)mod());
if (x < 0) x += mod();
return (unsigned int) x;
}
constexpr DynamicModular() : val_(0) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && std::is_unsigned<T>::value
> * = nullptr>
constexpr DynamicModular(T v) : val_(v%mod()) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && !std::is_unsigned<T>::value
> * = nullptr>
constexpr DynamicModular(T v) : val_(safe_mod(v)) {}
constexpr unsigned int val() const { return val_; }
constexpr DynamicModular& operator+=(DynamicModular x) {
val_ += x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr DynamicModular operator-() const { return {mod() - val_}; }
constexpr DynamicModular& operator-=(DynamicModular x) {
val_ += mod() - x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr DynamicModular& operator*=(DynamicModular x) {
auto v = (long long) val_ * x.val();
if (v >= mod()) v %= mod();
val_ = v;
return *this;
}
constexpr DynamicModular pow(long long p) const {
assert(p >= 0);
DynamicModular t = 1;
DynamicModular u = *this;
while (p) {
if (p & 1)
t *= u;
u *= u;
p >>= 1;
}
return t;
}
friend constexpr DynamicModular pow(DynamicModular x, long long p) {
return x.pow(p);
}
// TODO: implement when mod is not prime
constexpr DynamicModular inv() const { return pow(mod()-2); }
constexpr DynamicModular& operator/=(DynamicModular x) { return *this *= x.inv(); }
constexpr DynamicModular operator+(DynamicModular x) const { return DynamicModular(*this) += x; }
constexpr DynamicModular operator-(DynamicModular x) const { return DynamicModular(*this) -= x; }
constexpr DynamicModular operator*(DynamicModular x) const { return DynamicModular(*this) *= x; }
constexpr DynamicModular operator/(DynamicModular x) const { return DynamicModular(*this) /= x; }
constexpr DynamicModular& operator++() { return *this += 1; }
constexpr DynamicModular operator++(int) { DynamicModular c = *this; ++(*this); return c; }
constexpr DynamicModular& operator--() { return *this -= 1; }
constexpr DynamicModular operator--(int) { DynamicModular c = *this; --(*this); return c; }
constexpr bool operator==(DynamicModular x) const { return val() == x.val(); }
constexpr bool operator!=(DynamicModular x) const { return val() != x.val(); }
constexpr bool is_square() const {
return val() == 0 or pow((mod()-1)/2) == 1;
}
/**
* Return x s.t. x * x = a mod p
* reference: https://zenn.dev/peria/articles/c6afc72b6b003c
*/
constexpr DynamicModular sqrt() const {
// assert mod is prime
if (!is_square())
throw std::runtime_error("not square");
if (val() < 2)
return val();
auto mod_eight = mod() % 8;
if (mod_eight == 3 || mod_eight == 7) {
return pow((mod()+1)/4);
} else if (mod_eight == 5) {
auto x = pow((mod()+3)/8);
if (x * x != *this)
x *= DynamicModular(2).pow((mod()-1)/4);
return x;
} else {
DynamicModular d = 2;
while (d.is_square())
++d;
auto t = mod()-1;
int s = bm::ctz(t);
t >>= s;
auto a = pow(t);
auto D = d.pow(t);
int m = 0;
DynamicModular dt = 1;
DynamicModular du = D;
for (int i = 0; i < s; i++) {
if ((a*dt).pow(1u<<(s-1-i)) == -1) {
m |= 1u << i;
dt *= du;
}
du *= du;
}
return pow((t+1)/2) * D.pow(m/2);
}
}
friend std::ostream& operator<<(std::ostream& os, const DynamicModular& x) {
return os << x.val();
}
friend std::istream& operator>>(std::istream& is, DynamicModular& x) {
return is >> x.val_;
}
};
template<int Id>
unsigned int DynamicModular<Id>::mod_;
#include <vector>
template<class ModInt>
struct ModularUtil {
static constexpr int mod = ModInt::mod();
static struct inv_table {
std::vector<ModInt> tb{0,1};
inv_table() : tb({0,1}) {}
} inv_;
void set_inv(int n) {
int m = inv_.tb.size();
if (m > n) return;
inv_.tb.resize(n+1);
for (int i = m; i < n+1; i++)
inv_.tb[i] = -inv_.tb[mod % i] * (mod / i);
}
ModInt& inv(int i) {
set_inv(i);
return inv_.tb[i];
}
};
template<class ModInt>
typename ModularUtil<ModInt>::inv_table ModularUtil<ModInt>::inv_;
#include <array>
namespace math {
constexpr int mod_pow_constexpr(int x, int p, int m) {
long long t = 1;
long long u = x;
while (p) {
if (p & 1) {
t *= u;
t %= m;
}
u *= u;
u %= m;
p >>= 1;
}
return (int) t;
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 880803841) return 26;
if (m == 998244353) return 3;
std::array<int, 20> divs{};
int cnt = 0;
int x = m-1;
if (x % 2 == 0) {
divs[cnt++] = 2;
x >>= bm::ctz(x);
}
for (int d = 3; d*d <= x; d += 2) {
if (x % d == 0) {
divs[cnt++] = d;
while (x % d == 0)
x /= d;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2; g < m; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (mod_pow_constexpr(g, (m-1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
return -1;
}
template<int m>
constexpr int primitive_root = primitive_root_constexpr(m);
}
#line 4 "test/yosupo/range_affine_range_sum-splay_tree.test.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll MOD = 998244353;
using mint = Modular<MOD>;
struct Sum {
mint a=0;
int sz=0;
Sum operator*(const Sum& r) const {
return {a+r.a, sz+r.sz};
}
};
struct Affine {
mint b=1, c=0;
Affine& operator*=(const Affine& r) {
b *= r.b;
c = c*r.b + r.c;
return *this;
}
Sum act(const Sum& a) const {
return {b*a.a + c*a.sz, a.sz};
}
};
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
int N,Q; cin>>N>>Q;
vector<Sum> A(N);
for (auto& a : A) {
cin>>a.a;
a.sz = 1;
}
SplayTreeList<Sum, Affine> rsq(A.begin(), A.end());
for (int q = 0; q < Q; q++) {
int t; cin>>t;
if (t == 0) {
int l,r,b,c; cin>>l>>r>>b>>c;
rsq.update(l,r, {b,c});
} else if (t == 1) {
int l,r; cin>>l>>r;
auto ans = rsq.prod(l,r);
cout << ans.a << endl;
}
}
return 0;
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | example_00 |
AC |
6 ms | 3 MB |
| g++ | max_random_00 |
AC |
4652 ms | 70 MB |
| g++ | max_random_01 |
AC |
5061 ms | 70 MB |
| g++ | max_random_02 |
AC |
4766 ms | 70 MB |
| g++ | random_00 |
AC |
3835 ms | 55 MB |
| g++ | random_01 |
AC |
3931 ms | 65 MB |
| g++ | random_02 |
AC |
2864 ms | 10 MB |
| g++ | small_00 |
AC |
6 ms | 3 MB |
| g++ | small_01 |
AC |
6 ms | 3 MB |
| g++ | small_02 |
AC |
6 ms | 3 MB |
| g++ | small_03 |
AC |
6 ms | 3 MB |
| g++ | small_04 |
AC |
6 ms | 3 MB |
| g++ | small_05 |
AC |
6 ms | 3 MB |
| g++ | small_06 |
AC |
6 ms | 3 MB |
| g++ | small_07 |
AC |
6 ms | 3 MB |
| g++ | small_08 |
AC |
7 ms | 3 MB |
| g++ | small_09 |
AC |
7 ms | 3 MB |
| g++ | small_random_00 |
AC |
10 ms | 4 MB |
| g++ | small_random_01 |
AC |
9 ms | 4 MB |
| clang++ | example_00 |
AC |
6 ms | 3 MB |
| clang++ | max_random_00 |
AC |
4969 ms | 70 MB |
| clang++ | max_random_01 |
AC |
5163 ms | 70 MB |
| clang++ | max_random_02 |
AC |
5327 ms | 70 MB |
| clang++ | random_00 |
AC |
3778 ms | 55 MB |
| clang++ | random_01 |
AC |
3933 ms | 65 MB |
| clang++ | random_02 |
AC |
2541 ms | 10 MB |
| clang++ | small_00 |
AC |
6 ms | 3 MB |
| clang++ | small_01 |
AC |
7 ms | 3 MB |
| clang++ | small_02 |
AC |
7 ms | 3 MB |
| clang++ | small_03 |
AC |
7 ms | 3 MB |
| clang++ | small_04 |
AC |
7 ms | 3 MB |
| clang++ | small_05 |
AC |
7 ms | 3 MB |
| clang++ | small_06 |
AC |
7 ms | 3 MB |
| clang++ | small_07 |
AC |
7 ms | 3 MB |
| clang++ | small_08 |
AC |
7 ms | 3 MB |
| clang++ | small_09 |
AC |
7 ms | 3 MB |
| clang++ | small_random_00 |
AC |
12 ms | 4 MB |
| clang++ | small_random_01 |
AC |
11 ms | 4 MB |