cplib-cpp
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data_structure/test/queue_operate_all_composite.test.cpp
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- Last update: 2025-08-25 00:44:48+09:00
- Problem: https://judge.yosupo.jp/problem/queue_operate_all_composite
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Code
#include "../../modint.hpp"
#include "../sliding_window_aggregation.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/queue_operate_all_composite"
#include <iostream>
using namespace std;
using mint = ModInt<998244353>;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
LinearFunctionQueue<mint> swag;
int Q;
cin >> Q;
while (Q--) {
int q;
cin >> q;
if (q == 0) {
mint a, b;
cin >> a >> b;
swag.push({a, b});
}
if (q == 1) swag.pop();
if (q == 2) {
mint x;
cin >> x;
pair<mint, mint> f = swag.fold_all();
cout << (f.first * x + f.second).val() << '\n';
}
}
}#line 2 "modint.hpp"
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
static_assert(md > 1);
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr static ModInt fac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[n];
}
constexpr static ModInt facinv(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[n];
}
constexpr static ModInt doublefac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
long long k = (n + 1) / 2;
return (n & 1) ? ModInt::fac(k * 2) / (ModInt(2).pow(k) * ModInt::fac(k))
: ModInt::fac(k) * ModInt(2).pow(k);
}
constexpr static ModInt nCr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(r) * ModInt::facinv(n - r);
}
constexpr static ModInt nPr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(n - r);
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt::nCr(n, r);
r = std::min(r, n - r);
ModInt ret = ModInt::facinv(r);
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt::facinv(k), sum += k;
}
return ret * ModInt::fac(sum);
}
template <class... Args> static ModInt multinomial(Args... args) {
int sum = (0 + ... + args);
ModInt result = (1 * ... * ModInt::facinv(args));
return ModInt::fac(sum) * result;
}
// Catalan number, C_n = binom(2n, n) / (n + 1) = # of Dyck words of length 2n
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt::fac(n * 2) * ModInt::facinv(n + 1) * ModInt::facinv(n);
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#line 2 "data_structure/sliding_window_aggregation.hpp"
#include <stack>
#include <utility>
#line 5 "data_structure/sliding_window_aggregation.hpp"
// Sliding-Window Aggregation based queue
// - `std::queue`-like data structure with monoid operation
// - Each operation is amortized O(1)
// - Verification:
// https://www.hackerrank.com/contests/tsg-live-4-programming-contest/challenges/tsg-live-4-procon-lcm-interval/submissions/code/1317888077
// - Reference:
// https://github.com/NiMiLib/NoshiMochiLibrary/blob/queue_aggregation/lib/data_structure/sequence/queue_aggregation.hpp
template <typename T_VAL, typename T_PROD, T_PROD (*val2prod)(T_VAL), T_PROD (*op)(T_PROD, T_PROD)>
struct swag_queue {
std::stack<std::pair<T_VAL, T_PROD>, std::vector<std::pair<T_VAL, T_PROD>>> front_stack,
back_stack;
T_PROD ID_;
swag_queue(T_PROD id_prod) : ID_(id_prod) {}
bool empty() const { return front_stack.empty() and back_stack.empty(); }
int size() const { return front_stack.size() + back_stack.size(); }
T_PROD fold_all() const {
if (empty())
return ID_;
else if (front_stack.empty())
return back_stack.top().second;
else if (back_stack.empty())
return front_stack.top().second;
else
return op(front_stack.top().second, back_stack.top().second);
}
void push(const T_VAL &x) {
if (back_stack.empty())
back_stack.emplace(x, val2prod(x));
else
back_stack.emplace(x, op(back_stack.top().second, val2prod(x)));
}
T_VAL pop() {
if (front_stack.empty()) {
front_stack.emplace(back_stack.top().first, val2prod(back_stack.top().first));
back_stack.pop();
while (!back_stack.empty()) {
T_VAL t = back_stack.top().first;
front_stack.emplace(t, op(val2prod(t), front_stack.top().second));
back_stack.pop();
}
}
T_VAL t = front_stack.top().first;
front_stack.pop();
return t;
}
};
template <typename T> T swag_op_id(T x) { return x; };
template <typename T> T swag_op_linear_merge(T l, T r) {
return std::make_pair(l.first * r.first, l.second * r.first + r.second);
};
// Linear function composition
// `f(x) = first * x + second`, operate most recently added function first
template <typename T>
struct LinearFunctionQueue
: public swag_queue<std::pair<T, T>, std::pair<T, T>, swag_op_id, swag_op_linear_merge> {
LinearFunctionQueue()
: swag_queue<std::pair<T, T>, std::pair<T, T>, swag_op_id, swag_op_linear_merge>::swag_queue(
std::pair<T, T>(1, 0)) {}
};
#line 3 "data_structure/test/queue_operate_all_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/queue_operate_all_composite"
#line 5 "data_structure/test/queue_operate_all_composite.test.cpp"
using namespace std;
using mint = ModInt<998244353>;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
LinearFunctionQueue<mint> swag;
int Q;
cin >> Q;
while (Q--) {
int q;
cin >> q;
if (q == 0) {
mint a, b;
cin >> a >> b;
swag.push({a, b});
}
if (q == 1) swag.pop();
if (q == 2) {
mint x;
cin >> x;
pair<mint, mint> f = swag.fold_all();
cout << (f.first * x + f.second).val() << '\n';
}
}
}