#ifndef cwB23Tree_h #define cwB23Tree_h namespace cw { namespace b23 { /* This is a binary tree implemented as a (2-3 tree) See: docs/2-3-trees.pdf or https://cs.wellesley.edu/~cs231/handouts/2-3-trees.pdf */ template< typename K, typename V, K null_key > struct tree_str { typedef enum { kInvalidNodeTId, k1LeafTId, // leaf where kv0 is in use but kv1 is not k2LeafTId, // leaf where kv0 and kv1 are in use k2NodeTId, // node with a lo,hi branch but no middle branch k3NodeTId // node with a lo,hi, and middle branch } node_tid_t; typedef struct value_str { V value; struct value_str* link; } value_t; typedef struct key_value_str { K key; // Key for this k/v pair value_t* valueL; // Linked list of values which share the same key. bool is_empty() const { return key==null_key; } bool is_not_empty() const { return !is_empty(); } void set_empty() { key=null_key; valueL=nullptr; } } key_value_t; struct node_str; typedef struct match_result_str { struct node_str* node; key_value_t* kv; unsigned kv_idx; // 0 or 1 } match_result_t; typedef struct node_str { unsigned nid; struct node_str* parent; struct node_str* l_link; // low link struct node_str* m_link; // middle link struct node_str* h_link; // high link // If kv1 is not empty then kv1.key is > kv0.key key_value_t kv0; // kv0 always contains a valid key-value pair key_value_t kv1; // kv1 is only valid if this is a 3 node unsigned key_value_count() const { return kv1.is_empty() ? 1 : 2; } const K& min_key() const { return kv0.key; } const K& max_key() const { return kv1.is_empty() ? kv0.key : kv1.key; } // Leaf nodes have no child pointers, but may have one or two key-value pairs. bool is_leaf() const { return this->l_link == nullptr; } bool is_not_leaf() const { return !is_leaf(); } bool is_1_leaf() const { return is_leaf() && kv1.is_empty(); } bool is_2_leaf() const { return is_leaf() && kv1.is_not_empty(); } // 2 nodes have one key-value pair and valid l_link and h_link; bool is_2_node() const { return !this->is_leaf() && this->m_link == nullptr; } // 3 nodes have two key-value pairs and valid l,m,h links bool is_3_node() const { return !this->is_leaf() && this->m_link != nullptr; } node_tid_t type_id() const { return is_leaf() ? (is_1_leaf() ? k1LeafTId : k2LeafTId) : (is_2_node() ? k2NodeTId : k3NodeTId); } bool is_valid() { // if l_link is null then h_link and m_link are also null. if l_link is not null then neither is h_link. bool fl0 = l_link==nullptr ? (h_link==nullptr && m_link==nullptr) : h_link!=nullptr; // kv0 is never empty bool fl1 = kv0.is_not_empty() && kv0.valueL != nullptr; // m_link is null if kv1 is empty bool fl2 = kv1.is_empty() ? m_link==nullptr : m_link!=nullptr; return fl0 && fl1 && fl2; } unsigned height() const { if( is_leaf() ) return 0; return l_link->height() + 1; } match_result_t is_key_in_node( K key ) { match_result_t r; if( kv0.key == key ) { r.node = this; r.kv = &kv0; r.kv_idx = 0; } else { if( kv1.is_not_empty() and kv1.key == key ) { r.node = this; r.kv = &kv1; r.kv_idx = 1; } else { r.node = nullptr; r.kv = nullptr; r.kv_idx = 2; } } return r; } // Return the next node to this node given the key. // Return nullptr if this is a leaf node. struct node_str* next( K key ) { node_t* n = nullptr; assert( is_key_in_node(key) == false ); if( key < kv0.key ) { n = l_link; } else { if( key > (kv1.is_not_empty() ? kv1.key : kv0.key) ) n = h_link; else n = m_link; } return n; } } node_t; typedef struct node_block_str { struct node_block_str* link; node_t* nodeA; unsigned nodeN; unsigned next_avail_node_idx; // index next empty slot } node_block_t; typedef struct value_block_str { struct value_block_str* link; value_t* valueA; unsigned valueN; unsigned next_avail_value_idx; // index of next empty slot } value_block_t; node_t* _root = nullptr; node_block_t* _beg_node_block = nullptr; // First node in node block linked list node_block_t* _end_node_block = nullptr; // Last block in node block linked list (always partially empty) value_block_t* _beg_value_block = nullptr; // First node in value block linked list value_block_t* _end_value_block = nullptr; // Last block in value block linked list (always partially empty) node_t* _free_node_list = nullptr; // Linked list, through 'parent' of avail nodes. value_t* _free_value_list = nullptr; // unsigned _nodes_per_block = 0; unsigned _values_per_block = 0; unsigned _nid = 0; const char* node_tid_to_label( node_tid_t tid ) { switch(tid) { case kInvalidNodeTId: return ""; case k1LeafTId: return "1L"; case k2LeafTId: return "2L"; case k2NodeTId: return "2N"; case k3NodeTId: return "3N"; } return ""; } // Return the node and kv that matches the key. match_result_t key_to_node( K key ) { match_result_t r; node_t* n = _root; while(n != nullptr) { r = n->is_key_in_node(key); if( r.node != nullptr ) break; n = n->next(key); } return r; } node_block_t* _alloc_node_block( unsigned nodes_per_block ) { node_block_t* b = mem::allocZ(); b->nodeA = mem::allocZ( nodes_per_block ); b->nodeN = nodes_per_block; if( _beg_node_block == nullptr ) _beg_node_block = b; else _end_node_block->link = b; _end_node_block = b; return b; } value_block_t* _alloc_value_block( unsigned values_per_block ) { value_block_t* b = mem::allocZ(); b->valueA = mem::allocZ( values_per_block ); b->valueN = values_per_block; if( _beg_value_block == nullptr ) _beg_value_block = b; else _end_value_block->link = b; _end_value_block = b; return b; } void _alloc_value( key_value_t& kv, V new_value ) { value_t* v = nullptr; if( _free_value_list != nullptr ) { v = _free_value_list; _free_value_list = v->link; v->link = nullptr; } else { if( _end_value_block==nullptr || _end_value_block->next_avail_value_idx >= _end_value_block->valueN ) _alloc_value_block(_values_per_block); assert( _end_value_block!= nullptr && _end_value_block->next_avail_value_idx < _end_value_block->valueN ); v = _end_value_block->valueA + _end_value_block->next_avail_value_idx++; } v->value = new_value; v->link = kv.valueL; kv.valueL = v; } // Initialize a kv with a new key, value pair void _init_key_value( key_value_t& kv, K key, V value ) { kv.key = key; _alloc_value(kv,value); } // Initialize a kv from an existing kv pair void _move_key_value( key_value_t& lhs_kv, key_value_t& rhs_kv ) { lhs_kv = rhs_kv; rhs_kv.set_empty(); } node_t* _alloc_node( node_t* parent ) { node_t* n = nullptr; if( _free_node_list != nullptr ) { n = _free_node_list; memset(n,0,sizeof(*n)); _free_node_list = _free_node_list->parent; } else { // if the current node block has no available nodes then create a new node block if( _end_node_block==nullptr || _end_node_block->next_avail_node_idx >= _end_node_block->nodeN ) _alloc_node_block(_nodes_per_block); // a node block with available nodes must now exist assert( _end_node_block!= nullptr && _end_node_block->next_avail_node_idx < _end_node_block->nodeN ); // get the next available node n = _end_node_block->nodeA + _end_node_block->next_avail_node_idx++; } n->nid = _nid++; n->parent = parent; n->kv0.key = null_key; n->kv1.key = null_key; return n; } // allocate a new node with a new key / value pair node_t* _alloc_node( node_t* parent, K new_key, V new_value ) { node_t* n = _alloc_node(parent); // all new nodes have a valid k/v pair in kv0 _init_key_value( n->kv0, new_key, new_value ); return n; } // allocate a new node with an existing k/v apir. node_t* _alloc_node( node_t* parent, key_value_t& kv ) { node_t* n = _alloc_node(parent); _move_key_value( n->kv0, kv ); return n; } void _free_key_value( key_value_t& kv ) { // Free values by placing the values on the _free_value_list; value_t* v = kv.valueL; while( v != nullptr ) { value_t* v0 = v->link; // TODO: figure out how to call release on v->value // if release(v->value) exists // release(v->value); v->link = _free_value_list; _free_value_list = v; v = v0; } kv.set_empty(); } void _free_node( node_t* node ) { _free_key_value(node->kv0); _free_key_value(node->kv1); // track free nodes by forming a list using the 'parent' pointer node->parent = _free_node_list; _free_node_list = node; } rc_t create( unsigned nodes_per_block ) { rc_t rc = kOkRC; _nodes_per_block = nodes_per_block; _values_per_block= nodes_per_block; _alloc_node_block(nodes_per_block); _alloc_value_block(nodes_per_block); return rc; } void destroy() { value_block_t* vb = _beg_value_block; while( vb!=nullptr ) { value_block_t* vb0 = vb->link; mem::release(vb->valueA); mem::release(vb); vb=vb0; } node_block_t* nb = _beg_node_block; while( nb !=nullptr ) { node_block_t* nb0 = nb->link; mem::release(nb->nodeA); mem::release(nb); nb=nb0; } } void _insert_into_1_leaf(node_t* n, K key, V value ) { if( key > n->kv0.key ) _init_key_value(n->kv1,key,value); else { _move_key_value(n->kv1,n->kv0); _init_key_value(n->kv0,key,value); } } node_t* _2_leaf_to_2_node_sub_tree( node_t* n, K key, V value ) { assert( n->is_2_leaf() ); if( key < n->kv0.key ) { n->l_link = _alloc_node(n,key,value); n->h_link = _alloc_node(n,n->kv1); } else { if( key > n->kv1.key ) { n->l_link = _alloc_node(n,n->kv0); n->h_link = _alloc_node(n,key,value); _move_key_value(n->kv0,n->kv1); } else { n->l_link = _alloc_node(n,n->kv0); n->h_link = _alloc_node(n,n->kv1); _init_key_value(n->kv0,key,value); } } assert(n->is_2_node()); return n; } void _link_to_parent_l( node_t* parent, node_t* child ) { parent->l_link = child; child->parent = parent; } void _link_to_parent_m( node_t* parent, node_t* child ) { parent->m_link = child; child->parent = parent; } void _link_to_parent_h( node_t* parent, node_t* child ) { parent->h_link = child; child->parent = parent; } // convert 'n', a 2-node, into a 3-node by absorbing it's 2-node child void _2_node_to_3_node( node_t* n, node_t* child ) { assert( n->is_2_node() ); // if child is the l subtree if( child == n->l_link ) { _move_key_value(n->kv1,n->kv0); _move_key_value(n->kv0,child->kv0); _link_to_parent_l(n,child->l_link); _link_to_parent_m(n,child->h_link); } else // child must be the h subtree { assert( child == n->h_link ); _move_key_value(n->kv1,child->kv0); _link_to_parent_m(n,child->l_link); _link_to_parent_h(n,child->h_link); } _free_node(child); assert( n->is_3_node() ); } node_t* _2node_from_parts( node_t* parent, key_value_t& kv, node_t* l_subtree, node_t* h_subtree ) { node_t* h_node = _alloc_node(parent,kv); _link_to_parent_l(h_node,l_subtree); _link_to_parent_h(h_node,h_subtree); return h_node; } // Convert a 3-node to a balanced 2-node. // 'child' is a balanced sub-trees of 'n' void _3_node_to_balanced_2_node( node_t* n, node_t* child ) { assert( n->is_3_node() ); assert( child->is_2_node() ); // if the child is on the l-subtree if( child == n->l_link ) { // make l-key the central node and the h-key the balanced h-subtree n->h_link = _2node_from_parts(n,n->kv1,n->m_link,n->h_link); } else { if( child == n->h_link ) { // make h-key the central node and l-key the balanced l-subtree n->l_link = _2node_from_parts(n,n->kv0,n->l_link,n->m_link); _move_key_value(n->kv0,n->kv1); } else { // make m-subtree he central node and l-key the balanced l-subtree and h-key the balanced h-subtree assert( child == n->m_link ); n->l_link = _2node_from_parts(n,n->kv0,n->l_link,child->l_link); n->h_link = _2node_from_parts(n,n->kv1,child->h_link,n->h_link); _move_key_value(n->kv0,child->kv0); } } // n is now a 2-node - remove the old m_link n->m_link = nullptr; assert( n->is_2_node() ); assert( n->l_link->is_2_node() ); assert( n->h_link->is_2_node() ); } void _insert_up( node_t* n, node_t* sub_tree ) { while(1) { // if n is null then the root was already processed and we are done if( n == nullptr ) break; if( n->is_2_node() ) { // if n is a 2-node the sub-tree is absorbed ... _2_node_to_3_node(n,sub_tree); break; // .. and we are done } else // n is a 3-node { // only 2-nodes and 3-nodes can be accessed when going up the tree assert( n->is_3_node() ); // create a balanced 2-node from the 3-node + sub-tree _3_node_to_balanced_2_node(n,sub_tree); // the tree may now be imbalanced so continue upward sub_tree = n; n = n->parent; } } } void _insert_down( node_t* n, K key, V value ) { while(1) { // If the key already exists at node n->kv0 then insert it in the kv0 value list if( key == n->kv0.key ) { _alloc_value(n->kv0,value); return; } // If the key already exists at node n->kv1 then inser it in the kv1 value list if( n->kv1.is_not_empty() && key == n->kv1.key ) { _alloc_value(n->kv1,value); return; } switch( n->type_id() ) { case k1LeafTId: _insert_into_1_leaf(n,key,value); return; // the new k/v was absorbed - we're done. case k2LeafTId: if( key == 10 ) { printf("break\n"); } _insert_up( n->parent, _2_leaf_to_2_node_sub_tree(n, key, value )); return; // the new k/v inserted on the upward path case k2NodeTId: n = key < n->kv0.key ? n->l_link : n->h_link; break; case k3NodeTId: n = key < n->kv0.key ? n->l_link : (key < n->kv1.key ? n->m_link : n->h_link); break; default: assert(0); } } } void insert( K key, V value ) { if( _root == nullptr ) _root = _alloc_node(nullptr,key,value); else _insert_down(_root,key,value); } match_result_t _in_order_successor( const match_result_t& mr0 ) { assert( mr0.node != nullptr && mr0.node->is_not_leaf() ); match_result_t r; node_t* n; // if mr0 is a 2 node or the high value of a 3 node if( mr0.node->is_2_node() || (mr0.node->is_3_node() && mr0.kv_idx == 1) ) n = mr0.node->h_link; // get right subtree else { assert( mr0.node->is_3_node() && mr0.kv_idx == 0 ); n = mr0.node->m_link; } // go to left most leaf while( n->is_not_leaf() ) n = n->l_link; r.node = n; r.kv = &n->kv0; r.kv_idx = 0; return r; } void remove_key_value( K key, const V& value ) { } rc_t remove_key( K key ) { rc_t rc = kOkRC; match_result_t mr0 = key_to_node(key); match_result_t mr1; // the key does not exist in the tree. if( mr0.node == nullptr ) { rc = cwLogError(kEleNotFoundRC,"The element to remove was not found."); goto errLabel; } // if the target node is a leaf if( mr0.node->is_leaf() ) { if( mr0.node->is_2_leaf() ) { if( mr0.kv_idx == 0 ) _move_key_value(*mr0.kv0,*mr0.kv1); //done: no hole exists in the leaf node goto errLabel; } mr1 = mr0; } else // the target node is a 2 or 3 node { // locate the in-order sucessor mr1 = _in_order_successor(mr0); // the in-order successor must exist if n is a 2 or 3 node assert( mr0->kv!= nullptr && mr1.kv != nullptr ); // move the in order successor value to the target node _move_key_value(*mr0.kv,*mr1.kv); // mr1.kv is now empty // if mr1.node->kv0 is now empty if(mr1.node->is_2_leaf() && mr1.kv_idx == 0 ) { _move_key_value(*mr1.kv0,*mr1.kv1); // done: mr1.node is now a 1 leaf - we're done assert( mr1.node->is_1_leaf() ); goto errLabel; } } assert( mr1.node != nullptr && mr1.node->is_leaf() ); if( mr1->is_2_leaf() ) { } else { } // if key is found on internal node - replace with in-order successor. // if in-order successor is on a non-leaf node continue replacing // with in-order successor until the replacement leaves a hole // in a leaf node. // If the terminal node with the hole is a 2-leaf then change it to a 1-leaf : DONE // if the terminal node is a 3-leaf then errLabel: return rc; } void _print( const node_t* n, unsigned level ) { if( n->l_link != nullptr ) _print(n->l_link,level + 1); unsigned pnid = n->parent==nullptr ? 666 : n->parent->nid; printf("%i h:%i k0:%i %s id:%i par:%i\n",level,n->height(),n->kv0.key,node_tid_to_label(n->type_id()),n->nid,pnid); if( n->m_link != nullptr ) _print(n->m_link,level+1); if( n->kv1.is_not_empty() ) printf("%i h:%i k1:%i %s id:%i par:%i\n",level,n->height(),n->kv1.key,node_tid_to_label(n->type_id()),n->nid,pnid); if( n->h_link != nullptr ) _print(n->h_link,level+1); } void print(const node_t* n = nullptr) { unsigned level = 0; if( n == nullptr ) n = _root; _print(n,level); printf("done\n"); } }; rc_t test( const object_t* cfg ); } } #endif