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verify/aoj-DSL_2_B-dynamic_segment_tree.test.cpp
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- Last update: 2025-07-03 00:41:25+09:00
- Problem: https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_B
Depends on
algorithm/Math/Algebra/algebra.hpp
Code
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_B"
#include <iostream>
#include "../algorithm/DataStructure/SegmentTree/dynamic_segment_tree.hpp"
int main() {
int n;
int q;
std::cin >> n >> q;
algorithm::dynamic_segment_tree::range_sum_dynamic_segment_tree<int> segtree(n);
while(q--) {
int com;
std::cin >> com;
if(com == 0) {
int x;
int y;
std::cin >> x >> y;
--x;
auto &&now = segtree.prod(x);
segtree.set(x, now + y);
} else {
int x, y;
std::cin >> x >> y;
--x;
auto &&ans = segtree.prod(x, y);
std::cout << ans << "\n";
}
}
}#line 1 "verify/aoj-DSL_2_B-dynamic_segment_tree.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_B"
#include <iostream>
#line 1 "algorithm/DataStructure/SegmentTree/dynamic_segment_tree.hpp"
#include <algorithm>
#include <cassert>
#line 7 "algorithm/DataStructure/SegmentTree/dynamic_segment_tree.hpp"
#include <limits>
#include <memory>
#include <type_traits>
#include <utility>
#line 1 "algorithm/Math/Algebra/algebra.hpp"
#line 7 "algorithm/Math/Algebra/algebra.hpp"
#include <numeric>
#line 10 "algorithm/Math/Algebra/algebra.hpp"
namespace algorithm {
namespace algebra {
template <typename S>
class Set {
public:
using value_type = S;
protected:
value_type val;
public:
constexpr Set() : val() {}
constexpr Set(const value_type &val) : val(val) {}
constexpr Set(value_type &&val) : val(std::move(val)) {}
friend constexpr bool operator==(const Set &lhs, const Set &rhs) { return lhs.val == rhs.val; }
friend std::istream &operator>>(std::istream &is, Set &rhs) { return is >> rhs.val; }
friend std::ostream &operator<<(std::ostream &os, const Set &rhs) { return os << rhs.val; }
constexpr value_type value() const { return val; }
};
template <typename S, auto op>
class Semigroup : public Set<S> {
static_assert(std::is_invocable_r<S, decltype(op), S, S>::value);
using base_type = Set<S>;
public:
using value_type = typename base_type::value_type;
constexpr Semigroup() : base_type() {}
constexpr Semigroup(const value_type &val) : base_type(val) {}
constexpr Semigroup(value_type &&val) : base_type(std::move(val)) {}
friend constexpr Semigroup operator*(const Semigroup &lhs, const Semigroup &rhs) { return Semigroup(op(lhs.val, rhs.val)); }
static constexpr auto get_op() { return op; }
};
template <typename S, auto op, auto e>
class Monoid : public Semigroup<S, op> {
static_assert(std::is_invocable_r<S, decltype(e)>::value);
using base_type = Semigroup<S, op>;
public:
using value_type = typename base_type::value_type;
constexpr Monoid() : base_type() {}
constexpr Monoid(const value_type &val) : base_type(val) {}
constexpr Monoid(value_type &&val) : base_type(std::move(val)) {}
friend constexpr Monoid operator*(const Monoid &lhs, const Monoid &rhs) { return Monoid(op(lhs.val, rhs.val)); }
static constexpr auto get_e() { return e; }
static constexpr Monoid one() { return Monoid(e()); } // return identity element.
};
template <typename S, auto op, auto e, auto inverse>
class Group : public Monoid<S, op, e> {
static_assert(std::is_invocable_r<S, decltype(inverse), S>::value);
using base_type = Monoid<S, op, e>;
public:
using value_type = typename base_type::value_type;
constexpr Group() : base_type() {}
constexpr Group(const value_type &val) : base_type(val) {}
constexpr Group(value_type &&val) : base_type(std::move(val)) {}
friend constexpr Group operator*(const Group &lhs, const Group &rhs) { return Group(op(lhs.val, rhs.val)); }
static constexpr auto get_inverse() { return inverse; }
static constexpr Group one() { return Group(e()); } // return identity element.
constexpr Group inv() const { return Group(inverse(this->val)); } // return inverse element.
};
template <typename F, auto compose, auto id, typename X, auto mapping>
class OperatorMonoid : public Monoid<F, compose, id> {
static_assert(std::is_invocable_r<X, decltype(mapping), F, X>::value);
using base_type = Monoid<F, compose, id>;
public:
using value_type = typename base_type::value_type;
using acted_value_type = X;
constexpr OperatorMonoid() : base_type() {}
constexpr OperatorMonoid(const value_type &val) : base_type(val) {}
constexpr OperatorMonoid(value_type &&val) : base_type(std::move(val)) {}
friend constexpr OperatorMonoid operator*(const OperatorMonoid &lhs, const OperatorMonoid &rhs) { return OperatorMonoid(compose(lhs.val, rhs.val)); }
static constexpr auto get_mapping() { return mapping; }
static constexpr OperatorMonoid one() { return OperatorMonoid(id()); } // return identity mapping.
constexpr acted_value_type act(const acted_value_type &x) const { return mapping(this->val, x); }
template <class S>
constexpr S act(const S &x) const {
static_assert(std::is_base_of<Set<acted_value_type>, S>::value);
return S(mapping(this->val, x.value()));
}
};
namespace element {
template <typename S>
constexpr auto zero = []() -> S { return S(); };
template <typename S>
constexpr auto one = []() -> S { return 1; };
template <typename S>
constexpr auto min = []() -> S { return std::numeric_limits<S>::min(); };
template <typename S>
constexpr auto max = []() -> S { return std::numeric_limits<S>::max(); };
template <typename S>
constexpr auto one_below_max = []() -> S { return std::numeric_limits<S>::max() - 1; };
template <typename S>
constexpr auto lowest = []() -> S { return std::numeric_limits<S>::lowest(); };
template <typename S>
constexpr auto one_above_lowest = []() -> S { return std::numeric_limits<S>::lowest() + 1; };
} // namespace element
namespace uoperator {
template <typename S>
constexpr auto identity = [](const S &val) -> S { return val; };
template <typename S>
constexpr auto negate = [](const S &val) -> S { return -val; };
} // namespace uoperator
namespace boperator {
template <typename T, typename S = T>
constexpr auto plus = [](const T &lhs, const S &rhs) -> S { return lhs + rhs; };
template <typename T, typename S = T>
constexpr auto mul = [](const T &lhs, const S &rhs) -> S { return lhs * rhs; };
template <typename T, typename S = T>
constexpr auto bit_and = [](const T &lhs, const S &rhs) -> S { return lhs & rhs; };
template <typename T, typename S = T>
constexpr auto bit_or = [](const T &lhs, const S &rhs) -> S { return lhs | rhs; };
template <typename T, typename S = T>
constexpr auto bit_xor = [](const T &lhs, const S &rhs) -> S { return lhs ^ rhs; };
template <typename T, typename S = T>
constexpr auto min = [](const T &lhs, const S &rhs) -> S { return std::min<S>(lhs, rhs); };
template <typename T, typename S = T>
constexpr auto max = [](const T &lhs, const S &rhs) -> S { return std::max<S>(lhs, rhs); };
template <typename T, typename S = T>
constexpr auto gcd = [](const T &lhs, const S &rhs) -> S { return std::gcd(lhs, rhs); };
template <typename T, typename S = T>
constexpr auto lcm = [](const T &lhs, const S &rhs) -> S { return std::lcm(lhs, rhs); };
template <typename F, auto id, typename X = F>
constexpr auto assign_if_not_id = [](const F &lhs, const X &rhs) -> X {
static_assert(std::is_invocable_r<F, decltype(id)>::value);
return (lhs == id() ? rhs : lhs);
};
} // namespace boperator
namespace monoid {
template <typename S>
using minimum = Monoid<S, boperator::min<S>, element::max<S>>;
template <typename S>
using minimum_safe = Monoid<S, boperator::min<S>, element::one_below_max<S>>;
template <typename S>
using maximum = Monoid<S, boperator::max<S>, element::lowest<S>>;
template <typename S>
using maximum_safe = Monoid<S, boperator::max<S>, element::one_above_lowest<S>>;
template <typename S>
using addition = Monoid<S, boperator::plus<S>, element::zero<S>>;
template <typename S>
using multiplication = Monoid<S, boperator::mul<S>, element::one<S>>;
template <typename S>
using bit_xor = Monoid<S, boperator::bit_xor<S>, element::zero<S>>;
} // namespace monoid
namespace group {
template <typename S>
using addition = Group<S, boperator::plus<S>, element::zero<S>, uoperator::negate<S>>;
template <typename S>
using bit_xor = Group<S, boperator::bit_xor<S>, element::zero<S>, uoperator::identity<S>>;
} // namespace group
namespace operator_monoid {
template <typename F, typename X = F>
using assign_for_minimum = OperatorMonoid<
F, boperator::assign_if_not_id<F, element::max<F>>, element::max<F>,
X, boperator::assign_if_not_id<F, element::max<F>, X>>;
template <typename F, typename X = F>
using assign_for_maximum = OperatorMonoid<
F, boperator::assign_if_not_id<F, element::lowest<F>>, element::lowest<F>,
X, boperator::assign_if_not_id<F, element::lowest<F>, X>>;
template <typename F, typename X = F>
using addition = OperatorMonoid<F, boperator::plus<F>, element::zero<F>, X, boperator::plus<F, X>>;
} // namespace operator_monoid
} // namespace algebra
} // namespace algorithm
#line 13 "algorithm/DataStructure/SegmentTree/dynamic_segment_tree.hpp"
namespace algorithm {
namespace dynamic_segment_tree {
template <class Monoid>
class DynamicSegmentTree {
public:
using monoid_type = Monoid;
using value_type = monoid_type::value_type;
using size_type = std::size_t;
private:
struct Node;
using node_pointer = std::unique_ptr<Node>;
struct Node {
size_type index;
monoid_type value;
monoid_type product;
node_pointer left, right;
explicit Node(size_type index, const monoid_type &value) : index(index), value(value), product(value), left(nullptr), right(nullptr) {}
};
size_type m_sz; // m_sz:=(要素数).
node_pointer m_root; // m_root:=(根のポインタ).
void update(const node_pointer &p) const {
const monoid_type &lhs = (p->left ? p->left->product : monoid_type::one());
const monoid_type &rhs = (p->right ? p->right->product : monoid_type::one());
p->product = lhs * p->value * rhs;
}
void set(node_pointer &p, size_type k, monoid_type a, size_type l, size_type r) {
if(!p) {
p = std::make_unique<Node>(k, a);
return;
}
if(p->index == k) {
p->value = a;
update(p);
return;
}
size_type mid = l + (r - l) / 2;
if(k < mid) {
if(p->index < k) std::swap(k, p->index), std::swap(a, p->value);
set(p->left, k, a, l, mid);
} else {
if(k < p->index) std::swap(k, p->index), std::swap(a, p->value);
set(p->right, k, a, mid, r);
}
update(p);
}
monoid_type prod(const node_pointer &p, size_type k, size_type l, size_type r) const {
if(!p) return monoid_type::one();
if(p->index == k) return p->value;
size_type mid = l + (r - l) / 2;
return (k < mid ? prod(p->left, k, l, mid) : prod(p->right, k, mid, r));
}
monoid_type prod(const node_pointer &p, size_type l, size_type r, size_type ll, size_type rr) const {
if(!p or r <= ll or rr <= l) return monoid_type::one();
if(l <= ll and rr <= r) return p->product;
size_type mid = ll + (rr - ll) / 2;
return prod(p->left, l, r, ll, mid) * (l <= p->index and p->index < r ? p->value : monoid_type::one()) * prod(p->right, l, r, mid, rr);
}
template <typename Pred>
size_type most_right(const node_pointer &p, size_type l, Pred pred, size_type ll, size_type rr, monoid_type &product) const {
if(!p or rr <= l) return rr;
if(l <= ll and pred((product * p->product).value())) {
product = product * p->product;
return rr;
}
size_type mid = ll + (rr - ll) / 2;
size_type itr = most_right(p->left, l, pred, ll, mid, product);
if(itr < mid) return itr;
if(l <= p->index) {
product = product * p->value;
if(!pred(product.value())) return p->index;
}
return most_right(p->right, l, pred, mid, rr, product);
}
template <typename Pred>
size_type most_left(const node_pointer &p, size_type r, Pred pred, size_type ll, size_type rr, monoid_type &product) const {
if(!p or r <= ll) return ll;
if(rr <= r and pred((p->product * product).value())) {
product = p->product * product;
return ll;
}
size_type mid = ll + (rr - ll) / 2;
size_type itr = most_left(p->right, r, pred, mid, rr, product);
if(mid < itr) return itr;
if(p->index < r) {
product = p->value * product;
if(!pred(product.value())) return p->index + 1;
}
return most_left(p->left, r, pred, ll, mid, product);
}
void reset(node_pointer &p, size_type l, size_type r, size_type ll, size_type rr) {
if(!p or r <= ll or rr <= l) return;
if(l <= ll and rr <= r) {
p.reset();
return;
}
size_type mid = ll + (rr - ll) / 2;
reset(p->left, l, r, ll, mid);
reset(p->right, l, r, mid, rr);
if(l <= p->index and p->index < r) {
if(!p->left and !p->right) {
p.reset();
return;
}
p->value = monoid_type::one();
}
update(p);
}
void print(std::ostream &os, const node_pointer &p, bool &first) const {
if(!p) return;
print(os, p->left, first);
os << (first ? "{" : " {") << p->index << ", " << p->value << "}";
first = false;
print(os, p->right, first);
}
public:
DynamicSegmentTree() : DynamicSegmentTree(std::numeric_limits<size_type>::max()) {};
explicit DynamicSegmentTree(size_type n) : m_sz(n), m_root(nullptr) {}
// 要素数を取得する．
size_type size() const { return m_sz; }
// k番目の要素をaに置き換える．O(log N).
void set(size_type k, const value_type &a) { set(k, monoid_type(a)); }
void set(size_type k, const monoid_type &a) {
assert(k < size());
set(m_root, k, a, 0, m_sz);
}
// k番目の要素を取得する．O(log N).
value_type prod(size_type k) const {
assert(k < size());
return prod(m_root, k, 0, m_sz).value();
}
// 区間[l,r)の要素の総積を求める．O(log N).
value_type prod(size_type l, size_type r) const {
assert(l <= r and r <= size());
return prod(m_root, l, r, 0, m_sz).value();
}
// 区間全体の要素の総積を取得する．O(1).
value_type prod_all() const { return (m_root ? m_root->product : monoid_type::one()).value(); }
// pred(prod(l,r))==true となる区間の最右位値rを二分探索する．
// ただし，区間[l,n)の要素はpred(S)によって区分化されていること．また，pred(e)==true であること．O(log N).
template <bool (*pred)(value_type)>
size_type most_right(size_type l) const {
return most_right(l, [](const value_type &x) -> bool { return pred(x); });
}
template <typename Pred>
size_type most_right(size_type l, Pred pred) const {
static_assert(std::is_invocable_r<bool, Pred, value_type>::value);
assert(l <= size());
assert(pred(monoid_type::one().value()));
monoid_type &&product = monoid_type::one();
return most_right(m_root, l, pred, 0, m_sz, product);
}
// pred(prod(l,r))==true となる区間の最左位値lを二分探索する．
// ただし，区間[0,r)の要素はpred(S)によって区分化されていること．また，pred(e)==true であること．O(log N).
template <bool (*pred)(value_type)>
size_type most_left(int r) const {
return most_left(r, [](const value_type &x) -> bool { return pred(x); });
}
template <typename Pred>
size_type most_left(size_type r, Pred pred) const {
static_assert(std::is_invocable_r<bool, Pred, value_type>::value);
assert(r <= size());
assert(pred(monoid_type::one().value()));
value_type &&product = monoid_type::one();
return most_left(m_root, r, pred, 0, m_sz, product);
}
void reset(size_type k) { reset(m_root, k, k + 1, 0, m_sz); }
void reset(size_type l, size_type r) {
assert(l <= r and r <= size());
reset(m_root, l, r, 0, m_sz);
}
void reset() { m_root.reset(); }
friend std::ostream &operator<<(std::ostream &os, const DynamicSegmentTree &rhs) {
os << "[";
bool first = true;
rhs.print(os, rhs.m_root, first);
return os << "]";
}
};
template <typename S>
using range_minimum_dynamic_segment_tree = DynamicSegmentTree<algebra::monoid::minimum<S>>;
template <typename S>
using range_maximum_dynamic_segment_tree = DynamicSegmentTree<algebra::monoid::maximum<S>>;
template <typename S>
using range_sum_dynamic_segment_tree = DynamicSegmentTree<algebra::monoid::addition<S>>;
} // namespace dynamic_segment_tree
} // namespace algorithm
#line 6 "verify/aoj-DSL_2_B-dynamic_segment_tree.test.cpp"
int main() {
int n;
int q;
std::cin >> n >> q;
algorithm::dynamic_segment_tree::range_sum_dynamic_segment_tree<int> segtree(n);
while(q--) {
int com;
std::cin >> com;
if(com == 0) {
int x;
int y;
std::cin >> x >> y;
--x;
auto &&now = segtree.prod(x);
segtree.set(x, now + y);
} else {
int x, y;
std::cin >> x >> y;
--x;
auto &&ans = segtree.prod(x, y);
std::cout << ans << "\n";
}
}
}