#line 1 "test/yosupo-judge/point_set_range_composite/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#include <iostream>
#include <utility>
#line 3 "Mylib/AlgebraicStructure/Monoid/affine.cpp"
namespace haar_lib {
template <typename T>
struct affine_monoid {
using value_type = std::pair<T, T>;
value_type operator()() const { return std::make_pair(1, 0); }
value_type operator()(const value_type &a, const value_type &b) const {
return std::make_pair(a.first * b.first, a.first * b.second + a.second);
}
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/dual.cpp"
namespace haar_lib {
template <typename Monoid>
struct dual_monoid {
using value_type = typename Monoid::value_type;
const static Monoid M;
value_type operator()() const { return M(); }
value_type operator()(const value_type &a, const value_type &b) const { return M(b, a); }
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>
namespace haar_lib {
template <typename Monoid>
class segment_tree {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int depth_, size_, hsize_;
std::vector<value_type> data_;
public:
segment_tree() {}
segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, M_()) {}
auto operator[](int i) const {
assert(0 <= i and i < hsize_);
return data_[hsize_ + i];
}
auto fold(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) ret_right = M_(data_[--R], ret_right);
if (L & 1) ret_left = M_(ret_left, data_[L++]);
L >>= 1, R >>= 1;
}
return M_(ret_left, ret_right);
}
auto fold_all() const {
return data_[1];
}
void set(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = x;
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
void update(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = M_(data_[i], x);
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, M_());
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<value_type>(hsize_, val));
}
private:
template <bool Lower, typename F>
int bound(const int l, const int r, value_type x, F f) const {
std::vector<int> pl, pr;
int L = l + hsize_;
int R = r + hsize_;
while (L < R) {
if (R & 1) pr.push_back(--R);
if (L & 1) pl.push_back(L++);
L >>= 1, R >>= 1;
}
std::reverse(pr.begin(), pr.end());
pl.insert(pl.end(), pr.begin(), pr.end());
value_type a = M_();
for (int i : pl) {
auto b = M_(a, data_[i]);
if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
while (i < hsize_) {
const auto c = M_(a, data_[i << 1 | 0]);
if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
i = i << 1 | 0;
} else {
a = c;
i = i << 1 | 1;
}
}
return i - hsize_;
}
a = b;
}
return r;
}
public:
template <typename F = std::less<value_type>>
int lower_bound(int l, int r, value_type x, F f = F()) const {
return bound<true>(l, r, x, f);
}
template <typename F = std::less<value_type>>
int upper_bound(int l, int r, value_type x, F f = F()) const {
return bound<false>(l, r, x, f);
}
};
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuples.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuples.cpp"
#include <tuple>
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples_with_index.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuplesWithIndex {
struct iter {
using value_type = std::tuple<int, Args...>;
value_type value;
bool fetched = false;
int N;
int c = 0;
value_type operator*() {
if (not fetched) {
std::tuple<Args...> temp;
std::cin >> temp;
value = std::tuple_cat(std::make_tuple(c), temp);
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuplesWithIndex(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples_with_index(int N) {
return InputTuplesWithIndex<Args...>(N);
}
} // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"
namespace haar_lib {
template <int32_t M>
class modint {
uint32_t val_;
public:
constexpr static auto mod() { return M; }
constexpr modint() : val_(0) {}
constexpr modint(int64_t n) {
if (n >= M)
val_ = n % M;
else if (n < 0)
val_ = n % M + M;
else
val_ = n;
}
constexpr auto &operator=(const modint &a) {
val_ = a.val_;
return *this;
}
constexpr auto &operator+=(const modint &a) {
if (val_ + a.val_ >= M)
val_ = (uint64_t) val_ + a.val_ - M;
else
val_ += a.val_;
return *this;
}
constexpr auto &operator-=(const modint &a) {
if (val_ < a.val_) val_ += M;
val_ -= a.val_;
return *this;
}
constexpr auto &operator*=(const modint &a) {
val_ = (uint64_t) val_ * a.val_ % M;
return *this;
}
constexpr auto &operator/=(const modint &a) {
val_ = (uint64_t) val_ * a.inv().val_ % M;
return *this;
}
constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }
constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }
constexpr auto &operator++() {
*this += 1;
return *this;
}
constexpr auto &operator--() {
*this -= 1;
return *this;
}
constexpr auto operator++(int) {
auto t = *this;
*this += 1;
return t;
}
constexpr auto operator--(int) {
auto t = *this;
*this -= 1;
return t;
}
constexpr static modint pow(int64_t n, int64_t p) {
if (p < 0) return pow(n, -p).inv();
int64_t ret = 1, e = n % M;
for (; p; (e *= e) %= M, p >>= 1)
if (p & 1) (ret *= e) %= M;
return ret;
}
constexpr static modint inv(int64_t a) {
int64_t b = M, u = 1, v = 0;
while (b) {
int64_t t = a / b;
a -= t * b;
std::swap(a, b);
u -= t * v;
std::swap(u, v);
}
u %= M;
if (u < 0) u += M;
return u;
}
constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }
constexpr auto pow(int64_t p) const { return pow(val_, p); }
constexpr auto inv() const { return inv(val_); }
friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }
friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }
friend std::istream &operator>>(std::istream &s, modint &a) {
s >> a.val_;
return s;
}
friend std::ostream &operator<<(std::ostream &s, const modint &a) {
s << a.val_;
return s;
}
template <int N>
static auto div() {
static auto value = inv(N);
return value;
}
explicit operator int32_t() const noexcept { return val_; }
explicit operator int64_t() const noexcept { return val_; }
};
} // namespace haar_lib
#line 11 "test/yosupo-judge/point_set_range_composite/main.test.cpp"
namespace hl = haar_lib;
using mint = hl::modint<998244353>;
using M = hl::dual_monoid<hl::affine_monoid<mint>>;
int main() {
int N, Q;
std::cin >> N >> Q;
auto seg = hl::segment_tree<M>(N);
for (auto [i, a, b] : hl::input_tuples_with_index<int, int>(N)) {
seg.set(i, {a, b});
}
for (auto [t] : hl::input_tuples<int>(Q)) {
if (t == 0) {
int p, c, d;
std::cin >> p >> c >> d;
seg.set(p, {c, d});
} else {
int l, r, x;
std::cin >> l >> r >> x;
auto [a, b] = seg.fold(l, r);
std::cout << a * x + b << std::endl;
}
}
return 0;
}
test/yosupo-judge/point_set_range_composite/main.test.cpp
Segment tree
(Mylib/DataStructure/SegmentTree/segment_tree.cpp)