proconlib
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tests/avl_tree/set.test.cpp
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- Last update: 2025-01-22 03:51:11+00:00
- Problem: https://judge.yosupo.jp/problem/point_set_range_composite
Depends on
- Reversible self-balancing binary search tree based on AVL tree (tools/avl_tree.hpp)
- tools/detail/avl_tree_impl.hpp
- Fixed point combinator (tools/fix.hpp)
Code
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite
#include <utility>
#include <variant>
#include <iostream>
#include <vector>
#include "atcoder/modint.hpp"
#include "tools/avl_tree.hpp"
using mint = atcoder::modint998244353;
using S = std::pair<mint, mint>;
struct SM {
using T = S;
static T op(const T& x, const T& y) {
return T(y.first * x.first, y.first * x.second + y.second);
}
static T e() {
return T(mint::raw(1), mint::raw(0));
}
};
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
std::vector<S> init;
init.reserve(N);
for (int i = 0; i < N; ++i) {
int a, b;
std::cin >> a >> b;
init.emplace_back(mint::raw(a), mint::raw(b));
}
tools::avl_tree<SM>::buffer buffer;
tools::avl_tree<SM> avl_tree(buffer, init);
for (int q = 0; q < Q; ++q) {
int t;
std::cin >> t;
if (t == 0) {
int p, c, d;
std::cin >> p >> c >> d;
avl_tree.set(p, S(mint::raw(c), mint::raw(d)));
} else {
int l, r, x;
std::cin >> l >> r >> x;
const auto [a, b] = avl_tree.prod(l, r);
std::cout << (a * mint::raw(x) + b).val() << '\n';
}
}
return 0;
}
#line 1 "tests/avl_tree/set.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite
#include <utility>
#include <variant>
#include <iostream>
#include <vector>
#line 1 "lib/ac-library/atcoder/modint.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "lib/ac-library/atcoder/internal_math.hpp"
#line 5 "lib/ac-library/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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 == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "lib/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "lib/ac-library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 14 "lib/ac-library/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 1 "tools/avl_tree.hpp"
#line 1 "tools/detail/avl_tree_impl.hpp"
#line 6 "tools/detail/avl_tree_impl.hpp"
#include <functional>
#line 8 "tools/detail/avl_tree_impl.hpp"
#include <algorithm>
#line 11 "tools/detail/avl_tree_impl.hpp"
#include <cmath>
#line 1 "tools/fix.hpp"
#line 6 "tools/fix.hpp"
namespace tools {
template <typename F>
struct fix : F {
template <typename G>
fix(G&& g) : F({::std::forward<G>(g)}) {
}
template <typename... Args>
decltype(auto) operator()(Args&&... args) const {
return F::operator()(*this, ::std::forward<Args>(args)...);
}
};
template <typename F>
fix(F&&) -> fix<::std::decay_t<F>>;
}
#line 13 "tools/detail/avl_tree_impl.hpp"
namespace tools {
namespace detail {
namespace avl_tree {
struct nop_monoid {
using T = ::std::monostate;
static constexpr T op(T, T) {
return T{};
}
static constexpr T e() {
return T{};
}
};
template <typename SM>
typename SM::T nop(typename nop_monoid::T, const typename SM::T& x) {
return x;
}
template <bool Reversible, typename SM, typename FM = nop_monoid, auto mapping = nop<SM>>
class avl_tree_impl {
private:
using S = typename SM::T;
using F = typename FM::T;
static_assert(
::std::is_convertible_v<decltype(mapping), ::std::function<S(F, S)>>,
"mapping must work as S(F, S)");
constexpr static bool is_lazy = !::std::is_same_v<FM, nop_monoid>;
struct node {
int id;
int l_id;
int r_id;
int height;
int size;
S prod;
::std::conditional_t<Reversible, S, ::std::monostate> rprod;
bool rev;
F lazy;
};
public:
class buffer {
private:
::std::vector<node> m_nodes;
public:
buffer() {
if constexpr (Reversible) {
this->m_nodes.push_back(node{0, 0, 0, 0, 0, SM::e(), SM::e(), false, FM::e()});
} else {
this->m_nodes.push_back(node{0, 0, 0, 0, 0, SM::e(), ::std::monostate{}, false, FM::e()});
}
}
buffer(const buffer&) = default;
buffer(buffer&&) = default;
~buffer() = default;
buffer& operator=(const buffer&) = default;
buffer& operator=(buffer&&) = default;
friend ::tools::detail::avl_tree::avl_tree_impl<Reversible, SM, FM, mapping>;
};
private:
buffer *m_buffer;
int m_root_id;
void fetch(const int id) {
auto& node = this->m_buffer->m_nodes[id];
const auto& l_node = this->m_buffer->m_nodes[node.l_id];
const auto& r_node = this->m_buffer->m_nodes[node.r_id];
node.height = 1 + ::std::max(l_node.height, r_node.height);
node.size = l_node.size + r_node.size;
node.prod = SM::op(l_node.prod, r_node.prod);
if constexpr (Reversible) {
node.rprod = SM::op(r_node.rprod, l_node.rprod);
}
}
void propagate(const int id) {
auto& node = this->m_buffer->m_nodes[id];
auto& l_node = this->m_buffer->m_nodes[node.l_id];
auto& r_node = this->m_buffer->m_nodes[node.r_id];
assert(!(node.size == 0) || (node.id == 0 && node.l_id == 0 && node.r_id == 0));
assert(!(node.size == 1) || (node.id > 0 && node.l_id == 0 && node.r_id == 0));
assert(!(node.size > 1) || (node.id > 0 && node.l_id > 0 && node.r_id > 0));
if constexpr (Reversible) {
if (node.rev) {
if (node.size > 1) {
l_node.rev = !l_node.rev;
r_node.rev = !r_node.rev;
::std::swap(node.l_id, node.r_id);
::std::swap(node.prod, node.rprod);
}
node.rev = false;
}
}
if constexpr (is_lazy) {
if (node.lazy != FM::e()) {
if (node.size > 1) {
l_node.lazy = FM::op(node.lazy, l_node.lazy);
r_node.lazy = FM::op(node.lazy, r_node.lazy);
}
node.prod = mapping(node.lazy, node.prod);
if constexpr (Reversible) {
node.rprod = mapping(node.lazy, node.rprod);
}
node.lazy = FM::e();
}
}
}
int add_node(const S& x) {
const int id = this->m_buffer->m_nodes.size();
if constexpr (Reversible) {
this->m_buffer->m_nodes.push_back(node{id, 0, 0, 1, 1, x, x, false, FM::e()});
} else {
this->m_buffer->m_nodes.push_back(node{id, 0, 0, 1, 1, x, ::std::monostate{}, false, FM::e()});
}
return id;
}
int add_node(const int l_id, const int r_id) {
const int id = this->m_buffer->m_nodes.size();
if constexpr (Reversible) {
this->m_buffer->m_nodes.push_back(node{id, l_id, r_id, 0, 0, SM::e(), SM::e(), false, FM::e()});
} else {
this->m_buffer->m_nodes.push_back(node{id, l_id, r_id, 0, 0, SM::e(), ::std::monostate{}, false, FM::e()});
}
this->fetch(id);
return id;
}
int rotate_l(const int id) {
auto& node = this->m_buffer->m_nodes[id];
auto& r_node = this->m_buffer->m_nodes[node.r_id];
assert(node.size > 1);
assert(node.id > 0);
assert(node.l_id > 0);
assert(node.r_id > 0);
assert(r_node.size > 1);
assert(r_node.id > 0);
assert(r_node.l_id > 0);
assert(r_node.r_id > 0);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
this->propagate(node.l_id);
this->propagate(node.r_id);
this->propagate(r_node.l_id);
this->propagate(r_node.r_id);
}
node.r_id = r_node.l_id;
r_node.l_id = node.id;
this->fetch(id);
this->fetch(r_node.id);
return r_node.id;
}
int rotate_r(const int id) {
auto& node = this->m_buffer->m_nodes[id];
auto& l_node = this->m_buffer->m_nodes[node.l_id];
assert(node.size > 1);
assert(node.id > 0);
assert(node.l_id > 0);
assert(node.r_id > 0);
assert(l_node.size > 1);
assert(l_node.id > 0);
assert(l_node.l_id > 0);
assert(l_node.r_id > 0);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
this->propagate(node.l_id);
this->propagate(node.r_id);
this->propagate(l_node.l_id);
this->propagate(l_node.r_id);
}
node.l_id = l_node.r_id;
l_node.r_id = node.id;
this->fetch(id);
this->fetch(l_node.id);
return l_node.id;
}
int height_diff(const int id) {
const auto& node = this->m_buffer->m_nodes[id];
const auto& l_node = this->m_buffer->m_nodes[node.l_id];
const auto& r_node = this->m_buffer->m_nodes[node.r_id];
return l_node.height - r_node.height;
}
int balance(const int id) {
auto& node = this->m_buffer->m_nodes[id];
const auto diff = this->height_diff(id);
assert(::std::abs(diff) <= 2);
if (diff == 2) {
if (this->height_diff(node.l_id) < 0) node.l_id = this->rotate_l(node.l_id);
return this->rotate_r(id);
} else if (diff == -2) {
if (this->height_diff(node.r_id) > 0) node.r_id = this->rotate_r(node.r_id);
return this->rotate_l(id);
} else {
return id;
}
}
void set(const int id, const int p, const S& x) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= p && p < node.size);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 1) {
node.prod = x;
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
if (p < half) {
this->set(node.l_id, p, x);
if constexpr (Reversible || is_lazy) {
this->propagate(node.r_id);
}
} else {
if constexpr (Reversible || is_lazy) {
this->propagate(node.l_id);
}
this->set(node.r_id, p - half, x);
}
this->fetch(id);
}
}
S prod(const int id, const int l, const int r) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= l && l <= r && r <= node.size);
if (l == r) return SM::e();
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (l == 0 && r == node.size) {
return node.prod;
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
auto res = SM::e();
if (l < half) res = SM::op(res, this->prod(node.l_id, l, ::std::min(r, half)));
if (half < r) res = SM::op(res, this->prod(node.r_id, ::std::max(0, l - half), r - half));
return res;
}
}
template <bool SFINAE = is_lazy>
::std::enable_if_t<SFINAE, void> apply(const int id, const int l, const int r, const F& f) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= l && l <= r && r <= node.size);
if (l == r) return;
if (l == 0 && r == node.size) {
node.lazy = FM::op(f, node.lazy);
this->propagate(id);
} else {
this->propagate(id);
const auto half = this->m_buffer->m_nodes[node.l_id].size;
if (l < half) {
this->apply(node.l_id, l, ::std::min(r, half), f);
} else {
this->propagate(node.l_id);
}
if (half < r) {
this->apply(node.r_id, ::std::max(0, l - half), r - half, f);
} else {
this->propagate(node.r_id);
}
this->fetch(id);
}
}
int insert(const int id, const int p, const S& x) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= p && p <= node.size);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 0) {
return this->add_node(x);
} else if (node.size == 1) {
if (p == 0) {
return this->add_node(this->add_node(x), id);
} else {
return this->add_node(id, this->add_node(x));
}
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
if (p < half) {
if constexpr (Reversible || is_lazy) {
this->propagate(node.r_id);
}
const auto l_id = this->insert(node.l_id, p, x);
this->m_buffer->m_nodes[id].l_id = l_id;
} else {
if constexpr (Reversible || is_lazy) {
this->propagate(node.l_id);
}
const auto r_id = this->insert(node.r_id, p - half, x);
this->m_buffer->m_nodes[id].r_id = r_id;
}
this->fetch(id);
return this->balance(id);
}
}
int erase(const int id, const int p) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= p && p < node.size);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 1) {
return 0;
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
if (p < half) {
if constexpr (Reversible || is_lazy) {
this->propagate(node.r_id);
}
node.l_id = this->erase(node.l_id, p);
if (node.l_id == 0) return node.r_id;
} else {
if constexpr (Reversible || is_lazy) {
this->propagate(node.l_id);
}
node.r_id = this->erase(node.r_id, p - half);
if (node.r_id == 0) return node.l_id;
}
this->fetch(id);
return this->balance(id);
}
}
int merge(const int l_id, const int r_id, const int free_id) {
if (l_id == 0) {
if constexpr (Reversible || is_lazy) {
this->propagate(r_id);
}
return r_id;
}
if (r_id == 0) {
if constexpr (Reversible || is_lazy) {
this->propagate(l_id);
}
return l_id;
}
auto& l_node = this->m_buffer->m_nodes[l_id];
auto& r_node = this->m_buffer->m_nodes[r_id];
const auto diff = l_node.height - r_node.height;
if (diff >= 2) {
if constexpr (Reversible || is_lazy) {
this->propagate(l_id);
this->propagate(l_node.l_id);
}
const auto merged_id = this->merge(l_node.r_id, r_id, free_id);
this->m_buffer->m_nodes[l_id].r_id = merged_id;
this->fetch(l_id);
return this->balance(l_id);
} else if (diff <= -2) {
if constexpr (Reversible || is_lazy) {
this->propagate(r_id);
this->propagate(r_node.r_id);
}
const auto merged_id = this->merge(l_id, r_node.l_id, free_id);
this->m_buffer->m_nodes[r_id].l_id = merged_id;
this->fetch(r_id);
return this->balance(r_id);
} else {
if constexpr (Reversible || is_lazy) {
this->propagate(l_id);
this->propagate(r_id);
}
if (free_id == 0) {
return this->add_node(l_id, r_id);
} else {
auto& node = this->m_buffer->m_nodes[free_id];
node.l_id = l_id;
node.r_id = r_id;
if constexpr (Reversible) {
node.rev = false;
}
if constexpr (is_lazy) {
node.lazy = FM::e();
}
this->fetch(free_id);
return free_id;
}
}
}
::std::pair<int, int> split(const int id, const int i) {
auto& node = this->m_buffer->m_nodes[id];
assert(0 <= i && i <= node.size);
if (i == 0) return ::std::make_pair(0, id);
if (i == node.size) return ::std::make_pair(id, 0);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
const auto half = this->m_buffer->m_nodes[node.l_id].size;
if (i < half) {
const auto [l_id, r_id] = this->split(node.l_id, i);
return ::std::make_pair(l_id, this->merge(r_id, this->m_buffer->m_nodes[id].r_id, this->m_buffer->m_nodes[id].l_id));
} else if (i > half) {
const auto [l_id, r_id] = this->split(node.r_id, i - half);
return ::std::make_pair(this->merge(this->m_buffer->m_nodes[id].l_id, l_id, this->m_buffer->m_nodes[id].r_id), r_id);
} else {
return ::std::make_pair(node.l_id, node.r_id);
}
}
template <typename G>
::std::pair<int, S> max_right(const int id, const int l, const G& g, S carry) {
const auto& node = this->m_buffer->m_nodes[id];
assert(0 <= l && l <= node.size);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 0) {
return ::std::make_pair(0, carry);
} else if (node.size == 1) {
if (l == 0) {
const auto whole = SM::op(carry, node.prod);
if (g(whole)) return ::std::make_pair(1, whole);
return ::std::make_pair(0, carry);
} else {
assert(carry == SM::e());
return ::std::make_pair(1, carry);
}
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
int r;
if (l == 0) {
const auto whole = SM::op(carry, node.prod);
if (g(whole)) return ::std::make_pair(node.size, whole);
::std::tie(r, carry) = this->max_right(node.l_id, 0, g, carry);
if (r < half) return ::std::make_pair(r, carry);
::std::tie(r, carry) = this->max_right(node.r_id, 0, g, carry);
r += half;
return ::std::make_pair(r, carry);
} else {
assert(carry == SM::e());
if (l < half) {
::std::tie(r, carry) = this->max_right(node.l_id, l, g, carry);
if (r < half) return ::std::make_pair(r, carry);
}
::std::tie(r, carry) = this->max_right(node.r_id, ::std::max(0, l - half), g, carry);
r += half;
return ::std::make_pair(r, carry);
}
}
}
template <typename G>
::std::pair<int, S> min_left(const int id, const int r, const G& g, S carry) {
const auto& node = this->m_buffer->m_nodes[id];
assert(0 <= r && r <= node.size);
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 0) {
return ::std::make_pair(0, carry);
} else if (node.size == 1) {
if (r == node.size) {
const auto whole = SM::op(node.prod, carry);
if (g(whole)) return ::std::make_pair(0, whole);
return ::std::make_pair(1, carry);
} else {
assert(carry == SM::e());
return ::std::make_pair(0, carry);
}
} else {
const auto half = this->m_buffer->m_nodes[node.l_id].size;
int l;
if (r == node.size) {
const auto whole = SM::op(node.prod, carry);
if (g(whole)) return ::std::make_pair(0, whole);
::std::tie(l, carry) = this->min_left(node.r_id, node.size - half, g, carry);
l += half;
if (half < l) return ::std::make_pair(l, carry);
::std::tie(l, carry) = this->min_left(node.l_id, half, g, carry);
return ::std::make_pair(l, carry);
} else {
assert(carry == SM::e());
if (half < r) {
::std::tie(l, carry) = this->min_left(node.r_id, r - half, g, carry);
l += half;
if (half < l) return ::std::make_pair(l, carry);
}
::std::tie(l, carry) = this->min_left(node.l_id, ::std::min(half, r), g, carry);
return ::std::make_pair(l, carry);
}
}
}
public:
explicit operator ::std::vector<S>() const {
::std::vector<S> v;
if (!this->empty()) {
::tools::fix([&](auto&& dfs, const int id) -> void {
auto& node = this->m_buffer->m_nodes[id];
if constexpr (Reversible || is_lazy) {
this->propagate(id);
}
if (node.size == 1) {
v.push_back(node.prod);
} else {
dfs(node.l_id);
dfs(node.r_id);
}
})(this->m_root_id);
}
return v;
}
avl_tree_impl() = default;
explicit avl_tree_impl(buffer& buffer) : m_buffer(&buffer), m_root_id(0) {
}
avl_tree_impl(buffer& buffer, const ::std::vector<S>& v) : m_buffer(&buffer) {
this->m_root_id = v.empty() ? 0 : ::tools::fix([&](auto&& dfs, const int l, const int r) -> int {
if (r - l == 1) {
return this->add_node(v[l]);
} else {
return this->add_node(dfs(l, (l + r) / 2), dfs((l + r) / 2, r));
}
})(0, v.size());
}
avl_tree_impl(buffer& buffer, const int n) : avl_tree_impl(buffer, ::std::vector<S>(n, SM::e())) {
}
avl_tree_impl(const avl_tree_impl<Reversible, SM, FM, mapping>& other) : avl_tree_impl(*other.m_buffer, static_cast<::std::vector<S>>(other)) {
}
avl_tree_impl(avl_tree_impl<Reversible, SM, FM, mapping>&& other) : m_buffer(other.m_buffer), m_root_id(other.m_root_id) {
}
~avl_tree_impl() = default;
avl_tree_impl<Reversible, SM, FM, mapping>& operator=(const avl_tree_impl<Reversible, SM, FM, mapping>& other) {
this->m_buffer = other.m_buffer;
this->m_root_id = avl_tree_impl<Reversible, SM, FM, mapping>(other).m_root_id;
}
avl_tree_impl<Reversible, SM, FM, mapping>& operator=(avl_tree_impl<Reversible, SM, FM, mapping>&& other) {
this->m_buffer = other.m_buffer;
this->m_root_id = other.m_root_id;
}
int size() const {
return this->m_buffer->m_nodes[this->m_root_id].size;
}
bool empty() const {
return this->m_root_id == 0;
}
void set(const int p, const S& x) {
this->set(this->m_root_id, p, x);
}
S get(const int p) {
return this->prod(this->m_root_id, p, p + 1);
}
S prod(const int l, const int r) {
return this->prod(this->m_root_id, l, r);
}
S all_prod() {
return this->prod(this->m_root_id, 0, this->size());
}
template <bool SFINAE = is_lazy>
::std::enable_if_t<SFINAE, void> apply(const int p, const F& f) {
this->apply(this->m_root_id, p, p + 1, f);
}
template <bool SFINAE = is_lazy>
::std::enable_if_t<SFINAE, void> apply(const int l, const int r, const F& f) {
this->apply(this->m_root_id, l, r, f);
}
void insert(const int p, const S& x) {
this->m_root_id = this->insert(this->m_root_id, p, x);
}
void erase(const int p) {
this->m_root_id = this->erase(this->m_root_id, p);
}
void merge(avl_tree_impl<Reversible, SM, FM, mapping>& other) {
assert(this->m_buffer == other.m_buffer);
this->m_root_id = this->merge(this->m_root_id, other.m_root_id, 0);
other.m_root_id = 0;
}
::std::pair<avl_tree_impl<Reversible, SM, FM, mapping>, avl_tree_impl<Reversible, SM, FM, mapping>> split(const int i) {
avl_tree_impl<Reversible, SM, FM, mapping> l(*this->m_buffer), r(*this->m_buffer);
::std::tie(l.m_root_id, r.m_root_id) = this->split(this->m_root_id, i);
return ::std::make_pair(l, r);
}
template <bool SFINAE = Reversible>
::std::enable_if_t<SFINAE, void> reverse(const int l, const int r) {
assert(0 <= l && l <= r && r <= this->size());
if (l == r) return;
if (l == 0) {
if (r == this->size()) {
this->m_buffer->m_nodes[this->m_root_id].rev = !this->m_buffer->m_nodes[this->m_root_id].rev;
} else {
const auto [l_id, r_id] = this->split(this->m_root_id, r);
this->m_buffer->m_nodes[l_id].rev = !this->m_buffer->m_nodes[l_id].rev;
this->m_root_id = this->merge(l_id, r_id, this->m_root_id);
}
} else {
if (r == this->size()) {
const auto [l_id, r_id] = this->split(this->m_root_id, l);
this->m_buffer->m_nodes[r_id].rev = !this->m_buffer->m_nodes[r_id].rev;
this->m_root_id = this->merge(l_id, r_id, this->m_root_id);
} else {
const auto [lm_id, r_id] = this->split(this->m_root_id, r);
const auto [l_id, m_id] = this->split(lm_id, l);
this->m_buffer->m_nodes[m_id].rev = !this->m_buffer->m_nodes[m_id].rev;
this->m_root_id = this->merge(this->merge(l_id, m_id, lm_id), r_id, this->m_root_id);
}
}
}
template <typename G>
int max_right(const int l, const G& g) {
return this->max_right(this->m_root_id, l, g, SM::e()).first;
}
template <typename G>
int min_left(const int r, const G& g) {
return this->min_left(this->m_root_id, r, g, SM::e()).first;
}
};
}
}
}
#line 5 "tools/avl_tree.hpp"
namespace tools {
template <typename SM, bool Reversible = false>
using avl_tree = ::tools::detail::avl_tree::avl_tree_impl<Reversible, SM>;
}
#line 9 "tests/avl_tree/set.test.cpp"
using mint = atcoder::modint998244353;
using S = std::pair<mint, mint>;
struct SM {
using T = S;
static T op(const T& x, const T& y) {
return T(y.first * x.first, y.first * x.second + y.second);
}
static T e() {
return T(mint::raw(1), mint::raw(0));
}
};
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
std::vector<S> init;
init.reserve(N);
for (int i = 0; i < N; ++i) {
int a, b;
std::cin >> a >> b;
init.emplace_back(mint::raw(a), mint::raw(b));
}
tools::avl_tree<SM>::buffer buffer;
tools::avl_tree<SM> avl_tree(buffer, init);
for (int q = 0; q < Q; ++q) {
int t;
std::cin >> t;
if (t == 0) {
int p, c, d;
std::cin >> p >> c >> d;
avl_tree.set(p, S(mint::raw(c), mint::raw(d)));
} else {
int l, r, x;
std::cin >> l >> r >> x;
const auto [a, b] = avl_tree.prod(l, r);
std::cout << (a * mint::raw(x) + b).val() << '\n';
}
}
return 0;
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | example_00 |
AC |
5 ms | 3 MB |
| g++ | max_random_00 |
AC |
487 ms | 41 MB |
| g++ | max_random_01 |
AC |
487 ms | 41 MB |
| g++ | max_random_02 |
AC |
489 ms | 42 MB |
| g++ | max_random_03 |
AC |
483 ms | 41 MB |
| g++ | max_random_04 |
AC |
495 ms | 42 MB |
| g++ | random_00 |
AC |
376 ms | 41 MB |
| g++ | random_01 |
AC |
412 ms | 40 MB |
| g++ | random_02 |
AC |
244 ms | 9 MB |
| g++ | random_03 |
AC |
96 ms | 40 MB |
| g++ | random_04 |
AC |
124 ms | 39 MB |
| g++ | small_00 |
AC |
5 ms | 4 MB |
| g++ | small_01 |
AC |
4 ms | 4 MB |
| g++ | small_02 |
AC |
4 ms | 4 MB |
| g++ | small_03 |
AC |
4 ms | 3 MB |
| g++ | small_04 |
AC |
4 ms | 4 MB |