cplib-cpp
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segmenttree/test/point-set-range-composite.test.cpp
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- Last update: 2025-08-25 00:44:48+09:00
- Problem: https://judge.yosupo.jp/problem/point_set_range_composite
Depends on
Code
#include "../../modint.hpp"
#include "../point-update-range-get_nonrecursive.hpp"
#include <iostream>
#include <utility>
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
using mint = ModInt<998244353>;
template <typename T>
struct PointSetRangeComposite
: public NonrecursiveSegmentTree<std::pair<T, T>, std::pair<T, T>, bool> {
using T_NODE = std::pair<T, T>;
using SegTree = NonrecursiveSegmentTree<T_NODE, T_NODE, bool>;
T_NODE merge_data(const T_NODE &vl, const T_NODE &vr) override {
return std::make_pair(vl.first * vr.first, vr.first * vl.second + vr.second);
};
T_NODE data2ret(const T_NODE &v, const bool &q) override { return v; }
T_NODE merge_ret(const T_NODE &vl, const T_NODE &vr) override { return merge_data(vl, vr); };
PointSetRangeComposite(const std::vector<T_NODE> &seq) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, T_NODE(1, 0));
};
};
int main() {
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
std::vector<std::pair<mint, mint>> A(N);
for (auto &p : A) { std::cin >> p.first >> p.second; }
PointSetRangeComposite<mint> s(A);
while (Q--) {
int q, l, r, x;
std::cin >> q >> l >> r >> x;
if (q) {
auto ret = s.get(l, r);
std::cout << ret.first * x + ret.second << '\n';
} else {
s.update(l, std::make_pair(r, x));
}
}
}#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 "segmenttree/point-update-range-get_nonrecursive.hpp"
#include <algorithm>
#line 4 "segmenttree/point-update-range-get_nonrecursive.hpp"
#include <functional>
#line 6 "segmenttree/point-update-range-get_nonrecursive.hpp"
#include <stack>
#line 8 "segmenttree/point-update-range-get_nonrecursive.hpp"
// CUT begin
// Nonrecursive Segment Tree (point-update, range-get)
// - Conditions for operations:
// - merge_data: [TDATA, TDATA] -> TDATA, e(x, y) == e(y, x)
// - data2ret: [TDATA, TQUERY] -> TRET
// - merge_ret: [TRET, TRET] -> TRET, g(defaultRET, x) == x, g(x, y) = g(y, x)
// - commutability f(e(x, y), q) == g(f(x, q), f(y, q))
template <typename TDATA, typename TRET, typename TQUERY> struct NonrecursiveSegmentTree {
int N;
TRET defaultRET;
virtual TDATA merge_data(const TDATA &, const TDATA &) = 0;
virtual TRET data2ret(const TDATA &, const TQUERY &) = 0;
virtual TRET merge_ret(const TRET &, const TRET &) = 0;
std::vector<TDATA> data;
inline TDATA &at(int i) { return data[i]; }
inline void _merge(int i) { at(i) = merge_data(at(i << 1), at((i << 1) + 1)); }
void initialize(const std::vector<TDATA> &seq, TRET RET_ZERO) {
N = seq.size();
defaultRET = RET_ZERO;
data = seq;
data.insert(data.end(), seq.begin(), seq.end());
for (int i = N - 1; i; i--) _merge(i);
}
NonrecursiveSegmentTree() = default;
void update(int pos, const TDATA &x) {
assert(pos >= 0 and pos < N);
at(pos + N) = x;
for (int i = pos + N; i > 1;) i >>= 1, _merge(i);
}
// [l, r), 0-indexed
TRET get(int l, int r, TQUERY query = NULL) {
assert(l >= 0 and r <= N);
TRET retl = defaultRET, retr = defaultRET;
l += N, r += N;
while (l < r) {
if (l & 1) retl = merge_ret(retl, data2ret(data[l++], query));
if (r & 1) retr = merge_ret(data2ret(data[--r], query), retr);
l >>= 1, r >>= 1;
}
return merge_ret(retl, retr);
}
// Calculate smallest r that satisfies condition(g(f(x_l, q), ..., f(x_{r - 1}, q)) == true
// Assumption: Monotonicity of g(x_l, ..., x_r) about r (l: fixed)
// Complexity: O(log N)
int binary_search(int l, std::function<bool(TRET)> condition, TQUERY query = NULL) {
std::stack<int> rs;
l += N;
int r = N * 2;
TRET retl = defaultRET;
if (condition(retl)) return l - N;
while (l < r) {
if (l & 1) {
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
l++;
retl = ret_tmp;
}
if (r & 1) rs.push(--r);
l >>= 1, r >>= 1;
}
while (!rs.empty()) {
l = rs.top();
rs.pop();
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
retl = ret_tmp;
}
return N;
}
template <typename T1, typename T2, typename T3>
friend std::ostream &operator<<(std::ostream &os, NonrecursiveSegmentTree<T1, T2, T3> s) {
os << "[SegmentTree (len: " << s.N << ')';
for (int i = 0; i < s.N; i++) os << s.at(i + s.N) << ',';
os << "]";
return os;
}
};
// Range Minimum Query
// - get: return min(x_l, ..., x_{r - 1})
template <typename T> struct RangeMinimumQuery : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return std::min(vl, vr); };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return std::min(vl, vr); };
RangeMinimumQuery(const std::vector<T> &seq, T defaultmin)
: SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, defaultmin);
};
};
template <typename T> struct PointUpdateRangeSum : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return vl + vr; };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return vl + vr; };
PointUpdateRangeSum(const std::vector<T> &seq, T zero) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, zero);
};
};
// Range Counting less than q Query
// - get: return (#{i | l <= i < r, x_i < q}, total sum of them).
template <typename T>
struct CountAndSumLessThan
: public NonrecursiveSegmentTree<std::vector<std::pair<T, T>>, std::pair<int, T>, T> {
using TDATA = std::vector<std::pair<T, T>>;
using TRET = std::pair<int, T>;
using TQUERY = T;
TDATA merge_data(const TDATA &vl, const TDATA &vr) override {
TDATA ret = vl;
ret.insert(ret.end(), vr.begin(), vr.end());
std::sort(ret.begin(), ret.end());
if (ret.size()) {
ret[0].second = ret[0].first;
for (size_t i = 1; i < ret.size(); i++)
ret[i].second = ret[i - 1].second + ret[i].first;
}
return ret;
}
TRET data2ret(const TDATA &vec, const TQUERY &q) override {
int i = std::lower_bound(vec.begin(), vec.end(), std::make_pair(q, q)) - vec.begin();
if (!i)
return std::make_pair(0, 0);
else
return std::make_pair(i, vec[i - 1].second);
}
TRET merge_ret(const TRET &l, const TRET &r) override {
return std::make_pair(l.first + r.first, l.second + r.second);
}
using SegTree = NonrecursiveSegmentTree<TDATA, TRET, TQUERY>;
CountAndSumLessThan(const std::vector<T> &seq) : SegTree::NonrecursiveSegmentTree() {
std::vector<TDATA> init;
for (auto x : seq) init.emplace_back(TDATA{std::pair<T, T>(x, x)});
SegTree::initialize(init, TRET(0, 0));
}
};
#line 4 "segmenttree/test/point-set-range-composite.test.cpp"
#include <utility>
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
using mint = ModInt<998244353>;
template <typename T>
struct PointSetRangeComposite
: public NonrecursiveSegmentTree<std::pair<T, T>, std::pair<T, T>, bool> {
using T_NODE = std::pair<T, T>;
using SegTree = NonrecursiveSegmentTree<T_NODE, T_NODE, bool>;
T_NODE merge_data(const T_NODE &vl, const T_NODE &vr) override {
return std::make_pair(vl.first * vr.first, vr.first * vl.second + vr.second);
};
T_NODE data2ret(const T_NODE &v, const bool &q) override { return v; }
T_NODE merge_ret(const T_NODE &vl, const T_NODE &vr) override { return merge_data(vl, vr); };
PointSetRangeComposite(const std::vector<T_NODE> &seq) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, T_NODE(1, 0));
};
};
int main() {
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
std::vector<std::pair<mint, mint>> A(N);
for (auto &p : A) { std::cin >> p.first >> p.second; }
PointSetRangeComposite<mint> s(A);
while (Q--) {
int q, l, r, x;
std::cin >> q >> l >> r >> x;
if (q) {
auto ret = s.get(l, r);
std::cout << ret.first * x + ret.second << '\n';
} else {
s.update(l, std::make_pair(r, x));
}
}
}