Persistent dynamic set implementation

        We some times need to maintain past version of a dynamic set. One way to do this is to copy the  entire set each time it's modified, but this solution is very slow and consumes Θ(n) memory. Using a binary search tree we can do much better. We just need to copy a simple path from the root to the added or deleted element, therefore only consuming Θ(h)  memory (h being the height).  For this we need to get rid of the parent node, since each node can have several parent from different states of the tree. 

        This implementation is a Red Black Tree so we need the parent node, but the use of a stack or a queue can solve this problem. Since the tree is balanced any modifications only consumes Θ(lg(n)) memory.

Client example:

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int main() { dts::PersistentSet<int, std::greater<int>> set; std::vector<std::function<bool(int)>> vec { [&](int x) { return set.add(x); }, [&](int x) { return set.remove(x); } }; for (unsigned j = 0; j < 300; ++j) { for (int i = 0; i < 200; ++i) vec[j % 2](rand() % 30); } for (unsigned i = 0; i < set.history_size(); ++i) { std::for_each(set.begin(i), set.end(), [](int x) {std::cout << x << ",";}); std::cout << std::endl; } set.roll_back(); return 0; }

Persistent set:

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#pragma once #include <functional> #include <utility> #include <iostream> #include <stack> #include <memory> #include <deque> #include <iterator> #include <type_traits> #include <stack> #include <stdexcept> #include <vector> namespace dts { template <typename T, typename Func = std::less<T>> class PersistentSet { public: PersistentSet(); PersistentSet(Func); bool add(const T&); bool add(T&&); bool remove(const T&); bool empty() const; size_t history_size() const; void roll_back(); class TreeIterator : public std::iterator<std::forward_iterator_tag, std::remove_cv_t<T>, std::ptrdiff_t, const T*, const T&> { using node = typename dts::PersistentSet< std::remove_cv_t<T>, Func >::Nodeptr; node itr; node nil; std::stack<node> path; node find_successor(node n) { n = n->right; if (n != nil) { while (n->left != nil) { path.push(n); n = n->left; } } else { n = path.top(); path.pop(); } return n; } public: explicit TreeIterator(node n, node pnil) : nil(pnil) //begin { if (n == nil) itr = nil; else { path.push(nil); while (n->left != nil) { path.push(n); n = n->left; } itr = n; } } explicit TreeIterator(node pnil) // end : itr(pnil), nil(pnil) { } TreeIterator& operator++ () { itr = find_successor(itr); return *this; } TreeIterator operator++ (int) { TreeIterator tmp(*this); itr = find_successor(itr); return tmp; } bool operator == (const TreeIterator& rhs) const { return itr == rhs.itr; } bool operator != (const TreeIterator& rhs) const { return itr != rhs.itr; } const T& operator* () const { return itr->key; } const T& operator-> () const { return itr->key; } }; typedef TreeIterator const_iterator; const_iterator begin() const { return begin(roots.size() - 1); } const_iterator begin(size_t index) const { if (index >= roots.size()) throw std::out_of_range("out of range"); return const_iterator(roots[index], nil); } const_iterator end() const { return const_iterator(nil); } private: struct Node; using Nodeptr = std::shared_ptr<Node>; struct Node { T key; bool isRed; Nodeptr left; Nodeptr right; Node(const T& pkey, bool pisRed, Nodeptr pleft, Nodeptr pright) : key(pkey), isRed(pisRed), left(pleft), right(pright) { } Node(T&& pkey, bool pisRed, Nodeptr pleft, Nodeptr pright) : key(std::move(pkey)), isRed(pisRed), left(pleft), right(pright) { } }; std::vector<Nodeptr> roots; Func cmp; Nodeptr nil; template <typename TT> Nodeptr create_node(TT&&); Nodeptr copy_node(Nodeptr) const; template <typename TT> bool generic_add(TT&&); template <typename TT> Nodeptr add_recursive(std::deque<Nodeptr>&, TT&&, Nodeptr&); void balance_add(std::deque<Nodeptr> &x); template <typename ChildA, typename ChildB> void mirror_add_balance(Nodeptr&, Nodeptr&, std::deque<Nodeptr>&, ChildA, ChildB); Nodeptr remove_recursive(const T&, Nodeptr, std::deque<Nodeptr>&); template<typename F, typename NF, typename TT> Nodeptr find_and_build(TT&&, Nodeptr, std::deque<Nodeptr>&, F, NF); void delete_node(std::deque<Nodeptr> &); Nodeptr build_min_path(Nodeptr node, std::deque<Nodeptr>&); void transplant(Nodeptr, Nodeptr, Nodeptr); void balance_remove(Nodeptr x, std::deque<Nodeptr>&); template <typename ChildA, typename ChildB > void mirror_remove_balance(Nodeptr&, Nodeptr&, std::deque<Nodeptr> &, ChildA, ChildB); template <typename ChildA, typename ChildB > Nodeptr rotate(Nodeptr, Nodeptr, ChildA, ChildB); static Nodeptr& left(Nodeptr x) { return x->left; }; static Nodeptr& right(Nodeptr x) { return x->right; }; static Nodeptr pop_front(std::deque<Nodeptr>& deque) { auto front = deque.front(); deque.pop_front(); return front; }; }; template<typename T, typename Func> size_t PersistentSet<T, Func>::history_size() const { return roots.size(); } template<typename T, typename Func> bool PersistentSet<T, Func>::empty() const { return roots.back() == nil; } template<typename T, typename Func> void PersistentSet<T, Func>::roll_back() { if (!roots.empty()) roots.pop_back(); } template <typename K, typename Func> void PersistentSet<K, Func>::transplant( Nodeptr parent, Nodeptr removed, Nodeptr transplanted) { if (parent == nil) { roots.pop_back(); roots.push_back(transplanted); } else if (parent->left == removed) parent->left = transplanted; else parent->right = transplanted; } template<typename T, typename Func> PersistentSet<T, Func>::PersistentSet() : PersistentSet(Func()) { } template<typename T, typename Func> PersistentSet<T, Func>::PersistentSet(Func pcmp) : cmp(pcmp), roots(std::vector<Nodeptr>()), nil(std::make_shared<Node>(T(), false, nullptr, nullptr)) { roots.push_back(nil); } template<typename T, typename Func> template <typename ChildA, typename ChildB > typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::rotate( Nodeptr parent_of_x, Nodeptr x, ChildA childA, ChildB childB) { Nodeptr child_of_x = childB(x); childB(x) = childA(child_of_x); if (x == roots.back()) { roots.pop_back(); roots.push_back(child_of_x); } else if (x == childA(parent_of_x)) childA(parent_of_x) = child_of_x; else childB(parent_of_x) = child_of_x; childA(child_of_x) = x; return child_of_x; } template <typename T, typename Func> template<typename TT> bool PersistentSet<T, Func>::generic_add(TT&& element) { std::deque<Nodeptr> path; auto newRoot = add_recursive( path, std::forward<TT>(element), roots.back() ); bool added = newRoot != nullptr; if (added) { roots.push_back(newRoot); path.push_back(nil); balance_add(path); } return added; } template<typename T, typename Func> template<typename F, typename NF, typename TT> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::find_and_build( TT&& element, Nodeptr node, std::deque<Nodeptr> &path, F if_found, NF if_not_found) { if (node == nil) return if_not_found(element, path); bool is_less = cmp(element, node->key); bool is_equal = !is_less && !cmp(node->key, element); if (is_equal) return if_found(node, path); auto direction = is_less ? left : right; auto child = find_and_build( std::forward<TT>(element), direction(node), path, if_found, if_not_found ); if (child == nullptr) return child; auto copy = copy_node(node); path.push_back(copy); direction(copy) = child; return copy; } template<typename T, typename Func> template<typename TT> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::add_recursive(std::deque<Nodeptr>& path, TT &&element, Nodeptr & node) { auto if_not_found = [&](auto pelement, auto& path) { auto copy = create_node(std::forward<T>(pelement)); path.push_back(copy); return copy; }; auto if_found = [](auto node, auto& path) { return nullptr; }; return find_and_build(element, node, path, if_found, if_not_found); } template <typename T, typename Func> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::remove_recursive(const T& element, Nodeptr node, std::deque<Nodeptr>& path) { auto if_not_found = [](auto element, auto& path) { return nullptr; }; auto if_found = [&](auto pnode, auto& ppath) { auto copy = copy_node(pnode); ppath.push_back(copy); return copy; }; return find_and_build(element, node, path, if_found, if_not_found); } template <typename T, typename Func> bool PersistentSet<T, Func>::add(const T& element) { return generic_add(const_cast<T&> (element)); } template <typename T, typename Func> bool PersistentSet<T, Func>::add(T&& element) { return generic_add(std::move(element)); } template<typename T, typename Func> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::copy_node(Nodeptr node) const { if (node == nil) return nil; return std::make_shared<Node>(node->key, node->isRed, node->left, node->right); } template <typename T, typename Func> template <typename TT> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::create_node(TT&& key) { return std::make_shared<Node>(std::forward<TT>(key), true, nil, nil); } template <typename T, typename Func> void PersistentSet<T, Func>::delete_node(std::deque<Nodeptr> & path) { auto removed = path.front(); auto transplanted = removed->right; if (removed->left == nil) { path.pop_front(); transplant(path.front(), removed, transplanted); } else if (removed->right == nil) { path.pop_front(); transplanted = removed->left; transplant(path.front(), removed, transplanted); } else { auto temp = removed; removed->right = copy_node(removed->right); removed = build_min_path(removed->right, path); transplanted = removed->right; temp->key = std::move(removed->key); transplant(path.front(), removed, transplanted); } if (!removed->isRed) balance_remove(transplanted, path); } template <typename T, typename Func> typename PersistentSet<T, Func>::Nodeptr PersistentSet<T, Func>::build_min_path(Nodeptr node, std::deque<Nodeptr>& path) { while (node->left != nil) { node->left = copy_node(node->left); path.push_front(node); node = node->left; } return node; } template <typename T, typename Func> void PersistentSet<T, Func>::balance_remove(Nodeptr extra_black, std::deque<Nodeptr>& path) { auto parent = pop_front(path); while (extra_black != roots.back() && !extra_black->isRed) { if (parent->left == extra_black) mirror_remove_balance(extra_black, parent, path, left, right); else mirror_remove_balance(extra_black, parent, path, right, left); } auto new_node = copy_node(extra_black); transplant(parent, extra_black, new_node); new_node->isRed = false; } template <typename T, typename Func> template <typename ChildA, typename ChildB > void PersistentSet<T, Func>::mirror_remove_balance( Nodeptr& extra_black, Nodeptr& parent, std::deque<Nodeptr> & path, ChildA childA, ChildB childB) { Nodeptr brother = childB(parent); if (brother->isRed) { brother = childB(parent) = copy_node(brother); std::swap(brother->isRed, parent->isRed); rotate(path.front(), parent, childA, childB); path.push_front(brother); brother = childB(parent); } if (!brother->left->isRed && !brother->right->isRed) { brother = childB(parent) = copy_node(brother); brother->isRed = true; extra_black = parent; parent = pop_front(path); } else { if (!childB(brother)->isRed) { brother = childB(parent) = copy_node(brother); childA(brother) = copy_node(childA(brother)); std::swap(brother->isRed, childA(brother)->isRed); brother = rotate(parent, brother, childB, childA); } brother = childB(parent) = copy_node(brother); childB(brother) = copy_node(childB(brother)); brother->isRed = parent->isRed; parent->isRed = false; childB(brother)->isRed = false; rotate(path.front(), parent, childA, childB); extra_black = roots.back(); parent = nil; } } template <typename T, typename Func> bool PersistentSet<T, Func>::remove(const T& element) { std::deque<Nodeptr> path; auto node = remove_recursive( element, roots.back(), path ); bool exist = node != nullptr; if (exist) { roots.push_back(node); path.push_back(nil); delete_node(path); } return exist; } template <typename T, typename Func> void PersistentSet<T, Func>::balance_add(std::deque<Nodeptr>& path) { auto no_compliant = pop_front(path); auto parent = pop_front(path); while (parent->isRed) { if (path.front()->left == parent) mirror_add_balance(parent, no_compliant, path, left, right); else mirror_add_balance(parent, no_compliant, path, right, left); } roots.back()->isRed = false; } template <typename T, typename Func> template <typename ChildA, typename ChildB > void PersistentSet<T, Func>:: mirror_add_balance( Nodeptr &parent, Nodeptr &no_compliant, std::deque<Nodeptr>& path, ChildA childA, ChildB childB) { Nodeptr &uncle = childB(path.front()); if (uncle->isRed) { uncle = copy_node(uncle); parent->isRed = false; uncle->isRed = false; path.front()->isRed = true; no_compliant = pop_front(path); parent = pop_front(path); } else { if (no_compliant == childB(parent)) { std::swap(no_compliant, parent); rotate(path.front(), no_compliant, childA, childB); } auto grand_parent = pop_front(path); std::swap(grand_parent->isRed, parent->isRed); rotate(path.front(), grand_parent, childB, childA); } } }