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#include "data-structure/segtree/persistent_segment_tree.hpp"
#pragma once #include <bit> #include <memory> #include <numeric> #include <vector> /** * @brief Persistent Segment Tree */ template <typename M> class PersistentSegmentTree { using T = M::T; public: PersistentSegmentTree() = default; explicit PersistentSegmentTree(int n) : PersistentSegmentTree(std::vector<T>(n, M::id())) {} explicit PersistentSegmentTree(const std::vector<T>& v) : root(std::make_shared<Node>()), size(std::bit_ceil(v.size())) { build(v, root, 0, size); } T operator[](int k) const { return fold(k, k + 1); } PersistentSegmentTree update(int k, const T& x) const { return PersistentSegmentTree(update(k, x, root, 0, size), size); } T fold(int l, int r) const { return fold(l, r, root, 0, size); } private: struct Node; using node_ptr = std::shared_ptr<Node>; struct Node { T val; node_ptr left, right; Node() : val(M::id()), left(nullptr), right(nullptr) {} Node(const T& val, const node_ptr& left, const node_ptr& right) : val(val), left(left), right(right) {} }; node_ptr root; int size; PersistentSegmentTree(const node_ptr& root, int size) : root(root), size(size) {} void build(const std::vector<T>& v, const node_ptr& n, int l, int r) const { if (r - l == 1) { n->val = l < (int)v.size() ? v[l] : M::id(); return; } int m = std::midpoint(l, r); n->left = std::make_shared<Node>(); build(v, n->left, l, m); n->right = std::make_shared<Node>(); build(v, n->right, m, r); n->val = M::op(n->left->val, n->right->val); } node_ptr update(int k, const T& x, const node_ptr& n, int l, int r) const { if (r - l == 1) { return std::make_shared<Node>(x, nullptr, nullptr); } int m = std::midpoint(l, r); if (k < m) { auto left = update(k, x, n->left, l, m); T val = M::op(left->val, n->right->val); return std::make_shared<Node>(val, left, n->right); } else { auto right = update(k, x, n->right, m, r); T val = M::op(n->left->val, right->val); return std::make_shared<Node>(val, n->left, right); } } T fold(int a, int b, const node_ptr& n, int l, int r) const { if (r <= a || b <= l) return M::id(); if (a <= l && r <= b) return n->val; int m = std::midpoint(l, r); return M::op(fold(a, b, n->left, l, m), fold(a, b, n->right, m, r)); } };
#line 2 "data-structure/segtree/persistent_segment_tree.hpp" #include <bit> #include <memory> #include <numeric> #include <vector> /** * @brief Persistent Segment Tree */ template <typename M> class PersistentSegmentTree { using T = M::T; public: PersistentSegmentTree() = default; explicit PersistentSegmentTree(int n) : PersistentSegmentTree(std::vector<T>(n, M::id())) {} explicit PersistentSegmentTree(const std::vector<T>& v) : root(std::make_shared<Node>()), size(std::bit_ceil(v.size())) { build(v, root, 0, size); } T operator[](int k) const { return fold(k, k + 1); } PersistentSegmentTree update(int k, const T& x) const { return PersistentSegmentTree(update(k, x, root, 0, size), size); } T fold(int l, int r) const { return fold(l, r, root, 0, size); } private: struct Node; using node_ptr = std::shared_ptr<Node>; struct Node { T val; node_ptr left, right; Node() : val(M::id()), left(nullptr), right(nullptr) {} Node(const T& val, const node_ptr& left, const node_ptr& right) : val(val), left(left), right(right) {} }; node_ptr root; int size; PersistentSegmentTree(const node_ptr& root, int size) : root(root), size(size) {} void build(const std::vector<T>& v, const node_ptr& n, int l, int r) const { if (r - l == 1) { n->val = l < (int)v.size() ? v[l] : M::id(); return; } int m = std::midpoint(l, r); n->left = std::make_shared<Node>(); build(v, n->left, l, m); n->right = std::make_shared<Node>(); build(v, n->right, m, r); n->val = M::op(n->left->val, n->right->val); } node_ptr update(int k, const T& x, const node_ptr& n, int l, int r) const { if (r - l == 1) { return std::make_shared<Node>(x, nullptr, nullptr); } int m = std::midpoint(l, r); if (k < m) { auto left = update(k, x, n->left, l, m); T val = M::op(left->val, n->right->val); return std::make_shared<Node>(val, left, n->right); } else { auto right = update(k, x, n->right, m, r); T val = M::op(n->left->val, right->val); return std::make_shared<Node>(val, n->left, right); } } T fold(int a, int b, const node_ptr& n, int l, int r) const { if (r <= a || b <= l) return M::id(); if (a <= l && r <= b) return n->val; int m = std::midpoint(l, r); return M::op(fold(a, b, n->left, l, m), fold(a, b, n->right, m, r)); } };