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verify/lc_data_structure/lc_range_affine_range_sum.test.cpp
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- Last update: 2024-05-04 00:04:19+09:00
- Problem: https://judge.yosupo.jp/problem/range_affine_range_sum
Depends on
- algebra/monoid_f/monoid_affine.hpp
- algebra/monoid_s/monoid_sum_size.hpp
- algebra/monoid_s_f/monoid_sum_size_affine.hpp
- Lazy Segment Tree (遅延セグメント木)
(data_structure/lazy_segment_tree.hpp)
- Static Modint
(math/static_modint.hpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include <bits/stdc++.h>
#include "algebra/monoid_s_f/monoid_sum_size_affine.hpp"
#include "data_structure/lazy_segment_tree.hpp"
#include "math/static_modint.hpp"
using mint = mint998;
int main() {
int N, Q;
std::cin >> N >> Q;
std::vector<std::pair<mint, int>> A(N);
for (int i = 0; i < N; i++) {
int a;
std::cin >> a;
A[i] = {mint(a), 1};
}
LazySegmentTree<MonoidSumSizeAffine<mint>> seg(A);
while (Q--) {
int t;
std::cin >> t;
if (t == 0) {
int l, r, b, c;
std::cin >> l >> r >> b >> c;
seg.apply(l, r, {b, c});
} else {
int l, r;
std::cin >> l >> r;
std::cout << seg.prod(l, r).first.val() << '\n';
}
}
return 0;
}#line 1 "verify/lc_data_structure/lc_range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include <bits/stdc++.h>
#line 2 "algebra/monoid_s/monoid_sum_size.hpp"
// MS
template <class T> struct MonoidSumSize {
using S = std::pair<T, int>;
static constexpr S op(S a, S b) { return {a.first + b.first, a.second + b.second}; }
static constexpr S e() { return {T(0), 0}; }
};
#line 2 "algebra/monoid_f/monoid_affine.hpp"
// MF
template <class T> struct MonoidAffine {
using F = std::pair<T, T>; // a * x + b -> {a, b}
// f(x) = f.first * x + f.second, g(x) = g.first * x + g.second
// f(g(x)) = f.first * (g.first * x + g.second) + f.second
// = f.first * g.first * x + f.first * g.second + f.second
static constexpr F composition(F f, F g) { return {f.first * g.first, f.first * g.second + f.second}; }
static constexpr F id() { return {T(1), T(0)}; }
};
#line 4 "algebra/monoid_s_f/monoid_sum_size_affine.hpp"
// https://atcoder.jp/contests/practice2/tasks/practice2_k
// MSF
template <class T> struct MonoidSumSizeAffine {
using MS = MonoidSumSize<T>;
using MF = MonoidAffine<T>;
using S = typename MS::S;
using F = typename MF::F;
static constexpr S mapping(F f, S x) { return {f.first * x.first + f.second * x.second, x.second}; }
};
#line 4 "data_structure/lazy_segment_tree.hpp"
template <class MSF> struct LazySegmentTree {
public:
using S = typename MSF::S;
using F = typename MSF::F;
using MS = typename MSF::MS;
using MF = typename MSF::MF;
LazySegmentTree() : LazySegmentTree(0) {}
LazySegmentTree(int n) : LazySegmentTree(std::vector<S>(n, MS::e())) {}
LazySegmentTree(const std::vector<S>& v) : n((int)(v.size())) {
log = 0;
while ((1U << log) < (unsigned int)(n)) log++;
size = 1 << log;
d = std::vector<S>(size << 1, MS::e());
lz = std::vector<F>(size, MF::id());
for (int i = 0; i < n; i++) d[i + size] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, const S& x) {
assert(0 <= p and p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
void chset(int p, const S& x) {
assert(0 <= p and p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = MS::op(d[p], x);
for (int i = 1; i <= log; i++) update(p >> i);
}
S operator[](int p) {
assert(0 <= p and p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S get(int p) {
assert(0 <= p and p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) {
assert(0 <= l and l <= r and r <= n);
if (l == r) return MS::e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = MS::e(), smr = MS::e();
while (l < r) {
if (l & 1) sml = MS::op(sml, d[l++]);
if (r & 1) smr = MS::op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return MS::op(sml, smr);
}
S all_prod() { return d[1]; }
void apply(int p, const F& f) {
assert(0 <= p and p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = MSF::mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, const F& f) {
assert(0 <= l and l <= r and r <= n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <class G> int max_right(int l, G& g) {
assert(0 <= l and l <= n);
assert(g(MS::e()));
if (l == n) return n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = MS::e();
do {
while ((l & 1) == 0) l >>= 1;
if (!g(MS::op(sm, d[l]))) {
while (l < size) {
push(l);
l <<= 1;
if (g(MS::op(sm, d[l]))) {
sm = MS::op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = MS::op(sm, d[l]);
l++;
} while ((l & -l) != l);
return n;
}
template <class G> int min_left(int r, G& g) {
assert(0 <= r and r <= n);
assert(g(MS::e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = MS::e();
do {
r--;
while (r > 1 and (r & 1)) r >>= 1;
if (!g(MS::op(d[r], sm))) {
while (r < size) {
push(r);
r = (r << 1) | 1;
if (g(MS::op(d[r], sm))) {
sm = MS::op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = MS::op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int n, log, size;
std::vector<S> d;
std::vector<F> lz;
inline void update(int k) { d[k] = MS::op(d[k << 1], d[(k << 1) | 1]); }
void all_apply(int k, const F& f) {
d[k] = MSF::mapping(f, d[k]);
if (k < size) lz[k] = MF::composition(f, lz[k]);
}
void push(int k) {
all_apply(k << 1, lz[k]);
all_apply((k << 1) | 1, lz[k]);
lz[k] = MF::id();
}
};
#line 2 "math/static_modint.hpp"
#line 4 "math/static_modint.hpp"
// constexpr ... for constexpr bool prime()
template <int m> struct StaticModint {
using mint = StaticModint;
unsigned int _v;
static constexpr int mod() { return m; }
static constexpr unsigned int umod() { return m; }
constexpr StaticModint() : _v(0) {}
template <class T> constexpr StaticModint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
constexpr unsigned int val() const { return _v; }
constexpr mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr mint operator++(int) {
mint result = *this;
++*this;
return result;
}
constexpr mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint &operator*=(const mint &rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint &operator/=(const mint &rhs) { return (*this *= rhs.inv()); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(n >= 0);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend std::ostream &operator<<(std::ostream &os, const mint &v) { return os << v.val(); }
static constexpr bool prime = []() -> bool {
if (m == 1) return false;
if (m == 2 || m == 7 || m == 61) return true;
if (m % 2 == 0) return false;
unsigned int d = m - 1;
while (d % 2 == 0) d /= 2;
for (unsigned int a : {2, 7, 61}) {
unsigned int t = d;
mint y = mint(a).pow(t);
while (t != m - 1 and y != 1 and y != m - 1) {
y *= y;
t <<= 1;
}
if (y != m - 1 and t % 2 == 0) {
return false;
}
}
return true;
}();
static constexpr std::pair<int, int> inv_gcd(int a, int b) {
if (a == 0) return {b, 0};
int s = b, t = a, m0 = 0, m1 = 1;
while (t) {
const int u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
};
using mint107 = StaticModint<1000000007>;
using mint998 = StaticModint<998244353>;
#line 8 "verify/lc_data_structure/lc_range_affine_range_sum.test.cpp"
using mint = mint998;
int main() {
int N, Q;
std::cin >> N >> Q;
std::vector<std::pair<mint, int>> A(N);
for (int i = 0; i < N; i++) {
int a;
std::cin >> a;
A[i] = {mint(a), 1};
}
LazySegmentTree<MonoidSumSizeAffine<mint>> seg(A);
while (Q--) {
int t;
std::cin >> t;
if (t == 0) {
int l, r, b, c;
std::cin >> l >> r >> b >> c;
seg.apply(l, r, {b, c});
} else {
int l, r;
std::cin >> l >> r;
std::cout << seg.prod(l, r).first.val() << '\n';
}
}
return 0;
}