sotanishy's code snippets for competitive programming
View the Project on GitHub sotanishy/cp-library-cpp
#include "data-structure/segtree/sortable_segment_tree.hpp"
通常のセグメント木の機能に加えて,区間ソートクエリを処理することができる.ソートされた区間を,キーを添字とする動的セグメント木で管理することでこれを実現する.キーは distinct な 64-bit 整数である.
空間計算量: $O(n\log m)$, $m$ はキーの最大値
SortableSegmentTree(long long max_key, vector<pair<long long, T>> kv)
void update(int k, long long key, T val)
key
val
T fold(int l, int r)
void sort(int l, int r, bool descending = false)
#pragma once #include <memory> #include <numeric> #include <set> #include <utility> #include <vector> #include "segment_tree.hpp" template <typename M> class SortableSegmentTree { using T = M::T; public: SortableSegmentTree() = default; explicit SortableSegmentTree(long long max_key, const std::vector<std::pair<long long, T>>& kv) : n(kv.size()), max_key(max_key), st_all(n), st_sorted(n), rev(n) { for (int k = 0; k < n; ++k) { auto [key, val] = kv[k]; st_sorted[k] = std::make_unique<Node>(); st_sorted[k]->update(key, val, 0, max_key); st_all.update(k, val); left.insert(k); } left.insert(n); } void update(int k, long long key, const T& val) { split(k), split(k + 1); st_sorted[k] = std::make_unique<Node>(); st_sorted[k]->update(key, val, 0, max_key); st_all.update(k, val); } T fold(int l, int r) { split(l), split(r); return st_all.fold(l, r); } void sort(int l, int r, bool descending = false) { if (r - l <= 1) return; split(l), split(r); auto it = ++left.find(l); while (it != left.end() && *it < r) { st_sorted[l] = join(std::move(st_sorted[l]), std::move(st_sorted[*it])); st_all.update(*it, M::id()); rev[*it] = false; it = left.erase(it); } if (st_sorted[l]) { st_all.update(l, !descending ? st_sorted[l]->val_forward : st_sorted[l]->val_backward); rev[l] = descending; } } private: struct Node; using node_ptr = std::unique_ptr<Node>; struct Node { int sz; T val_forward, val_backward; node_ptr left, right; Node() : sz(0), val_forward(M::id()), val_backward(M::id()), left(nullptr), right(nullptr) {} void recalc() { int sl = left ? left->sz : 0; int sr = right ? right->sz : 0; sz = sl + sr; T vl_forward = left ? left->val_forward : M::id(); T vr_forward = right ? right->val_forward : M::id(); val_forward = M::op(vl_forward, vr_forward); T vl_backward = left ? left->val_backward : M::id(); T vr_backward = right ? right->val_backward : M::id(); val_backward = M::op(vr_backward, vl_backward); } void update(long long key, const T& x, long long l, long long r) { if (r - l == 1) { sz = 1; val_forward = val_backward = x; return; } long long m = std::midpoint(l, r); if (key < m) { if (!left) left = std::make_unique<Node>(); left->update(key, x, l, m); } else { if (!right) right = std::make_unique<Node>(); right->update(key, x, m, r); } recalc(); } }; static std::pair<node_ptr, node_ptr> split(node_ptr t, int k) { if (k == 0) return {nullptr, std::move(t)}; if (k == t->sz) return {std::move(t), nullptr}; int szl = t->left ? t->left->sz : 0; auto t2 = std::make_unique<Node>(); if (k < szl) { std::tie(t2->left, t->left) = split(std::move(t->left), k); std::swap(t, t2); } else { std::tie(t->right, t2->right) = split(std::move(t->right), k - szl); } t->recalc(), t2->recalc(); return {std::move(t), std::move(t2)}; } static node_ptr join(node_ptr t1, node_ptr t2) { if (!t1) return t2; if (!t2) return t1; t1->left = join(std::move(t1->left), std::move(t2->left)); t1->right = join(std::move(t1->right), std::move(t2->right)); t1->recalc(); return t1; } int n; long long max_key; std::set<int> left; SegmentTree<M> st_all; std::vector<node_ptr> st_sorted; std::vector<bool> rev; void split(int k) { int l = *--left.upper_bound(k); if (l == k) return; if (!rev[l]) { std::tie(st_sorted[l], st_sorted[k]) = split(std::move(st_sorted[l]), k - l); } else { std::tie(st_sorted[k], st_sorted[l]) = split(std::move(st_sorted[l]), l + st_sorted[l]->sz - k); rev[k] = true; } left.insert(k); if (st_sorted[l]) { st_all.update(l, !rev[l] ? st_sorted[l]->val_forward : st_sorted[l]->val_backward); } if (st_sorted[k]) { st_all.update(k, !rev[k] ? st_sorted[k]->val_forward : st_sorted[k]->val_backward); } } };
#line 2 "data-structure/segtree/sortable_segment_tree.hpp" #include <memory> #include <numeric> #include <set> #include <utility> #include <vector> #line 2 "data-structure/segtree/segment_tree.hpp" #include <algorithm> #include <bit> #line 5 "data-structure/segtree/segment_tree.hpp" template <typename M> class SegmentTree { using T = M::T; public: SegmentTree() = default; explicit SegmentTree(int n) : SegmentTree(std::vector<T>(n, M::id())) {} explicit SegmentTree(const std::vector<T>& v) : size(std::bit_ceil(v.size())), node(2 * size, M::id()) { std::ranges::copy(v, node.begin() + size); for (int i = size - 1; i > 0; --i) { node[i] = M::op(node[2 * i], node[2 * i + 1]); } } T operator[](int k) const { return node[k + size]; } void update(int k, const T& x) { k += size; node[k] = x; while (k >>= 1) node[k] = M::op(node[2 * k], node[2 * k + 1]); } T fold(int l, int r) const { T vl = M::id(), vr = M::id(); for (l += size, r += size; l < r; l >>= 1, r >>= 1) { if (l & 1) vl = M::op(vl, node[l++]); if (r & 1) vr = M::op(node[--r], vr); } return M::op(vl, vr); } template <typename F> int find_first(int l, F cond) const { T v = M::id(); for (l += size; l > 0; l >>= 1) { if (l & 1) { T nv = M::op(v, node[l]); if (cond(nv)) { while (l < size) { nv = M::op(v, node[2 * l]); if (cond(nv)) { l = 2 * l; } else { v = nv, l = 2 * l + 1; } } return l + 1 - size; } v = nv; ++l; } } return -1; } template <typename F> int find_last(int r, F cond) const { T v = M::id(); for (r += size; r > 0; r >>= 1) { if (r & 1) { --r; T nv = M::op(node[r], v); if (cond(nv)) { while (r < size) { nv = M::op(node[2 * r + 1], v); if (cond(nv)) { r = 2 * r + 1; } else { v = nv, r = 2 * r; } } return r - size; } v = nv; } } return -1; } private: int size; std::vector<T> node; }; #line 9 "data-structure/segtree/sortable_segment_tree.hpp" template <typename M> class SortableSegmentTree { using T = M::T; public: SortableSegmentTree() = default; explicit SortableSegmentTree(long long max_key, const std::vector<std::pair<long long, T>>& kv) : n(kv.size()), max_key(max_key), st_all(n), st_sorted(n), rev(n) { for (int k = 0; k < n; ++k) { auto [key, val] = kv[k]; st_sorted[k] = std::make_unique<Node>(); st_sorted[k]->update(key, val, 0, max_key); st_all.update(k, val); left.insert(k); } left.insert(n); } void update(int k, long long key, const T& val) { split(k), split(k + 1); st_sorted[k] = std::make_unique<Node>(); st_sorted[k]->update(key, val, 0, max_key); st_all.update(k, val); } T fold(int l, int r) { split(l), split(r); return st_all.fold(l, r); } void sort(int l, int r, bool descending = false) { if (r - l <= 1) return; split(l), split(r); auto it = ++left.find(l); while (it != left.end() && *it < r) { st_sorted[l] = join(std::move(st_sorted[l]), std::move(st_sorted[*it])); st_all.update(*it, M::id()); rev[*it] = false; it = left.erase(it); } if (st_sorted[l]) { st_all.update(l, !descending ? st_sorted[l]->val_forward : st_sorted[l]->val_backward); rev[l] = descending; } } private: struct Node; using node_ptr = std::unique_ptr<Node>; struct Node { int sz; T val_forward, val_backward; node_ptr left, right; Node() : sz(0), val_forward(M::id()), val_backward(M::id()), left(nullptr), right(nullptr) {} void recalc() { int sl = left ? left->sz : 0; int sr = right ? right->sz : 0; sz = sl + sr; T vl_forward = left ? left->val_forward : M::id(); T vr_forward = right ? right->val_forward : M::id(); val_forward = M::op(vl_forward, vr_forward); T vl_backward = left ? left->val_backward : M::id(); T vr_backward = right ? right->val_backward : M::id(); val_backward = M::op(vr_backward, vl_backward); } void update(long long key, const T& x, long long l, long long r) { if (r - l == 1) { sz = 1; val_forward = val_backward = x; return; } long long m = std::midpoint(l, r); if (key < m) { if (!left) left = std::make_unique<Node>(); left->update(key, x, l, m); } else { if (!right) right = std::make_unique<Node>(); right->update(key, x, m, r); } recalc(); } }; static std::pair<node_ptr, node_ptr> split(node_ptr t, int k) { if (k == 0) return {nullptr, std::move(t)}; if (k == t->sz) return {std::move(t), nullptr}; int szl = t->left ? t->left->sz : 0; auto t2 = std::make_unique<Node>(); if (k < szl) { std::tie(t2->left, t->left) = split(std::move(t->left), k); std::swap(t, t2); } else { std::tie(t->right, t2->right) = split(std::move(t->right), k - szl); } t->recalc(), t2->recalc(); return {std::move(t), std::move(t2)}; } static node_ptr join(node_ptr t1, node_ptr t2) { if (!t1) return t2; if (!t2) return t1; t1->left = join(std::move(t1->left), std::move(t2->left)); t1->right = join(std::move(t1->right), std::move(t2->right)); t1->recalc(); return t1; } int n; long long max_key; std::set<int> left; SegmentTree<M> st_all; std::vector<node_ptr> st_sorted; std::vector<bool> rev; void split(int k) { int l = *--left.upper_bound(k); if (l == k) return; if (!rev[l]) { std::tie(st_sorted[l], st_sorted[k]) = split(std::move(st_sorted[l]), k - l); } else { std::tie(st_sorted[k], st_sorted[l]) = split(std::move(st_sorted[l]), l + st_sorted[l]->sz - k); rev[k] = true; } left.insert(k); if (st_sorted[l]) { st_all.update(l, !rev[l] ? st_sorted[l]->val_forward : st_sorted[l]->val_backward); } if (st_sorted[k]) { st_all.update(k, !rev[k] ? st_sorted[k]->val_forward : st_sorted[k]->val_backward); } } };