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Dynamic Segment Tree
(DataStructure/dynamicsegtree.hpp)
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- Last update: 2025-04-27 22:54:33+09:00
- Include:
#include "DataStructure/dynamicsegtree.hpp"
Code
#pragma once
template <class S, S (*op)(S, S), S (*e)()> class DynamicSegmenttree {
public:
DynamicSegmenttree(size_t n) : n(n), root(nullptr) {}
void set(size_t p, S x) {
assert(p < n);
set(root, 0, n, p, x);
}
S get(size_t p) const {
assert(p < n);
return get(root, 0, n, p);
}
S query(size_t l, size_t r) const {
assert(l <= r && r <= n);
return prod(root, 0, n, l, r);
}
S query() const {
return root ? root->product : e();
}
void reset(size_t l, size_t r) {
assert(l <= r && r <= n);
return reset(root, 0, n, l, r);
}
template <bool (*f)(S)> size_t max_right(size_t l) const {
return max_right(l, [](S x) { return f(x); });
}
template <class F> size_t max_right(size_t l, const F &f) const {
assert(l <= n);
S product = e();
assert(f(product));
return max_right(root, 0, n, l, f, product);
}
template <bool (*f)(S)> size_t min_left(size_t r) const {
return min_left(r, [](S x) { return f(x); });
}
template <class F> size_t min_left(size_t r, const F &f) const {
assert(r <= n);
S product = e();
assert(f(product));
return min_left(root, 0, n, r, f, product);
}
private:
struct node;
using node_ptr = std::unique_ptr<node>;
struct node {
size_t index;
S value, product;
node_ptr left, right;
node(size_t index, S value)
: index(index), value(value), product(value), left(nullptr),
right(nullptr) {}
void update() {
product = op(op(left ? left->product : e(), value),
right ? right->product : e());
}
};
const size_t n;
node_ptr root;
void set(node_ptr &t, size_t a, size_t b, size_t p, S x) const {
if (!t) {
t = std::make_unique<node>(p, x);
return;
}
if (t->index == p) {
t->value = x;
t->update();
return;
}
size_t c = (a + b) >> 1;
if (p < c) {
if (t->index < p)
std::swap(t->index, p), std::swap(t->value, x);
set(t->left, a, c, p, x);
} else {
if (p < t->index)
std::swap(p, t->index), std::swap(x, t->value);
set(t->right, c, b, p, x);
}
t->update();
}
S get(const node_ptr &t, size_t a, size_t b, size_t p) const {
if (!t)
return e();
if (t->index == p)
return t->value;
size_t c = (a + b) >> 1;
if (p < c)
return get(t->left, a, c, p);
else
return get(t->right, c, b, p);
}
S prod(const node_ptr &t, size_t a, size_t b, size_t l, size_t r) const {
if (!t || b <= l || r <= a)
return e();
if (l <= a && b <= r)
return t->product;
size_t c = (a + b) >> 1;
S result = prod(t->left, a, c, l, r);
if (l <= t->index && t->index < r)
result = op(result, t->value);
return op(result, prod(t->right, c, b, l, r));
}
void reset(node_ptr &t, size_t a, size_t b, size_t l, size_t r) const {
if (!t || b <= l || r <= a)
return;
if (l <= a && b <= r) {
t.reset();
return;
}
size_t c = (a + b) >> 1;
reset(t->left, a, c, l, r);
reset(t->right, c, b, l, r);
t->update();
}
template <class F>
size_t max_right(const node_ptr &t, size_t a, size_t b, size_t l,
const F &f, S &product) const {
if (!t || b <= l)
return n;
if (f(op(product, t->product))) {
product = op(product, t->product);
return n;
}
size_t c = (a + b) >> 1;
size_t result = max_right(t->left, a, c, l, f, product);
if (result != n)
return result;
if (l <= t->index) {
product = op(product, t->value);
if (!f(product))
return t->index;
}
return max_right(t->right, c, b, l, f, product);
}
template <class F>
size_t min_left(const node_ptr &t, size_t a, size_t b, size_t r, const F &f,
S &product) const {
if (!t || r <= a)
return 0;
if (f(op(t->product, product))) {
product = op(t->product, product);
return 0;
}
size_t c = (a + b) >> 1;
size_t result = min_left(t->right, c, b, r, f, product);
if (result != 0)
return result;
if (t->index < r) {
product = op(t->value, product);
if (!f(product))
return t->index + 1;
}
return min_left(t->left, a, c, r, f, product);
}
};
/**
* @brief Dynamic Segment Tree
*/#line 2 "DataStructure/dynamicsegtree.hpp"
template <class S, S (*op)(S, S), S (*e)()> class DynamicSegmenttree {
public:
DynamicSegmenttree(size_t n) : n(n), root(nullptr) {}
void set(size_t p, S x) {
assert(p < n);
set(root, 0, n, p, x);
}
S get(size_t p) const {
assert(p < n);
return get(root, 0, n, p);
}
S query(size_t l, size_t r) const {
assert(l <= r && r <= n);
return prod(root, 0, n, l, r);
}
S query() const {
return root ? root->product : e();
}
void reset(size_t l, size_t r) {
assert(l <= r && r <= n);
return reset(root, 0, n, l, r);
}
template <bool (*f)(S)> size_t max_right(size_t l) const {
return max_right(l, [](S x) { return f(x); });
}
template <class F> size_t max_right(size_t l, const F &f) const {
assert(l <= n);
S product = e();
assert(f(product));
return max_right(root, 0, n, l, f, product);
}
template <bool (*f)(S)> size_t min_left(size_t r) const {
return min_left(r, [](S x) { return f(x); });
}
template <class F> size_t min_left(size_t r, const F &f) const {
assert(r <= n);
S product = e();
assert(f(product));
return min_left(root, 0, n, r, f, product);
}
private:
struct node;
using node_ptr = std::unique_ptr<node>;
struct node {
size_t index;
S value, product;
node_ptr left, right;
node(size_t index, S value)
: index(index), value(value), product(value), left(nullptr),
right(nullptr) {}
void update() {
product = op(op(left ? left->product : e(), value),
right ? right->product : e());
}
};
const size_t n;
node_ptr root;
void set(node_ptr &t, size_t a, size_t b, size_t p, S x) const {
if (!t) {
t = std::make_unique<node>(p, x);
return;
}
if (t->index == p) {
t->value = x;
t->update();
return;
}
size_t c = (a + b) >> 1;
if (p < c) {
if (t->index < p)
std::swap(t->index, p), std::swap(t->value, x);
set(t->left, a, c, p, x);
} else {
if (p < t->index)
std::swap(p, t->index), std::swap(x, t->value);
set(t->right, c, b, p, x);
}
t->update();
}
S get(const node_ptr &t, size_t a, size_t b, size_t p) const {
if (!t)
return e();
if (t->index == p)
return t->value;
size_t c = (a + b) >> 1;
if (p < c)
return get(t->left, a, c, p);
else
return get(t->right, c, b, p);
}
S prod(const node_ptr &t, size_t a, size_t b, size_t l, size_t r) const {
if (!t || b <= l || r <= a)
return e();
if (l <= a && b <= r)
return t->product;
size_t c = (a + b) >> 1;
S result = prod(t->left, a, c, l, r);
if (l <= t->index && t->index < r)
result = op(result, t->value);
return op(result, prod(t->right, c, b, l, r));
}
void reset(node_ptr &t, size_t a, size_t b, size_t l, size_t r) const {
if (!t || b <= l || r <= a)
return;
if (l <= a && b <= r) {
t.reset();
return;
}
size_t c = (a + b) >> 1;
reset(t->left, a, c, l, r);
reset(t->right, c, b, l, r);
t->update();
}
template <class F>
size_t max_right(const node_ptr &t, size_t a, size_t b, size_t l,
const F &f, S &product) const {
if (!t || b <= l)
return n;
if (f(op(product, t->product))) {
product = op(product, t->product);
return n;
}
size_t c = (a + b) >> 1;
size_t result = max_right(t->left, a, c, l, f, product);
if (result != n)
return result;
if (l <= t->index) {
product = op(product, t->value);
if (!f(product))
return t->index;
}
return max_right(t->right, c, b, l, f, product);
}
template <class F>
size_t min_left(const node_ptr &t, size_t a, size_t b, size_t r, const F &f,
S &product) const {
if (!t || r <= a)
return 0;
if (f(op(t->product, product))) {
product = op(t->product, product);
return 0;
}
size_t c = (a + b) >> 1;
size_t result = min_left(t->right, c, b, r, f, product);
if (result != 0)
return result;
if (t->index < r) {
product = op(t->value, product);
if (!f(product))
return t->index + 1;
}
return min_left(t->left, a, c, r, f, product);
}
};
/**
* @brief Dynamic Segment Tree
*/