CP-Algorithms Library
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cp-algo/structures/treap.hpp
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- Last update: 2024-11-21 04:22:30+01:00
- Include:
#include "cp-algo/structures/treap.hpp"
Depends on
Verified with
- Build Cartesian Tree (verify/structures/treap/cartesian_tree.test.cpp)
- Dynamic Range Affine Range Sum (verify/structures/treap/dynamic_sequence_range_affine_range_sum.test.cpp)
- Range Reverse Range Sum (verify/structures/treap/range_reverse_range_sum.test.cpp)
Code
#ifndef CP_ALGO_STRUCTURES_TREAP_HPP
#define CP_ALGO_STRUCTURES_TREAP_HPP
#include "../random/rng.hpp"
#include "treap/common.hpp"
#include <array>
namespace cp_algo::structures::treap {
template<typename meta>
struct node {
using treap = node*;
meta _meta;
int prior = (int)random::rng();
size_t size = 1;
treap children[2] = {nullptr, nullptr};
enum subtree {L, R};
node() {}
node(meta _meta): _meta(_meta) {}
node(meta _meta, int prior): _meta(_meta), prior(prior) {}
static treap make_treap(auto...args) {
return new node(args...);
}
treap pull() {
_meta.pull(children[L], children[R]);
size = 1 + _safe(children[L], size) + _safe(children[R], size);
return this;
}
treap push() {
_meta.push(children[L], children[R]);
return this;
}
// set i-th child and pull metadata
treap set(subtree i, treap t) {
children[i] = t;
return pull();
}
// push changes and detach the i-th child
treap cut(subtree i) {
return children[i];
}
static treap merge(treap A, treap B) {
if(!_safe(A, push()) || !_safe(B, push())) {
return A ? A : B;
} else if(A->prior < B->prior) {
return A->set(R, merge(A->cut(R), B));
} else {
return B->set(L, merge(A, B->cut(L)));
}
}
// return {L, R}, where |L|=k or L=A when |A| < k
static std::array<treap, 2> split(treap A, size_t k) {
if(!_safe(A, push())) {
return {nullptr, nullptr};
} else if(_safe(A->children[L], size) >= k) {
auto [split_L, split_R] = split(A->cut(L), k);
return {split_L, A->set(L, split_R)};
} else {
k -= _safe(A->children[L], size) + 1;
auto [split_L, split_R] = split(A->cut(R), k);
return {A->set(R, split_L), split_R};
}
}
static void exec_on_segment(treap &A, size_t l, size_t r, auto func) {
auto [LM, R] = split(A, r);
auto [L, M] = split(LM, l);
func(M);
A = merge(L, merge(M, R));
}
static void insert(treap &A, size_t pos, treap t) {
auto [L, R] = split(A, pos);
A = merge(L, merge(t, R));
}
static void erase(treap &A, size_t pos) {
auto [L, MR] = split(A, pos);
auto [M, R] = split(MR, 1);
delete M;
A = merge(L, R);
}
static void exec_on_each(treap &A, auto func) {
if(A) {
exec_on_each(A->children[L], func);
func(A);
exec_on_each(A->children[R], func);
}
}
treap pull_all() {
_safe(children[L], pull_all());
_safe(children[R], pull_all());
return pull();
}
treap push_all() {
push();
_safe(children[L], push_all());
_safe(children[R], push_all());
return this;
}
static treap build(auto const& nodes) {
std::vector<treap> st;
for(auto cur: nodes) {
while(st.size() >= 2 && st[st.size() - 2]->prior > cur->prior) {
st.pop_back();
}
if(!st.empty() && st.back()->prior > cur->prior) {
cur->set(L, st.back());
st.pop_back();
}
if(!st.empty() && st.back()->prior < cur->prior) {
st.back()->set(R, cur);
}
st.push_back(cur);
}
return st.empty() ? nullptr : st[0]->pull_all();
}
};
struct null_meta {
void pull(auto const, auto const) {}
void push(auto&, auto&) {}
};
}
#endif // CP_ALGO_STRUCTURES_TREAP_HPP#line 1 "cp-algo/structures/treap.hpp"
#line 1 "cp-algo/random/rng.hpp"
#include <chrono>
#include <random>
namespace cp_algo::random {
uint64_t rng() {
static std::mt19937_64 rng(
std::chrono::steady_clock::now().time_since_epoch().count()
);
return rng();
}
}
#line 1 "cp-algo/structures/treap/common.hpp"
#define _safe(t, op) (t ? t->op : typename std::remove_reference_t<decltype(t->op)>())
#line 5 "cp-algo/structures/treap.hpp"
#include <array>
namespace cp_algo::structures::treap {
template<typename meta>
struct node {
using treap = node*;
meta _meta;
int prior = (int)random::rng();
size_t size = 1;
treap children[2] = {nullptr, nullptr};
enum subtree {L, R};
node() {}
node(meta _meta): _meta(_meta) {}
node(meta _meta, int prior): _meta(_meta), prior(prior) {}
static treap make_treap(auto...args) {
return new node(args...);
}
treap pull() {
_meta.pull(children[L], children[R]);
size = 1 + _safe(children[L], size) + _safe(children[R], size);
return this;
}
treap push() {
_meta.push(children[L], children[R]);
return this;
}
// set i-th child and pull metadata
treap set(subtree i, treap t) {
children[i] = t;
return pull();
}
// push changes and detach the i-th child
treap cut(subtree i) {
return children[i];
}
static treap merge(treap A, treap B) {
if(!_safe(A, push()) || !_safe(B, push())) {
return A ? A : B;
} else if(A->prior < B->prior) {
return A->set(R, merge(A->cut(R), B));
} else {
return B->set(L, merge(A, B->cut(L)));
}
}
// return {L, R}, where |L|=k or L=A when |A| < k
static std::array<treap, 2> split(treap A, size_t k) {
if(!_safe(A, push())) {
return {nullptr, nullptr};
} else if(_safe(A->children[L], size) >= k) {
auto [split_L, split_R] = split(A->cut(L), k);
return {split_L, A->set(L, split_R)};
} else {
k -= _safe(A->children[L], size) + 1;
auto [split_L, split_R] = split(A->cut(R), k);
return {A->set(R, split_L), split_R};
}
}
static void exec_on_segment(treap &A, size_t l, size_t r, auto func) {
auto [LM, R] = split(A, r);
auto [L, M] = split(LM, l);
func(M);
A = merge(L, merge(M, R));
}
static void insert(treap &A, size_t pos, treap t) {
auto [L, R] = split(A, pos);
A = merge(L, merge(t, R));
}
static void erase(treap &A, size_t pos) {
auto [L, MR] = split(A, pos);
auto [M, R] = split(MR, 1);
delete M;
A = merge(L, R);
}
static void exec_on_each(treap &A, auto func) {
if(A) {
exec_on_each(A->children[L], func);
func(A);
exec_on_each(A->children[R], func);
}
}
treap pull_all() {
_safe(children[L], pull_all());
_safe(children[R], pull_all());
return pull();
}
treap push_all() {
push();
_safe(children[L], push_all());
_safe(children[R], push_all());
return this;
}
static treap build(auto const& nodes) {
std::vector<treap> st;
for(auto cur: nodes) {
while(st.size() >= 2 && st[st.size() - 2]->prior > cur->prior) {
st.pop_back();
}
if(!st.empty() && st.back()->prior > cur->prior) {
cur->set(L, st.back());
st.pop_back();
}
if(!st.empty() && st.back()->prior < cur->prior) {
st.back()->set(R, cur);
}
st.push_back(cur);
}
return st.empty() ? nullptr : st[0]->pull_all();
}
};
struct null_meta {
void pull(auto const, auto const) {}
void push(auto&, auto&) {}
};
}