lyx_mirror/src/support/weighted_btree.h

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// $Id: btree.h 72 2008-01-25 12:47:26Z tb $
/** \file btree.h
* Contains the main B+ tree implementation template class btree.
*/
/*
* STX B+ Tree Template Classes v0.8.1
* Copyright (C) 2008 Timo Bingmann
* 2008 Stefan Schimanski (weighted variant)
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by the
* Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* This library is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
* for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef _STX_RA_BTREE_H_
#define _STX_RA_BTREE_H_
// *** Required Headers from the STL
#include <algorithm>
#include <functional>
#include <istream>
#include <ostream>
#include <assert.h>
// *** Debugging Macros
#ifdef BTREE_DEBUG
#include <iostream>
/// Print out debug information to std::cout if BTREE_DEBUG is defined.
#define BTREE_PRINT(x) do { if (debug) (std::cout << x); } while(0)
/// Assertion only if BTREE_DEBUG is defined. This is not used in verify().
#define BTREE_ASSERT(x) do { assert(x); } while(0)
#else
/// Print out debug information to std::cout if BTREE_DEBUG is defined.
#define BTREE_PRINT(x) do { } while(0)
/// Assertion only if BTREE_DEBUG is defined. This is not used in verify().
#define BTREE_ASSERT(x) do { } while(0)
#endif
/// The maximum of a and b. Used in some compile-time formulas.
#define BTREE_MAX(a,b) ((a) < (b) ? (b) : (a))
#ifndef BTREE_FRIENDS
/// The macro BTREE_FRIENDS can be used by outside class to access the B+
/// tree internals. This was added for wxBTreeDemo to be able to draw the
/// tree.
#define BTREE_FRIENDS friend class btree_friend;
#endif
/// STX - Some Template Extensions namespace
namespace stx {
/** Generates default traits for a B+ tree used as a set. It estimates leaf and
* inner node sizes by assuming a cache line size of 256 bytes. */
template <typename _Key>
struct btree_default_set_traits
{
/// If true, the tree will self verify it's invariants after each insert()
/// or erase(). The header must have been compiled with BTREE_DEBUG defined.
static const bool selfverify = false;
/// If true, the tree will print out debug information and a tree dump
/// during insert() or erase() operation. The header must have been
/// compiled with BTREE_DEBUG defined and key_type must be std::ostream
/// printable.
static const bool debug = false;
/// Number of slots in each leaf of the tree. Estimated so that each node
/// has a size of about 256 bytes.
static const int leafslots = BTREE_MAX( 8, 256 / (sizeof(_Key)) );
/// Number of slots in each inner node of the tree. Estimated so that each node
/// has a size of about 256 bytes.
static const int innerslots = BTREE_MAX( 8, 256 / (sizeof(_Key) + sizeof(void*)) );
};
/** Generates default traits for a B+ tree used as a map. It estimates leaf and
* inner node sizes by assuming a cache line size of 256 bytes. */
template <typename _Key, typename _Data>
struct btree_default_map_traits
{
/// If true, the tree will self verify it's invariants after each insert()
/// or erase(). The header must have been compiled with BTREE_DEBUG defined.
static const bool selfverify = false;
/// If true, the tree will print out debug information and a tree dump
/// during insert() or erase() operation. The header must have been
/// compiled with BTREE_DEBUG defined and key_type must be std::ostream
/// printable.
static const bool debug = false;
/// Number of slots in each leaf of the tree. Estimated so that each node
/// has a size of about 256 bytes.
static const int leafslots = BTREE_MAX( 8, 256 / (sizeof(_Key) + sizeof(_Data)) );
/// Number of slots in each inner node of the tree. Estimated so that each node
/// has a size of about 256 bytes.
static const int innerslots = BTREE_MAX( 8, 256 / (sizeof(_Key) + sizeof(void*)) );
};
struct Void {};
/** @brief Basic class implementing a base B+ tree data structure in memory.
*
* The base implementation of a memory B+ tree. It is based on the
* implementation in Cormen's Introduction into Algorithms, Jan Jannink's paper
* and other algorithm resources. Almost all STL-required function calls are
* implemented. The asymptotic time requirements of the STL are not always
* fulfilled in theory, however in practice this B+ tree performs better than a
* red-black tree by using more memory. The insertion function splits the nodes
* on the recursion unroll. Erase is largely based on Jannink's ideas.
*
* This class is specialized into btree_set, btree_multiset, btree_map and
* btree_multimap using default template parameters and facade functions.
*/
template <typename _Key,
typename _Weight = size_t,
typename _Data = Void,
typename _Value = std::pair<_Key, _Data>,
typename _Compare = std::less<_Key>,
typename _Traits = btree_default_map_traits<_Key, _Data>,
bool _Duplicates = false>
class weighted_btree
{
public:
// *** Template Parameter Types
/// First template parameter: The key type of the B+ tree. This is stored
/// in inner nodes and leaves
typedef _Key key_type;
///
typedef _Weight weight_type;
/// Second template parameter: The data type associated with each
/// key. Stored in the B+ tree's leaves
typedef _Data data_type;
/// Third template parameter: Composition pair of key and data types, this
/// is required by the STL standard. The B+ tree does not store key and
/// data together. If value_type == key_type then the B+ tree implements a
/// set.
typedef _Value value_type;
/// Fourth template parameter: Key comparison function object
typedef _Compare key_compare;
/// Fifth template parameter: Traits object used to define more parameters
/// of the B+ tree
typedef _Traits traits;
/// Sixth template parameter: Allow duplicate keys in the B+ tree. Used to
/// implement multiset and multimap.
static const bool allow_duplicates = _Duplicates;
// The macro BTREE_FRIENDS can be used by outside class to access the B+
// tree internals. This was added for wxBTreeDemo to be able to draw the
// tree.
BTREE_FRIENDS
public:
// *** Constructed Types
/// Typedef of our own type
typedef weighted_btree<key_type, weight_type, data_type, value_type,
key_compare, traits, allow_duplicates> btree_self;
/// Size type used to count keys
typedef size_t size_type;
/// The pair of key_type and data_type, this may be different from value_type.
typedef std::pair<key_type, data_type> pair_type;
public:
// *** Static Constant Options and Values of the B+ Tree
/// Base B+ tree parameter: The number of key/data slots in each leaf
static const unsigned short leafslotmax = traits::leafslots;
/// Base B+ tree parameter: The number of key slots in each inner node,
/// this can differ from slots in each leaf.
static const unsigned short innerslotmax = traits::innerslots;
/// Computed B+ tree parameter: The minimum number of key/data slots used
/// in a leaf. If fewer slots are used, the leaf will be merged or slots
/// shifted from it's siblings.
static const unsigned short minleafslots = (leafslotmax / 2);
/// Computed B+ tree parameter: The minimum number of key slots used
/// in an inner node. If fewer slots are used, the inner node will be
/// merged or slots shifted from it's siblings.
static const unsigned short mininnerslots = (innerslotmax / 2);
/// Debug parameter: Enables expensive and thorough checking of the B+ tree
/// invariants after each insert/erase operation.
static const bool selfverify = traits::selfverify;
/// Debug parameter: Prints out lots of debug information about how the
/// algorithms change the tree. Requires the header file to be compiled
/// with BTREE_DEBUG and the key type must be std::ostream printable.
static const bool debug = traits::debug;
private:
// *** Node Classes for In-Memory Nodes
/// The header structure of each node in-memory. This structure is extended
/// by inner_node or leaf_node.
struct node
{
/// Level in the b-tree, if level == 0 -> leaf node
unsigned short level;
/// Number of key slotuse use, so number of valid children or data
/// pointers
unsigned short slotuse;
///
weight_type weight;
/// Delayed initialisation of constructed node
inline void initialize(const unsigned short l)
{
level = l;
slotuse = 0;
weight = 0;
}
/// True if this is a leaf node
inline bool isleafnode() const
{
return (level == 0);
}
};
/// Extended structure of a inner node in-memory. Contains only keys and no
/// data items.
struct inner_node : public node
{
/// Keys of children or data pointers
key_type slotkey[innerslotmax];
/// Pointers to children
node* childid[innerslotmax+1];
/// Set variables to initial values
inline void initialize(const unsigned short l)
{
node::initialize(l);
}
/// True if the node's slots are full
inline bool isfull() const
{
return (node::slotuse == innerslotmax);
}
/// True if few used entries, less than half full
inline bool isfew() const
{
return (node::slotuse <= mininnerslots);
}
/// True if node has too few entries
inline bool isunderflow() const
{
return (node::slotuse < mininnerslots);
}
};
/// Extended structure of a leaf node in memory. Contains pairs of keys and
/// data items. Key and data slots are kept in separate arrays, because the
/// key array is traversed very often compared to accessing the data items.
struct leaf_node : public node
{
/// Double linked list pointers to traverse the leaves
leaf_node *prevleaf;
/// Double linked list pointers to traverse the leaves
leaf_node *nextleaf;
/// Keys of children or data pointers
key_type slotkey[leafslotmax];
/// Array of data
data_type slotdata[leafslotmax];
/// Array of weights
weight_type weights[leafslotmax];
/// Set variables to initial values
inline void initialize()
{
node::initialize(0);
prevleaf = nextleaf = NULL;
}
/// True if the node's slots are full
inline bool isfull() const
{
return (node::slotuse == leafslotmax);
}
/// True if few used entries, less than half full
inline bool isfew() const
{
return (node::slotuse <= minleafslots);
}
/// True if node has too few entries
inline bool isunderflow() const
{
return (node::slotuse < minleafslots);
}
};
private:
// *** Template Magic to Convert a pair or key/data types to a value_type
/// \internal For sets the second pair_type is an empty struct, so the
/// value_type should only be the first.
template <typename value_type, typename pair_type>
struct btree_pair_to_value
{
/// Convert a fake pair type to just the first component
inline value_type operator()(pair_type& p) const {
return p.first;
}
/// Convert a fake pair type to just the first component
inline value_type operator()(const pair_type& p) const {
return p.first;
}
};
/// \internal For maps value_type is the same as the pair_type
template <typename value_type>
struct btree_pair_to_value<value_type, value_type>
{
/// Identity "convert" a real pair type to just the first component
inline value_type operator()(pair_type& p) const {
return p;
}
/// Identity "convert" a real pair type to just the first component
inline value_type operator()(const pair_type& p) const {
return p;
}
};
/// Using template specialization select the correct converter used by the
/// iterators
typedef btree_pair_to_value<value_type, pair_type> pair_to_value_type;
public:
// *** Iterators and Reverse Iterators
class iterator;
class const_iterator;
/// STL-like iterator object for B+ tree items. The iterator points to a
/// specific slot number in a leaf.
class iterator
{
public:
// *** Types
/// The key type of the btree. Returned by key().
typedef typename weighted_btree::key_type key_type;
///
typedef typename weighted_btree::weight_type weight_type;
/// The data type of the btree. Returned by data().
typedef typename weighted_btree::data_type data_type;
/// The value type of the btree. Returned by operator*().
typedef typename weighted_btree::value_type value_type;
/// The pair type of the btree.
typedef typename weighted_btree::pair_type pair_type;
/// Reference to the value_type. Required by the reverse_iterator.
typedef value_type& reference;
/// Pointer to the value_type. Required by the reverse_iterator.
typedef value_type* pointer;
/// STL-magic iterator category
typedef std::bidirectional_iterator_tag iterator_category;
/// STL-magic
typedef ptrdiff_t difference_type;
/// Our own type
typedef iterator self;
private:
friend class weighted_btree;
// *** Members
/// The currently referenced leaf node of the tree
typename weighted_btree::leaf_node* currnode;
/// Current key/data slot referenced
unsigned short currslot;
/// Friendly to the const_iterator, so it may access the two data items directly
friend class weighted_btree<key_type, weight_type, data_type, value_type, key_compare, traits, allow_duplicates>::const_iterator;
/// Evil! A temporary value_type to STL-correctly deliver operator* and
/// operator->
mutable value_type temp_value;
// The macro BTREE_FRIENDS can be used by outside class to access the B+
// tree internals. This was added for wxBTreeDemo to be able to draw the
// tree.
BTREE_FRIENDS
public:
// *** Methods
/// Constructor of a mutable iterator
inline iterator(typename weighted_btree::leaf_node *l, unsigned short s)
: currnode(l), currslot(s)
{ }
/// Dereference the iterator, this is not a value_type& because key and
/// value are not stored together
inline reference operator*() const
{
temp_value = pair_to_value_type()( pair_type(currnode->slotkey[currslot],
currnode->slotdata[currslot]) );
return temp_value;
}
/// Dereference the iterator. Do not use this if possible, use key()
/// and data() instead. The B+ tree does not stored key and data
/// together.
inline pointer operator->() const
{
temp_value = pair_to_value_type()( pair_type(currnode->slotkey[currslot],
currnode->slotdata[currslot]) );
return &temp_value;
}
/// Key of the current slot
inline const key_type& key() const
{
return currnode->slotkey[currslot];
}
/// Weight of the current slot
inline weight_type weight() const
{
return currnode->weights[currslot];
}
/// Writable reference to the current data object
inline data_type& data() const
{
return currnode->slotdata[currslot];
}
/// Prefix++ advance the iterator to the next slot
inline self& operator++()
{
if (currslot + 1 < currnode->slotuse) {
++currslot;
}
else if (currnode->nextleaf != NULL) {
currnode = currnode->nextleaf;
currslot = 0;
}
else {
// this is end()
currslot = currnode->slotuse;
}
return *this;
}
/// Postfix++ advance the iterator to the next slot
inline self operator++(int)
{
self tmp = *this; // copy ourselves
if (currslot + 1 < currnode->slotuse) {
++currslot;
}
else if (currnode->nextleaf != NULL) {
currnode = currnode->nextleaf;
currslot = 0;
}
else {
// this is end()
currslot = currnode->slotuse;
}
return tmp;
}
/// Prefix-- backstep the iterator to the last slot
inline self& operator--()
{
if (currslot > 0) {
--currslot;
}
else if (currnode->prevleaf != NULL) {
currnode = currnode->prevleaf;
currslot = currnode->slotuse - 1;
}
else {
// this is begin()
currslot = 0;
}
return *this;
}
/// Postfix-- backstep the iterator to the last slot
inline self operator--(int)
{
self tmp = *this; // copy ourselves
if (currslot > 0) {
--currslot;
}
else if (currnode->prevleaf != NULL) {
currnode = currnode->prevleaf;
currslot = currnode->slotuse - 1;
}
else {
// this is begin()
currslot = 0;
}
return tmp;
}
/// Equality of iterators
inline bool operator==(const self& x) const
{
return (x.currnode == currnode) && (x.currslot == currslot);
}
/// Inequality of iterators
inline bool operator!=(const self& x) const
{
return (x.currnode != currnode) || (x.currslot != currslot);
}
};
/// STL-like read-only iterator object for B+ tree items. The iterator
/// points to a specific slot number in a leaf.
class const_iterator
{
public:
// *** Types
/// The key type of the btree. Returned by key().
typedef typename weighted_btree::key_type key_type;
/// The data type of the btree. Returned by data().
typedef typename weighted_btree::data_type data_type;
/// The value type of the btree. Returned by operator*().
typedef typename weighted_btree::value_type value_type;
/// The pair type of the btree.
typedef typename weighted_btree::pair_type pair_type;
/// Reference to the value_type. Required by the reverse_iterator.
typedef const value_type& reference;
/// Pointer to the value_type. Required by the reverse_iterator.
typedef const value_type* pointer;
/// STL-magic iterator category
typedef std::bidirectional_iterator_tag iterator_category;
/// STL-magic
typedef ptrdiff_t difference_type;
/// Our own type
typedef const_iterator self;
private:
friend class weighted_btree;
// *** Members
/// The currently referenced leaf node of the tree
const typename weighted_btree::leaf_node* currnode;
/// Current key/data slot referenced
unsigned short currslot;
/// Evil! A temporary value_type to STL-correctly deliver operator* and
/// operator->
mutable value_type temp_value;
// The macro BTREE_FRIENDS can be used by outside class to access the B+
// tree internals. This was added for wxBTreeDemo to be able to draw the
// tree.
BTREE_FRIENDS
public:
// *** Methods
/// Constructor of a const iterator
inline const_iterator(const typename weighted_btree::leaf_node *l, unsigned short s)
: currnode(l), currslot(s)
{ }
/// Copy-constructor from a mutable const iterator
inline const_iterator(const iterator &it)
: currnode(it.currnode), currslot(it.currslot)
{ }
/// Dereference the iterator. Do not use this if possible, use key()
/// and data() instead. The B+ tree does not stored key and data
/// together.
inline reference operator*() const
{
temp_value = pair_to_value_type()( pair_type(currnode->slotkey[currslot],
currnode->slotdata[currslot]) );
return temp_value;
}
/// Dereference the iterator. Do not use this if possible, use key()
/// and data() instead. The B+ tree does not stored key and data
/// together.
inline pointer operator->() const
{
temp_value = pair_to_value_type()( pair_type(currnode->slotkey[currslot],
currnode->slotdata[currslot]) );
return &temp_value;
}
/// Key of the current slot
inline const key_type& key() const
{
return currnode->slotkey[currslot];
}
/// Weight of the current slot
inline weight_type weight() const
{
return currnode->weights[currslot];
}
/// Read-only reference to the current data object
inline const data_type& data() const
{
return currnode->slotdata[currslot];
}
/// Prefix++ advance the iterator to the next slot
inline self& operator++()
{
if (currslot + 1 < currnode->slotuse) {
++currslot;
}
else if (currnode->nextleaf != NULL) {
currnode = currnode->nextleaf;
currslot = 0;
}
else {
// this is end()
currslot = currnode->slotuse;
}
return *this;
}
/// Postfix++ advance the iterator to the next slot
inline self operator++(int)
{
self tmp = *this; // copy ourselves
if (currslot + 1 < currnode->slotuse) {
++currslot;
}
else if (currnode->nextleaf != NULL) {
currnode = currnode->nextleaf;
currslot = 0;
}
else {
// this is end()
currslot = currnode->slotuse;
}
return tmp;
}
/// Prefix-- backstep the iterator to the last slot
inline self& operator--()
{
if (currslot > 0) {
--currslot;
}
else if (currnode->prevleaf != NULL) {
currnode = currnode->prevleaf;
currslot = currnode->slotuse - 1;
}
else {
// this is begin()
currslot = 0;
}
return *this;
}
/// Postfix-- backstep the iterator to the last slot
inline self operator--(int)
{
self tmp = *this; // copy ourselves
if (currslot > 0) {
--currslot;
}
else if (currnode->prevleaf != NULL) {
currnode = currnode->prevleaf;
currslot = currnode->slotuse - 1;
}
else {
// this is begin()
currslot = 0;
}
return tmp;
}
/// Equality of iterators
inline bool operator==(const self& x) const
{
return (x.currnode == currnode) && (x.currslot == currslot);
}
/// Inequality of iterators
inline bool operator!=(const self& x) const
{
return (x.currnode != currnode) || (x.currslot != currslot);
}
};
/// create mutable reverse iterator by using STL magic
typedef std::reverse_iterator<iterator> reverse_iterator;
/// create constant reverse iterator by using STL magic
typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
public:
// *** Small Statistics Structure
/** A small struct containing basic statistics about the B+ tree. It can be
* fetched using get_stats(). */
struct tree_stats
{
/// Number of items in the B+ tree
size_type itemcount;
/// Number of leaves in the B+ tree
size_type leaves;
/// Number of inner nodes in the B+ tree
size_type innernodes;
/// Base B+ tree parameter: The number of key/data slots in each leaf
static const unsigned short leafslots = btree_self::leafslotmax;
/// Base B+ tree parameter: The number of key slots in each inner node.
static const unsigned short innerslots = btree_self::innerslotmax;
/// Zero initialized
inline tree_stats()
: itemcount(0),
leaves(0), innernodes(0)
{
}
/// Return the total number of nodes
inline size_type nodes() const
{
return innernodes + leaves;
}
/// Return the average fill of leaves
inline double avgfill_leaves() const
{
return static_cast<double>(itemcount) / (leaves * leafslots);
}
};
private:
// *** Tree Object Data Members
/// Pointer to the B+ tree's root node, either leaf or inner node
node* root;
/// Pointer to first leaf in the double linked leaf chain
leaf_node *headleaf;
/// Pointer to last leaf in the double linked leaf chain
leaf_node *tailleaf;
/// Other small statistics about the B+ tree
tree_stats stats;
/// Key comparison object. More comparison functions are generated from
/// this < relation.
key_compare key_less;
public:
// *** Constructors and Destructor
/// Default constructor initializing an empty B+ tree with the standard key
/// comparison function
inline weighted_btree()
: root(NULL), headleaf(NULL), tailleaf(NULL)
{
}
/// Constructor initializing an empty B+ tree with a special key
/// comparison object
inline weighted_btree(const key_compare &kcf)
: root(NULL), headleaf(NULL), tailleaf(NULL),
key_less(kcf)
{
}
/// Constructor initializing a B+ tree with the range [first,last)
template <class InputIterator>
inline weighted_btree(InputIterator first, InputIterator last)
: root(NULL), headleaf(NULL), tailleaf(NULL)
{
insert(first, last);
}
/// Constructor initializing a B+ tree with the range [first,last) and a
/// special key comparison object
template <class InputIterator>
inline weighted_btree(InputIterator first, InputIterator last, const key_compare &kcf)
: root(NULL), headleaf(NULL), tailleaf(NULL),
key_less(kcf)
{
insert(first, last);
}
/// Frees up all used B+ tree memory pages
inline ~weighted_btree()
{
clear();
}
/// Fast swapping of two identical B+ tree objects.
void swap(btree_self& from)
{
std::swap(root, from.root);
std::swap(headleaf, from.headleaf);
std::swap(tailleaf, from.tailleaf);
std::swap(stats, from.stats);
std::swap(key_less, from.key_less);
}
public:
// *** Key and Value Comparison Function Objects
/// Function class to compare value_type objects. Required by the STL
class value_compare
{
protected:
/// Key comparison function from the template parameter
key_compare key_comp;
/// Constructor called from btree::value_comp()
inline value_compare(key_compare kc)
: key_comp(kc)
{ }
/// Friendly to the btree class so it may call the constructor
friend class weighted_btree<key_type, weight_type, data_type, value_type, key_compare, traits, allow_duplicates>;
public:
/// Function call "less"-operator resulting in true if x < y.
inline bool operator()(const value_type& x, const value_type& y) const
{
return key_comp(x.first, y.first);
}
};
/// Constant access to the key comparison object sorting the B+ tree
inline key_compare key_comp() const
{
return key_less;
}
/// Constant access to a constructed value_type comparison object. Required
/// by the STL
inline value_compare value_comp() const
{
return value_compare(key_less);
}
private:
// *** Convenient Key Comparison Functions Generated From key_less
/// True if a <= b ? constructed from key_less()
inline bool key_lessequal(const key_type &a, const key_type b) const
{
return !key_less(b, a);
}
/// True if a > b ? constructed from key_less()
inline bool key_greater(const key_type &a, const key_type &b) const
{
return key_less(b, a);
}
/// True if a >= b ? constructed from key_less()
inline bool key_greaterequal(const key_type &a, const key_type b) const
{
return !key_less(a, b);
}
/// True if a == b ? constructed from key_less(). This requires the <
/// relation to be a total order, otherwise the B+ tree cannot be sorted.
inline bool key_equal(const key_type &a, const key_type &b) const
{
return !key_less(a, b) && !key_less(b, a);
}
private:
// *** Node Object Allocation and Deallocation Functions
/// Allocate and initialize a leaf node
inline leaf_node* allocate_leaf()
{
leaf_node* n = new leaf_node;
n->initialize();
stats.leaves++;
return n;
}
/// Allocate and initialize an inner node
inline inner_node* allocate_inner(unsigned short l)
{
inner_node* n = new inner_node;
n->initialize(l);
stats.innernodes++;
return n;
}
/// Correctly free either inner or leaf node, destructs all contained key
/// and value objects
inline void free_node(node *n)
{
if (n->isleafnode()) {
delete static_cast<leaf_node*>(n);
stats.leaves--;
}
else {
delete static_cast<inner_node*>(n);
stats.innernodes--;
}
}
public:
// *** Fast Destruction of the B+ Tree
/// Frees all key/data pairs and all nodes of the tree
void clear()
{
if (root)
{
clear_recursive(root);
free_node(root);
root = NULL;
headleaf = tailleaf = NULL;
stats = tree_stats();
}
BTREE_ASSERT(stats.itemcount == 0);
}
private:
/// Recursively free up nodes
void clear_recursive(node *n)
{
if (n->isleafnode())
{
leaf_node *leafnode = static_cast<leaf_node*>(n);
for (unsigned int slot = 0; slot < leafnode->slotuse; ++slot)
{
// data objects are deleted by leaf_node's destructor
}
}
else
{
inner_node *innernode = static_cast<inner_node*>(n);
for (unsigned short slot = 0; slot < innernode->slotuse + 1; ++slot)
{
clear_recursive(innernode->childid[slot]);
free_node(innernode->childid[slot]);
}
}
}
public:
// *** STL Iterator Construction Functions
/// Constructs a read/data-write iterator that points to the first slot in
/// the first leaf of the B+ tree.
inline iterator begin()
{
return iterator(headleaf, 0);
}
/// Constructs a read/data-write iterator that points to the first invalid
/// slot in the last leaf of the B+ tree.
inline iterator end()
{
return iterator(tailleaf, tailleaf ? tailleaf->slotuse : 0);
}
/// Constructs a read-only constant iterator that points to the first slot
/// in the first leaf of the B+ tree.
inline const_iterator begin() const
{
return const_iterator(headleaf, 0);
}
/// Constructs a read-only constant iterator that points to the first
/// invalid slot in the last leaf of the B+ tree.
inline const_iterator end() const
{
return const_iterator(tailleaf, tailleaf ? tailleaf->slotuse : 0);
}
/// Constructs a read/data-write reverse iterator that points to the first
/// invalid slot in the last leaf of the B+ tree. Uses STL magic.
inline reverse_iterator rbegin()
{
return reverse_iterator(end());
}
/// Constructs a read/data-write reverse iterator that points to the first
/// slot in the first leaf of the B+ tree. Uses STL magic.
inline reverse_iterator rend()
{
return reverse_iterator(begin());
}
/// Constructs a read-only reverse iterator that points to the first
/// invalid slot in the last leaf of the B+ tree. Uses STL magic.
inline const_reverse_iterator rbegin() const
{
return const_reverse_iterator(end());
}
/// Constructs a read-only reverse iterator that points to the first slot
/// in the first leaf of the B+ tree. Uses STL magic.
inline const_reverse_iterator rend() const
{
return const_reverse_iterator(begin());
}
private:
// *** B+ Tree Node Binary Search Functions
/// Searches for the first key in the node n less or equal to key. Uses
/// binary search with an optional linear self-verification. This is a
/// template function, because the slotkey array is located at different
/// places in leaf_node and inner_node.
template <typename node_type>
inline int find_lower(const node_type *n, const key_type& key) const
{
if (n->slotuse == 0) return 0;
int lo = 0,
hi = n->slotuse - 1;
while(lo < hi)
{
int mid = (lo + hi) / 2;
if (key_lessequal(key, n->slotkey[mid])) {
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
if (hi < 0 || key_less(n->slotkey[hi], key))
hi++;
BTREE_PRINT("btree::find_lower: on " << n << " key " << key << " -> (" << lo << ") " << hi << ", ");
// verify result using simple linear search
if (selfverify)
{
int i = n->slotuse - 1;
while(i >= 0 && key_lessequal(key, n->slotkey[i]))
i--;
i++;
BTREE_PRINT("testfind: " << i << std::endl);
BTREE_ASSERT(i == hi);
}
else {
BTREE_PRINT(std::endl);
}
return hi;
}
/// Searches for the first summed weight in the node n less or equal to weight.
inline int find_summed_weight_lower(const inner_node *n, weight_type weight) const
{
if (n->slotuse == 0) return 0;
int i = 0;
weight_type w = n->childid[0]->weight;
while (i < n->slotuse && w <= weight) {
i++;
w += n->childid[i]->weight;
}
return i;
}
/// Searches for the first summed weight in the node n less or equal to weight.
inline int find_summed_weight_lower(const leaf_node *n, weight_type weight) const
{
if (n->slotuse == 0) return 0;
int i = 0;
weight_type w = n->weights[0];
while (i < n->slotuse && w <= weight) {
i++;
w += n->weights[i];
}
return i;
}
/// Searches for the first key in the node n greater than key. Uses binary
/// search with an optional linear self-verification. This is a template
/// function, because the slotkey array is located at different places in
/// leaf_node and inner_node.
template <typename node_type>
inline int find_upper(const node_type *n, const key_type& key) const
{
if (n->slotuse == 0) return 0;
int lo = 0,
hi = n->slotuse - 1;
while(lo < hi)
{
int mid = (lo + hi) / 2;
if (key_less(key, n->slotkey[mid])) {
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
if (hi < 0 || key_lessequal(n->slotkey[hi], key))
hi++;
BTREE_PRINT("btree::find_upper: on " << n << " key " << key << " -> (" << lo << ") " << hi << ", ");
// verify result using simple linear search
if (selfverify)
{
int i = n->slotuse - 1;
while(i >= 0 && key_less(key, n->slotkey[i]))
i--;
i++;
BTREE_PRINT("btree::find_upper testfind: " << i << std::endl);
BTREE_ASSERT(i == hi);
}
else {
BTREE_PRINT(std::endl);
}
return hi;
}
/// Searches for the first summed weight in the node n greater than weight.
inline int find_summed_weight_upper(const inner_node *n, weight_type weight) const
{
if (n->slotuse == 0) return 0;
int i = 0;
weight_type w = n->childid[0]->weight;
while (i < n->slotuse && w < weight) {
i++;
w += n->childid[i]->weight;
}
return i;
}
/// Searches for the first summed weight in the node n greater than weight.
inline int find_summed_weight_upper(const leaf_node *n, weight_type weight) const
{
if (n->slotuse == 0) return 0;
int i = 0;
weight_type w = n->weights[0];
while (i < n->slotuse && w < weight) {
i++;
w += n->weights[i];
}
return i;
}
public:
// *** Access Functions to the Item Count
/// Return the number of key/data pairs in the B+ tree
inline size_type size() const
{
return stats.itemcount;
}
///
inline weight_type summed_weight() const
{
if (root)
return root->weight;
else
return 0;
}
/// Returns true if there is at least one key/data pair in the B+ tree
inline bool empty() const
{
return (size() == size_type(0));
}
/// Returns the largest possible size of the B+ Tree. This is just a
/// function required by the STL standard, the B+ Tree can hold more items.
inline size_type max_size() const
{
return size_type(-1);
}
/// Return a const reference to the current statistics.
inline const struct tree_stats& get_stats() const
{
return stats;
}
public:
// *** Standard Access Functions Querying the Tree by Descending to a Leaf
/// Non-STL function checking whether a key is in the B+ tree. The same as
/// (find(k) != end()) or (count() != 0).
bool exists(const key_type &key) const
{
const node *n = root;
if (!n) return false;
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
const leaf_node *leaf = static_cast<const leaf_node*>(n);
int slot = find_lower(leaf, key);
return (slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot]));
}
/// Tries to locate a key in the B+ tree and returns an iterator to the
/// key/data slot if found. If unsuccessful it returns end().
iterator find(const key_type &key)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
unsigned short slot = find_lower(leaf, key);
return (slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot]))
? iterator(leaf, slot) : end();
}
/// Changes the weight of the first node with the given key to the
/// new weight.
void change_weight(iterator & it, weight_type w)
{
node *n = root;
if (!n) return;
if (it.weight() == w)
return;
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, it.key());
// two step because weight_type might be unsigned
n->weight -= it.weight();
n->weight += w;
n = inner->childid[slot];
}
BTREE_ASSERT(n == it.curnode);
n->weight -= it.weight();
n->weight += w;
it.currnode->weights[it.currslot] = w;
}
/// Tries to locate a summed weight in the B+ tree and returns an iterator to the
/// key/data slot if found. If unsuccessful it returns end(). It is
/// ignoring zero-weight nodes during this.
iterator find_summed_weight(weight_type weight)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_lower(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
unsigned short slot = find_summed_weight_lower(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->weights[s];
return (slot < leaf->slotuse && weight == 0)
? iterator(leaf, slot) : end();
}
///
weight_type summed_weight(const key_type &key)
{
node *n = root;
if (!n) return 0;
weight_type w = 0;
while(!n->isleafnode()) {
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
for (unsigned short s = 0; s < slot; ++s)
w += inner->childid[slot]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_lower(leaf, key);
for (unsigned short s = 0; s < slot; ++s)
w += leaf->childid[slot]->weight;
return (slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot]))
? iterator(leaf, slot) : end();
}
/// Tries to locate a key in the B+ tree and returns an constant iterator
/// to the key/data slot if found. If unsuccessful it returns end().
const_iterator find(const key_type &key) const
{
const node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
const leaf_node *leaf = static_cast<const leaf_node*>(n);
int slot = find_lower(leaf, key);
return (slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot]))
? const_iterator(leaf, slot) : end();
}
/// Tries to locate a summed weight in the B+ tree and returns an iterator to the
/// key/data slot if found. If unsuccessful it returns end(). It is
/// ignoring zero-weight nodes during this.
const_iterator find_summed_weight(weight_type weight) const
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_lower(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_summed_weight_lower(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->childid[s]->weight;
return (slot < leaf->slotuse && weight == 0)
? const_iterator(leaf, slot) : end();
}
/// Tries to locate a key in the B+ tree and returns the number of
/// identical key entries found.
size_type count(const key_type &key) const
{
const node *n = root;
if (!n) return 0;
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
const leaf_node *leaf = static_cast<const leaf_node*>(n);
int slot = find_lower(leaf, key);
size_type num = 0;
while (leaf && slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot]))
{
++num;
if (++slot >= leaf->slotuse)
{
leaf = leaf->nextleaf;
slot = 0;
}
}
return num;
}
/// Searches the B+ tree and returns an iterator to the first key less or
/// equal to the parameter. If unsuccessful it returns end().
iterator lower_bound(const key_type& key)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_lower(leaf, key);
return iterator(leaf, slot);
}
/// Searches the B+ tree and returns an iterator to the first summed weight
/// less or equal to the parameter. If unsuccessful it returns end().
iterator lower_summed_weight_bound(weight_type weight)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode()) {
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_lower(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_summed_weight_lower(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->weights[s];
return iterator(leaf, slot);
}
/// Searches the B+ tree and returns an constant iterator to the first key less or
/// equal to the parameter. If unsuccessful it returns end().
const_iterator lower_bound(const key_type& key) const
{
const node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_lower(inner, key);
n = inner->childid[slot];
}
const leaf_node *leaf = static_cast<const leaf_node*>(n);
int slot = find_lower(leaf, key);
return const_iterator(leaf, slot);
}
/// Searches the B+ tree and returns an iterator to the first summed weight
/// less or equal to the parameter. If unsuccessful it returns end().
const_iterator lower_summed_weight_bound(weight_type weight) const
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_lower(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_summed_weight_lower(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->weights[s];
return const_iterator(leaf, slot);
}
/// Searches the B+ tree and returns an iterator to the first key greater
/// than the parameter. If unsuccessful it returns end().
iterator upper_bound(const key_type& key)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_upper(inner, key);
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_upper(leaf, key);
return iterator(leaf, slot);
}
/// Searches the B+ tree and returns an constant iterator to the first key
/// greater than the parameter. If unsuccessful it returns end().
const_iterator upper_bound(const key_type& key) const
{
const node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_upper(inner, key);
n = inner->childid[slot];
}
const leaf_node *leaf = static_cast<const leaf_node*>(n);
int slot = find_upper(leaf, key);
return const_iterator(leaf, slot);
}
/// Searches the B+ tree and returns an iterator to the first summed weight
/// greater than the parameter. If unsuccessful it returns end().
iterator upper_summed_weight_bound(weight_type weight)
{
node *n = root;
if (!n) return end();
while(!n->isleafnode())
{
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_upper(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_summed_weight_upper(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->weights[s];
return iterator(leaf, slot);
}
/// Searches the B+ tree and returns an iterator to the first summed weight
/// greater than the parameter. If unsuccessful it returns end().
const_iterator upper_summed_weight_bound(weight_type weight) const
{
node *n = root;
if (!n) return end();
while(!n->isleafnode()) {
const inner_node *inner = static_cast<const inner_node*>(n);
int slot = find_summed_weight_upper(inner, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= inner->childid[s]->weight;
n = inner->childid[slot];
}
leaf_node *leaf = static_cast<leaf_node*>(n);
int slot = find_summed_weight_upper(leaf, weight);
for (unsigned short s = 0; s < slot; ++s)
weight -= leaf->weights[s];
return const_iterator(leaf, slot);
}
/// Searches the B+ tree and returns both lower_bound() and upper_bound().
inline std::pair<iterator, iterator> equal_range(const key_type& key)
{
return std::pair<iterator, iterator>(lower_bound(key), upper_bound(key));
}
/// Searches the B+ tree and returns both lower_bound() and upper_bound().
inline std::pair<const_iterator, const_iterator> equal_range(const key_type& key) const
{
return std::pair<const_iterator, const_iterator>(lower_bound(key), upper_bound(key));
}
/// Searches the B+ tree and returns both lower_summed_weight_bound() and upper_summed_weight_bound().
inline std::pair<iterator, iterator> equal_summed_weight_range(weight_type weight)
{
return std::pair<iterator, iterator>(lower_summed_weight_bound(weight), upper_summed_weight_bound(weight));
}
/// Searches the B+ tree and returns both lower_summed_weight_bound() and upper_summed_weight_bound().
inline std::pair<const_iterator, const_iterator> equal_summed_weight_range(weight_type weight) const
{
return std::pair<const_iterator, const_iterator>(lower_summed_weight_bound(weight), upper_summed_weight_bound(weight));
}
public:
// *** B+ Tree Object Comparison Functions
/// Equality relation of B+ trees of the same type. B+ trees of the same
/// size and equal elements (both key and data) are considered
/// equal. Beware of the random ordering of duplicate keys.
inline bool operator==(const btree_self &other) const
{
return (size() == other.size()) && std::equal(begin(), end(), other.begin());
}
/// Inequality relation. Based on operator==.
inline bool operator!=(const btree_self &other) const
{
return !(*this == other);
}
/// Total ordering relation of B+ trees of the same type. It uses
/// std::lexicographical_compare() for the actual comparison of elements.
inline bool operator<(const btree_self &other) const
{
return std::lexicographical_compare(begin(), end(), other.begin(), other.end());
}
/// Greater relation. Based on operator<.
inline bool operator>(const btree_self &other) const
{
return other < *this;
}
/// Less-equal relation. Based on operator<.
inline bool operator<=(const btree_self &other) const
{
return !(other < *this);
}
/// Greater-equal relation. Based on operator<.
inline bool operator>=(const btree_self &other) const
{
return !(*this < other);
}
public:
/// *** Fast Copy: Assign Operator and Copy Constructors
/// Assignment operator. All the key/data pairs are copied
inline btree_self& operator= (const btree_self &other)
{
if (this != &other)
{
clear();
key_less = other.key_comp();
if (other.size() != 0)
{
stats.leaves = stats.innernodes = 0;
root = copy_recursive(other.root);
stats = other.stats;
}
if (selfverify) verify();
}
return *this;
}
/// Copy constructor. The newly initialized B+ tree object will contain a
/// copy of all key/data pairs.
inline weighted_btree(const btree_self &other)
: root(NULL), headleaf(NULL), tailleaf(NULL),
stats( other.stats ),
key_less( other.key_comp() )
{
if (size() > 0)
{
stats.leaves = stats.innernodes = 0;
root = copy_recursive(other.root);
if (selfverify) verify();
}
}
private:
/// Recursively copy nodes from another B+ tree object
struct node* copy_recursive(const node *n)
{
if (n->isleafnode())
{
const leaf_node *leaf = static_cast<const leaf_node*>(n);
leaf_node *newleaf = allocate_leaf();
newleaf->slotuse = leaf->slotuse;
std::copy(leaf->slotkey, leaf->slotkey + leaf->slotuse, newleaf->slotkey);
std::copy(leaf->slotdata, leaf->slotdata + leaf->slotuse, newleaf->slotdata);
if (headleaf == NULL)
{
headleaf = tailleaf = newleaf;
newleaf->prevleaf = newleaf->nextleaf = NULL;
}
else
{
newleaf->prevleaf = tailleaf;
tailleaf->nextleaf = newleaf;
tailleaf = newleaf;
}
return newleaf;
}
else
{
const inner_node *inner = static_cast<const inner_node*>(n);
inner_node *newinner = allocate_inner(inner->level);
newinner->slotuse = inner->slotuse;
std::copy(inner->slotkey, inner->slotkey + inner->slotuse, newinner->slotkey);
for (unsigned short slot = 0; slot <= inner->slotuse; ++slot)
{
newinner->childid[slot] = copy_recursive(inner->childid[slot]);
}
return newinner;
}
}
public:
// *** Public Insertion Functions
/// Attempt to insert a key/data pair into the B+ tree. If the tree does not
/// allow duplicate keys, then the insert may fail if it is already
/// present.
inline std::pair<iterator, bool> insert(const pair_type& x, weight_type weight)
{
return insert_start(x.first, weight, x.second);
}
/// Attempt to insert a key/data pair into the B+ tree. Beware that if
/// key_type == data_type, then the template iterator insert() is called
/// instead. If the tree does not allow duplicate keys, then the insert may
/// fail if it is already present.
inline std::pair<iterator, bool> insert(const key_type& key, weight_type weight, const data_type& data)
{
return insert_start(key, weight, data);
}
/// Attempt to insert a key/data pair into the B+ tree. This function is the
/// same as the other insert, however if key_type == data_type then the
/// non-template function cannot be called. If the tree does not allow
/// duplicate keys, then the insert may fail if it is already present.
inline std::pair<iterator, bool> insert2(const key_type& key, weight_type weight, const data_type& data)
{
return insert_start(key, weight, data);
}
/// Attempt to insert a key/data pair into the B+ tree. The iterator hint
/// is currently ignored by the B+ tree insertion routine.
inline iterator insert(iterator /* hint */, const pair_type &x, weight_type weight)
{
return insert_start(x.first, weight, x.second).first;
}
/// Attempt to insert a key/data pair into the B+ tree. The iterator hint is
/// currently ignored by the B+ tree insertion routine.
inline iterator insert2(iterator /* hint */, const key_type& key, weight_type weight, const data_type& data)
{
return insert_start(key, weight, data).first;
}
/// Attempt to insert the range [first,last) of value_type pairs into the B+
/// tree. Each key/data pair is inserted individually.
template <typename InputIterator>
inline void insert(InputIterator first, InputIterator last)
{
InputIterator iter = first;
while(iter != last)
{
insert(*iter, iter->weight());
++iter;
}
}
private:
// *** Private Insertion Functions
/// Start the insertion descent at the current root and handle root
/// splits. Returns true if the item was inserted
std::pair<iterator, bool> insert_start(const key_type& key, weight_type weight, const data_type& value)
{
node *newchild = NULL;
key_type newkey = key_type();
if (!root)
{
root = headleaf = tailleaf = allocate_leaf();
}
std::pair<iterator, bool> r = insert_descend(root, key, weight, value, &newkey, &newchild);
if (newchild)
{
inner_node *newroot = allocate_inner(root->level + 1);
newroot->slotkey[0] = newkey;
newroot->childid[0] = root;
newroot->childid[1] = newchild;
newroot->weight = root->weight + newchild->weight;
newroot->slotuse = 1;
root = newroot;
}
// increment itemcount if the item was inserted
if (r.second) ++stats.itemcount;
#ifdef BTREE_DEBUG
if (debug) print(std::cout);
#endif
if (selfverify) {
verify();
BTREE_ASSERT(exists(key));
}
return r;
}
/**
* @brief Insert an item into the B+ tree.
*
* Descend down the nodes to a leaf, insert the key/data pair in a free
* slot. If the node overflows, then it must be split and the new split
* node inserted into the parent. Unroll / this splitting up to the root.
*/
std::pair<iterator, bool> insert_descend(node* n,
const key_type& key,
weight_type weight,
const data_type& value,
key_type* splitkey, node** splitnode)
{
if (!n->isleafnode())
{
inner_node *inner = static_cast<inner_node*>(n);
key_type newkey = key_type();
node *newchild = NULL;
int slot = find_lower(inner, key);
BTREE_PRINT("btree::insert_descend into " << inner->childid[slot] << std::endl);
weight_type oldw = inner->childid[slot]->weight;
std::pair<iterator, bool> r = insert_descend(inner->childid[slot],
key, weight, value, &newkey, &newchild);
n->weight += inner->childid[slot]->weight - oldw;
if (newchild)
{
BTREE_PRINT("btree::insert_descend newchild with key " << newkey << " node " << newchild << " at slot " << slot << std::endl);
if (inner->isfull())
{
split_inner_node(inner, splitkey, splitnode, slot);
BTREE_PRINT("btree::insert_descend done split_inner: putslot: " << slot << " putkey: " << newkey << " upkey: " << *splitkey << std::endl);
#ifdef BTREE_DEBUG
if (debug)
{
print_node(std::cout, inner);
print_node(std::cout, *splitnode);
}
#endif
// check if insert slot is in the split sibling node
BTREE_PRINT("btree::insert_descend switch: " << slot << " > " << inner->slotuse+1 << std::endl);
if (slot == inner->slotuse+1 && inner->slotuse < (*splitnode)->slotuse)
{
// special case when the insert slot matches the split
// place between the two nodes, then the insert key
// becomes the split key.
BTREE_ASSERT(inner->slotuse + 1 < innerslotmax);
inner_node *splitinner = static_cast<inner_node*>(*splitnode);
// move the split key and it's datum into the left node
inner->slotkey[inner->slotuse] = *splitkey;
inner->childid[inner->slotuse+1] = splitinner->childid[0];
inner->weight += splitinner->childid[0]->weight;
splitinner->weight -= splitinner->childid[0]->weight;
inner->slotuse++;
// set new split key and move corresponding datum into right node
splitinner->childid[0] = newchild;
splitinner->weight += newchild->weight;
*splitkey = newkey;
return r;
}
else if (slot >= inner->slotuse+1)
{
// in case the insert slot is in the newly create split
// node, we reuse the code below.
slot -= inner->slotuse+1;
inner = static_cast<inner_node*>(*splitnode);
BTREE_PRINT("btree::insert_descend switching to splitted node " << inner << " slot " << slot <<std::endl);
}
}
// put pointer to child node into correct slot
BTREE_ASSERT(slot >= 0 && slot <= inner->slotuse);
int i = inner->slotuse;
while(i > slot) {
inner->slotkey[i] = inner->slotkey[i - 1];
inner->childid[i + 1] = inner->childid[i];
i--;
}
inner->slotkey[slot] = newkey;
inner->childid[slot + 1] = newchild;
inner->slotuse++;
inner->weight += newchild->weight;
}
return r;
}
else // n->isleafnode() == true
{
leaf_node *leaf = static_cast<leaf_node*>(n);
unsigned short slot = find_lower(leaf, key);
if (!allow_duplicates && slot < leaf->slotuse && key_equal(key, leaf->slotkey[slot])) {
return std::pair<iterator, bool>(iterator(leaf, slot), false);
}
if (leaf->isfull())
{
split_leaf_node(leaf, splitkey, splitnode);
// check if insert slot is in the split sibling node
if (slot >= leaf->slotuse)
{
slot -= leaf->slotuse;
leaf = static_cast<leaf_node*>(*splitnode);
}
}
// put data item into correct data slot
int i = leaf->slotuse - 1;
BTREE_ASSERT(i + 1 < leafslotmax);
while(i >= 0 && key_less(key, leaf->slotkey[i])) {
leaf->slotkey[i + 1] = leaf->slotkey[i];
leaf->slotdata[i + 1] = leaf->slotdata[i];
leaf->weights[i + 1] = leaf->weights[i];
i--;
}
leaf->slotkey[i + 1] = key;
leaf->slotdata[i + 1] = value;
leaf->weights[i + 1] = weight;
leaf->weight += weight;
leaf->slotuse++;
if (splitnode && leaf != *splitnode && slot == leaf->slotuse-1)
{
// special case: the node was split, and the insert is at the
// last slot of the old node. then the splitkey must be
// updated.
*splitkey = key;
}
return std::pair<iterator, bool>(iterator(leaf, i + 1), true);
}
}
/// Split up a leaf node into two equally-filled sibling leaves. Returns
/// the new nodes and it's insertion key in the two parameters.
void split_leaf_node(leaf_node* leaf, key_type* _newkey, node** _newleaf)
{
BTREE_ASSERT(leaf->isfull());
unsigned int mid = leaf->slotuse / 2;
BTREE_PRINT("btree::split_leaf_node on " << leaf << std::endl);
leaf_node *newleaf = allocate_leaf();
newleaf->slotuse = leaf->slotuse - mid;
newleaf->nextleaf = leaf->nextleaf;
if (newleaf->nextleaf == NULL) {
BTREE_ASSERT(leaf == tailleaf);
tailleaf = newleaf;
}
else {
newleaf->nextleaf->prevleaf = newleaf;
}
for(unsigned int slot = mid; slot < leaf->slotuse; ++slot)
{
unsigned int ni = slot - mid;
newleaf->slotkey[ni] = leaf->slotkey[slot];
newleaf->slotdata[ni] = leaf->slotdata[slot];
newleaf->weights[ni] = leaf->weights[slot];
newleaf->weight += leaf->weights[slot];
leaf->weight -= leaf->weights[slot];
}
leaf->slotuse = mid;
leaf->nextleaf = newleaf;
newleaf->prevleaf = leaf;
*_newkey = leaf->slotkey[leaf->slotuse-1];
*_newleaf = newleaf;
}
/// Split up an inner node into two equally-filled sibling nodes. Returns
/// the new nodes and it's insertion key in the two parameters. Requires
/// the slot of the item will be inserted, so the nodes will be the same
/// size after the insert.
void split_inner_node(inner_node* inner, key_type* _newkey, node** _newinner, unsigned int addslot)
{
BTREE_ASSERT(inner->isfull());
unsigned int mid = inner->slotuse / 2;
BTREE_PRINT("btree::split_inner: mid " << mid << " addslot " << addslot << std::endl);
// if the split is uneven and the overflowing item will be put into the
// larger node, then the smaller split node may underflow
if (addslot <= mid && mid > inner->slotuse - (mid + 1))
mid--;
BTREE_PRINT("btree::split_inner: mid " << mid << " addslot " << addslot << std::endl);
BTREE_PRINT("btree::split_inner_node on " << inner << " into two nodes " << mid << " and " << inner->slotuse - (mid + 1) << " sized" << std::endl);
inner_node *newinner = allocate_inner(inner->level);
newinner->slotuse = inner->slotuse - (mid + 1);
for(unsigned int slot = mid + 1; slot < inner->slotuse; ++slot)
{
unsigned int ni = slot - (mid + 1);
newinner->slotkey[ni] = inner->slotkey[slot];
newinner->childid[ni] = inner->childid[slot];
newinner->weight += inner->childid[slot]->weight;
inner->weight -= inner->childid[slot]->weight;
}
newinner->childid[newinner->slotuse] = inner->childid[inner->slotuse];
newinner->weight += inner->childid[inner->slotuse]->weight;
inner->weight -= inner->childid[inner->slotuse]->weight;
inner->slotuse = mid;
*_newkey = inner->slotkey[mid];
*_newinner = newinner;
}
private:
// *** Support Class Encapsulating Deletion Results
/// Result flags of recursive deletion.
enum result_flags_t
{
/// Deletion successful and no fix-ups necessary.
btree_ok = 0,
/// Deletion not successful because key was not found.
btree_not_found = 1,
/// Deletion successful, the last key was updated so parent slotkeys
/// need updates.
btree_update_lastkey = 2,
/// Deletion successful, children nodes were merged and the parent
/// needs to remove the empty node.
btree_fixmerge = 4
};
/// \internal B+ tree recursive deletion has much information which is
/// needs to be passed upward.
struct result_t
{
/// Merged result flags
result_flags_t flags;
/// The key to be updated at the parent's slot
key_type lastkey;
/// Constructor of a result with a specific flag, this can also be used
/// as for implicit conversion.
inline result_t(result_flags_t f = btree_ok)
: flags(f), lastkey()
{ }
/// Constructor with a lastkey value.
inline result_t(result_flags_t f, const key_type &k)
: flags(f), lastkey(k)
{ }
/// Test if this result object has a given flag set.
inline bool has(result_flags_t f) const
{
return (flags & f) != 0;
}
/// Merge two results OR-ing the result flags and overwriting lastkeys.
inline result_t& operator|= (const result_t &other)
{
flags = result_flags_t(flags | other.flags);
// we overwrite existing lastkeys on purpose
if (other.has(btree_update_lastkey))
lastkey = other.lastkey;
return *this;
}
};
public:
// *** Public Erase Functions
/// Erases one (the first) of the key/data pairs associated with the given
/// key.
bool erase_one(const key_type &key)
{
BTREE_PRINT("btree::erase_one(" << key << ") on btree size " << size() << std::endl);
if (selfverify) verify();
result_t result = erase_one_descend(key, root, NULL, NULL, NULL, NULL, NULL, 0);
if (!result.has(btree_not_found))
--stats.itemcount;
#ifdef BTREE_DEBUG
if (debug) print(std::cout);
#endif
if (selfverify) verify();
return !result.has(btree_not_found);
}
/// Erases all the key/data pairs associated with the given key. This is
/// implemented using erase_one().
size_type erase(const key_type &key)
{
size_type c = 0;
while( erase_one(key) )
{
++c;
if (!allow_duplicates) break;
}
return c;
}
#ifdef BTREE_TODO
/// Erase the key/data pair referenced by the iterator.
void erase(iterator iter)
{
}
#endif
#ifdef BTREE_TODO
/// Erase all key/data pairs in the range [first,last). This function is
/// currently not implemented by the B+ Tree.
void erase(iterator /* first */, iterator /* last */)
{
abort();
}
#endif
private:
// *** Private Erase Functions
/** @brief Erase one (the first) key/data pair in the B+ tree matching key.
*
* Descends down the tree in search of key. During the descent the parent,
* left and right siblings and their parents are computed and passed
* down. Once the key/data pair is found, it is removed from the leaf. If
* the leaf underflows 6 different cases are handled. These cases resolve
* the underflow by shifting key/data pairs from adjacent sibling nodes,
* merging two sibling nodes or trimming the tree.
*/
result_t erase_one_descend(const key_type& key,
node *curr,
node *left, node *right,
inner_node *leftparent, inner_node *rightparent,
inner_node *parent, unsigned int parentslot)
{
if (curr->isleafnode())
{
leaf_node *leaf = static_cast<leaf_node*>(curr);
leaf_node *leftleaf = static_cast<leaf_node*>(left);
leaf_node *rightleaf = static_cast<leaf_node*>(right);
int slot = find_lower(leaf, key);
if (slot >= leaf->slotuse || !key_equal(key, leaf->slotkey[slot]))
{
BTREE_PRINT("Could not find key " << key << " to erase." << std::endl);
return btree_not_found;
}
BTREE_PRINT("Found key in leaf " << curr << " at slot " << slot << std::endl);
leaf->weight -= leaf->weights[slot];
for (int i = slot; i < leaf->slotuse - 1; i++)
{
leaf->slotkey[i] = leaf->slotkey[i + 1];
leaf->slotdata[i] = leaf->slotdata[i + 1];
leaf->weights[i] = leaf->weights[i + 1];
}
leaf->slotuse--;
result_t myres = btree_ok;
// if the last key of the leaf was changed, the parent is notified
// and updates the key of this leaf
if (slot == leaf->slotuse && parent)
{
if (parentslot < parent->slotuse)
{
BTREE_ASSERT(parent->childid[parentslot] == curr);
parent->slotkey[parentslot] = leaf->slotkey[leaf->slotuse - 1];
}
else
{
BTREE_PRINT("Scheduling lastkeyupdate: key " << leaf->slotkey[leaf->slotuse - 1] << std::endl);
myres |= result_t(btree_update_lastkey, leaf->slotkey[leaf->slotuse - 1]);
}
}
if (leaf->isunderflow() && !(leaf == root && leaf->slotuse >= 1))
{
// determine what to do about the underflow
// case : if this empty leaf is the root, there is no way to
// correct underflow
if (leftleaf == NULL && rightleaf == NULL)
{
return btree_ok;
}
// case : if both left and right leaves would underflow in case of
// a shift, then merging is necessary. choose the more local merger
// with our parent
else if ( (leftleaf == NULL || leftleaf->isfew()) && (rightleaf == NULL || rightleaf->isfew()) )
{
if (leftparent == parent)
myres |= merge_leaves(leftleaf, leaf, leftparent);
else
myres |= merge_leaves(leaf, rightleaf, rightparent);
}
// case : the right leaf has extra data, so balance right with current
else if ( (leftleaf != NULL && leftleaf->isfew()) && (rightleaf != NULL && !rightleaf->isfew()) )
{
if (rightparent == parent)
myres |= shift_left_leaf(leaf, rightleaf, rightparent, parentslot);
else
myres |= merge_leaves(leftleaf, leaf, leftparent);
}
// case : the left leaf has extra data, so balance left with current
else if ( (leftleaf != NULL && !leftleaf->isfew()) && (rightleaf != NULL && rightleaf->isfew()) )
{
if (leftparent == parent)
shift_right_leaf(leftleaf, leaf, leftparent, parentslot - 1);
else
myres |= merge_leaves(leaf, rightleaf, rightparent);
}
// case : both the leaf and right leaves have extra data and our
// parent, choose the leaf with more data
else if (leftparent == rightparent)
{
if (leftleaf->slotuse <= rightleaf->slotuse)
myres |= shift_left_leaf(leaf, rightleaf, rightparent, parentslot);
else
shift_right_leaf(leftleaf, leaf, leftparent, parentslot - 1);
}
else
{
if (leftparent == parent)
shift_right_leaf(leftleaf, leaf, leftparent, parentslot - 1);
else
myres |= shift_left_leaf(leaf, rightleaf, rightparent, parentslot);
}
}
return myres;
}
else // !curr->isleafnode()
{
inner_node *inner = static_cast<inner_node*>(curr);
inner_node *leftinner = static_cast<inner_node*>(left);
inner_node *rightinner = static_cast<inner_node*>(right);
node *myleft, *myright;
inner_node *myleftparent, *myrightparent;
int slot = find_lower(inner, key);
if (slot == 0) {
myleft = (left == NULL) ? NULL : (static_cast<inner_node*>(left))->childid[left->slotuse - 1];
myleftparent = leftparent;
}
else {
myleft = inner->childid[slot - 1];
myleftparent = inner;
}
if (slot == inner->slotuse) {
myright = (right == NULL) ? NULL : (static_cast<inner_node*>(right))->childid[0];
myrightparent = rightparent;
}
else {
myright = inner->childid[slot + 1];
myrightparent = inner;
}
BTREE_PRINT("erase_one_descend into " << inner->childid[slot] << std::endl);
result_t result = erase_one_descend(key,
inner->childid[slot],
myleft, myright,
myleftparent, myrightparent,
inner, slot);
result_t myres = btree_ok;
if (result.has(btree_not_found))
{
return result;
}
if (result.has(btree_update_lastkey))
{
if (parent && parentslot < parent->slotuse)
{
BTREE_PRINT("Fixing lastkeyupdate: key " << result.lastkey << " into parent " << parent << " at parentslot " << parentslot << std::endl);
BTREE_ASSERT(parent->childid[parentslot] == curr);
parent->slotkey[parentslot] = result.lastkey;
}
else
{
BTREE_PRINT("Forwarding lastkeyupdate: key " << result.lastkey << std::endl);
myres |= result_t(btree_update_lastkey, result.lastkey);
}
}
if (result.has(btree_fixmerge))
{
// either the current node or the next is empty and should be removed
if (inner->childid[slot]->slotuse != 0)
slot++;
// this is the child slot invalidated by the merge
BTREE_ASSERT(inner->childid[slot]->slotuse == 0);
inner->weight -= inner->childid[slot]->weight;
free_node(inner->childid[slot]);
for(int i = slot; i < inner->slotuse; i++)
{
inner->slotkey[i - 1] = inner->slotkey[i];
inner->childid[i] = inner->childid[i + 1];
}
inner->slotuse--;
if (inner->level == 1)
{
// fix split key for children leaves
slot--;
leaf_node *child = static_cast<leaf_node*>(inner->childid[slot]);
inner->slotkey[slot] = child->slotkey[ child->slotuse-1 ];
}
}
if (inner->isunderflow() && !(inner == root && inner->slotuse >= 1))
{
// case: the inner node is the root and has just one child. that child becomes the new root
if (leftinner == NULL && rightinner == NULL)
{
BTREE_ASSERT(inner == root);
BTREE_ASSERT(inner->slotuse == 0);
root = inner->childid[0];
inner->slotuse = 0;
free_node(inner);
return btree_ok;
}
// case : if both left and right leaves would underflow in case of
// a shift, then merging is necessary. choose the more local merger
// with our parent
else if ( (leftinner == NULL || leftinner->isfew()) && (rightinner == NULL || rightinner->isfew()) )
{
if (leftparent == parent)
myres |= merge_inner(leftinner, inner, leftparent, parentslot - 1);
else
myres |= merge_inner(inner, rightinner, rightparent, parentslot);
}
// case : the right leaf has extra data, so balance right with current
else if ( (leftinner != NULL && leftinner->isfew()) && (rightinner != NULL && !rightinner->isfew()) )
{
if (rightparent == parent)
shift_left_inner(inner, rightinner, rightparent, parentslot);
else
myres |= merge_inner(leftinner, inner, leftparent, parentslot - 1);
}
// case : the left leaf has extra data, so balance left with current
else if ( (leftinner != NULL && !leftinner->isfew()) && (rightinner != NULL && rightinner->isfew()) )
{
if (leftparent == parent)
shift_right_inner(leftinner, inner, leftparent, parentslot - 1);
else
myres |= merge_inner(inner, rightinner, rightparent, parentslot);
}
// case : both the leaf and right leaves have extra data and our
// parent, choose the leaf with more data
else if (leftparent == rightparent)
{
if (leftinner->slotuse <= rightinner->slotuse)
shift_left_inner(inner, rightinner, rightparent, parentslot);
else
shift_right_inner(leftinner, inner, leftparent, parentslot - 1);
}
else
{
if (leftparent == parent)
shift_right_inner(leftinner, inner, leftparent, parentslot - 1);
else
shift_left_inner(inner, rightinner, rightparent, parentslot);
}
}
return myres;
}
}
/// Merge two leaf nodes. The function moves all key/data pairs from right
/// to left and sets right's slotuse to zero. The right slot is then
/// removed by the calling parent node.
result_t merge_leaves(leaf_node* left, leaf_node* right, inner_node* parent)
{
BTREE_PRINT("Merge leaf nodes " << left << " and " << right << " with common parent " << parent << "." << std::endl);
(void)parent;
BTREE_ASSERT(left->isleafnode() && right->isleafnode());
BTREE_ASSERT(parent->level == 1);
BTREE_ASSERT(left->slotuse + right->slotuse < leafslotmax);
for (unsigned int i = 0; i < right->slotuse; i++)
{
left->slotkey[left->slotuse + i] = right->slotkey[i];
left->slotdata[left->slotuse + i] = right->slotdata[i];
left->weights[left->slotuse + i] = right->weights[i];
}
left->slotuse += right->slotuse;
left->weight += right->weight;
left->nextleaf = right->nextleaf;
if (left->nextleaf)
left->nextleaf->prevleaf = left;
else
tailleaf = left;
right->weight = 0;
right->slotuse = 0;
return btree_fixmerge;
}
/// Merge two inner nodes. The function moves all key/childid pairs from
/// right to left and sets right's slotuse to zero. The right slot is then
/// removed by the calling parent node.
static result_t merge_inner(inner_node* left, inner_node* right, inner_node* parent, unsigned int parentslot)
{
BTREE_PRINT("Merge inner nodes " << left << " and " << right << " with common parent " << parent << "." << std::endl);
BTREE_ASSERT(left->level == right->level);
BTREE_ASSERT(parent->level == left->level + 1);
BTREE_ASSERT(parent->childid[parentslot] == left);
BTREE_ASSERT(left->slotuse + right->slotuse < innerslotmax);
if (selfverify)
{
// find the left node's slot in the parent's children
unsigned int leftslot = 0;
while(leftslot <= parent->slotuse && parent->childid[leftslot] != left)
++leftslot;
BTREE_ASSERT(leftslot < parent->slotuse);
BTREE_ASSERT(parent->childid[leftslot] == left);
BTREE_ASSERT(parent->childid[leftslot+1] == right);
BTREE_ASSERT(parentslot == leftslot);
}
// retrieve the decision key from parent
left->slotkey[left->slotuse] = parent->slotkey[parentslot];
left->slotuse++;
// copy over keys and children from right
for (unsigned int i = 0; i < right->slotuse; i++)
{
left->slotkey[left->slotuse + i] = right->slotkey[i];
left->childid[left->slotuse + i] = right->childid[i];
}
left->slotuse += right->slotuse;
left->weight += right->weight;
left->childid[left->slotuse] = right->childid[right->slotuse];
right->weight = 0;
right->slotuse = 0;
return btree_fixmerge;
}
/// Balance two leaf nodes. The function moves key/data pairs from right to
/// left so that both nodes are equally filled. The parent node is updated
/// if possible.
static result_t shift_left_leaf(leaf_node *left, leaf_node *right, inner_node *parent, unsigned int parentslot)
{
BTREE_ASSERT(left->isleafnode() && right->isleafnode());
BTREE_ASSERT(parent->level == 1);
BTREE_ASSERT(left->nextleaf == right);
BTREE_ASSERT(left == right->prevleaf);
BTREE_ASSERT(left->slotuse < right->slotuse);
BTREE_ASSERT(parent->childid[parentslot] == left);
unsigned int shiftnum = (right->slotuse - left->slotuse) / 2;
BTREE_PRINT("Shifting (leaf) " << shiftnum << " entries to left " << left << " from right " << right << " with common parent " << parent << "." << std::endl);
BTREE_ASSERT(left->slotuse + shiftnum < leafslotmax);
// copy the first items from the right node to the last slot in the left node.
for(unsigned int i = 0; i < shiftnum; i++)
{
left->slotkey[left->slotuse + i] = right->slotkey[i];
left->slotdata[left->slotuse + i] = right->slotdata[i];
left->weights[left->slotuse + i] = right->weights[i];
left->weight += right->weights[i];
right->weight -= right->weights[i];
}
left->slotuse += shiftnum;
// shift all slots in the right node to the left
right->slotuse -= shiftnum;
for(int i = 0; i < right->slotuse; i++)
{
right->slotkey[i] = right->slotkey[i + shiftnum];
right->slotdata[i] = right->slotdata[i + shiftnum];
right->weights[i] = right->weights[i + shiftnum];
}
// fixup parent
if (parentslot < parent->slotuse) {
parent->slotkey[parentslot] = left->slotkey[left->slotuse - 1];
return btree_ok;
}
else { // the update is further up the tree
return result_t(btree_update_lastkey, left->slotkey[left->slotuse - 1]);
}
}
/// Balance two inner nodes. The function moves key/data pairs from right
/// to left so that both nodes are equally filled. The parent node is
/// updated if possible.
static void shift_left_inner(inner_node *left, inner_node *right, inner_node *parent, unsigned int parentslot)
{
BTREE_ASSERT(left->level == right->level);
BTREE_ASSERT(parent->level == left->level + 1);
BTREE_ASSERT(left->slotuse < right->slotuse);
BTREE_ASSERT(parent->childid[parentslot] == left);
unsigned int shiftnum = (right->slotuse - left->slotuse) / 2;
BTREE_PRINT("Shifting (inner) " << shiftnum << " entries to left " << left << " from right " << right << " with common parent " << parent << "." << std::endl);
BTREE_ASSERT(left->slotuse + shiftnum < innerslotmax);
if (selfverify)
{
// find the left node's slot in the parent's children and compare to parentslot
unsigned int leftslot = 0;
while(leftslot <= parent->slotuse && parent->childid[leftslot] != left)
++leftslot;
BTREE_ASSERT(leftslot < parent->slotuse);
BTREE_ASSERT(parent->childid[leftslot] == left);
BTREE_ASSERT(parent->childid[leftslot+1] == right);
BTREE_ASSERT(leftslot == parentslot);
}
// copy the parent's decision slotkey and childid to the first new key on the left
left->slotkey[left->slotuse] = parent->slotkey[parentslot];
left->slotuse++;
// copy the other items from the right node to the last slots in the left node.
for(unsigned int i = 0; i < shiftnum - 1; i++)
{
left->slotkey[left->slotuse + i] = right->slotkey[i];
left->childid[left->slotuse + i] = right->childid[i];
left->weight += right->childid[i]->weight;
right->weight -= right->childid[i]->weight;
}
left->slotuse += shiftnum - 1;
// fixup parent
parent->slotkey[parentslot] = right->slotkey[shiftnum - 1];
// last pointer in left
left->childid[left->slotuse] = right->childid[shiftnum - 1];
left->weight += right->childid[shiftnum - 1]->weight;
right->weight -= right->childid[shiftnum - 1]->weight;
// shift all slots in the right node
right->slotuse -= shiftnum;
for(int i = 0; i < right->slotuse; i++)
{
right->slotkey[i] = right->slotkey[i + shiftnum];
right->childid[i] = right->childid[i + shiftnum];
}
right->childid[right->slotuse] = right->childid[right->slotuse + shiftnum];
}
/// Balance two leaf nodes. The function moves key/data pairs from left to
/// right so that both nodes are equally filled. The parent node is updated
/// if possible.
static void shift_right_leaf(leaf_node *left, leaf_node *right, inner_node *parent, unsigned int parentslot)
{
BTREE_ASSERT(left->isleafnode() && right->isleafnode());
BTREE_ASSERT(parent->level == 1);
BTREE_ASSERT(left->nextleaf == right);
BTREE_ASSERT(left == right->prevleaf);
BTREE_ASSERT(parent->childid[parentslot] == left);
BTREE_ASSERT(left->slotuse > right->slotuse);
unsigned int shiftnum = (left->slotuse - right->slotuse) / 2;
BTREE_PRINT("Shifting (leaf) " << shiftnum << " entries to right " << right << " from left " << left << " with common parent " << parent << "." << std::endl);
if (selfverify)
{
// find the left node's slot in the parent's children
unsigned int leftslot = 0;
while(leftslot <= parent->slotuse && parent->childid[leftslot] != left)
++leftslot;
BTREE_ASSERT(leftslot < parent->slotuse);
BTREE_ASSERT(parent->childid[leftslot] == left);
BTREE_ASSERT(parent->childid[leftslot+1] == right);
BTREE_ASSERT(leftslot == parentslot);
}
// shift all slots in the right node
BTREE_ASSERT(right->slotuse + shiftnum < leafslotmax);
for(int i = right->slotuse; i >= 0; i--)
{
right->slotkey[i + shiftnum] = right->slotkey[i];
right->slotdata[i + shiftnum] = right->slotdata[i];
right->weights[i + shiftnum] = right->weights[i];
}
right->slotuse += shiftnum;
// copy the last items from the left node to the first slot in the right node.
for(unsigned int i = 0; i < shiftnum; i++)
{
right->slotkey[i] = left->slotkey[left->slotuse - shiftnum + i];
right->slotdata[i] = left->slotdata[left->slotuse - shiftnum + i];
right->weights[i] = left->weights[left->slotuse - shiftnum + i];
right->weight += left->weights[left->slotuse - shiftnum + i];
left->weight -= left->weights[left->slotuse - shiftnum + i];
}
left->slotuse -= shiftnum;
parent->slotkey[parentslot] = left->slotkey[left->slotuse-1];
}
/// Balance two inner nodes. The function moves key/data pairs from left to
/// right so that both nodes are equally filled. The parent node is updated
/// if possible.
static void shift_right_inner(inner_node *left, inner_node *right, inner_node *parent, unsigned int parentslot)
{
BTREE_ASSERT(left->level == right->level);
BTREE_ASSERT(parent->level == left->level + 1);
BTREE_ASSERT(left->slotuse > right->slotuse);
BTREE_ASSERT(parent->childid[parentslot] == left);
unsigned int shiftnum = (left->slotuse - right->slotuse) / 2;
BTREE_PRINT("Shifting (leaf) " << shiftnum << " entries to right " << right << " from left " << left << " with common parent " << parent << "." << std::endl);
if (selfverify)
{
// find the left node's slot in the parent's children
unsigned int leftslot = 0;
while(leftslot <= parent->slotuse && parent->childid[leftslot] != left)
++leftslot;
BTREE_ASSERT(leftslot < parent->slotuse);
BTREE_ASSERT(parent->childid[leftslot] == left);
BTREE_ASSERT(parent->childid[leftslot+1] == right);
BTREE_ASSERT(leftslot == parentslot);
}
// shift all slots in the right node
BTREE_ASSERT(right->slotuse + shiftnum < innerslotmax);
right->childid[right->slotuse + shiftnum] = right->childid[right->slotuse];
for(int i = right->slotuse-1; i >= 0; i--)
{
right->slotkey[i + shiftnum] = right->slotkey[i];
right->childid[i + shiftnum] = right->childid[i];
}
right->slotuse += shiftnum;
// copy the parent's decision slotkey and childid to the last new key on the right
right->slotkey[shiftnum - 1] = parent->slotkey[parentslot];
right->childid[shiftnum - 1] = left->childid[left->slotuse];
right->weight += left->childid[left->slotuse]->weight;
left->weight -= left->childid[left->slotuse]->weight;
// copy the remaining last items from the left node to the first slot in the right node.
for(unsigned int i = 0; i < shiftnum - 1; i++)
{
right->slotkey[i] = left->slotkey[left->slotuse - shiftnum + i + 1];
right->childid[i] = left->childid[left->slotuse - shiftnum + i + 1];
right->weight += left->childid[left->slotuse - shiftnum + i + 1]->weight;
left->weight -= left->childid[left->slotuse - shiftnum + i + 1]->weight;
}
// copy the first to-be-removed key from the left node to the parent's decision slot
parent->slotkey[parentslot] = left->slotkey[left->slotuse - shiftnum];
left->slotuse -= shiftnum;
}
#ifdef BTREE_DEBUG
public:
// *** Debug Printing
/// Print out the B+ tree structure with keys onto the given ostream. This
/// function requires that the header is compiled with BTREE_DEBUG and that
/// key_type is printable via std::ostream.
void print(std::ostream &os) const
{
if (root) {
print_node(os, root, 0, true);
}
}
/// Print out only the leaves via the double linked list.
void print_leaves(std::ostream &os) const
{
os << "leaves:" << std::endl;
const leaf_node *n = headleaf;
while(n)
{
os << " " << n << std::endl;
n = n->nextleaf;
}
}
private:
/// Recursively descend down the tree and print out nodes.
static void print_node(std::ostream &os, const node* node, unsigned int depth=0, bool recursive=false)
{
for(unsigned int i = 0; i < depth; i++) os << " ";
os << "node " << node << " level " << node->level << " weight " << node->weight << " slotuse " << node->slotuse << std::endl;
if (node->isleafnode())
{
const leaf_node *leafnode = static_cast<const leaf_node*>(node);
for(unsigned int i = 0; i < depth; i++) os << " ";
os << " leaf prev " << leafnode->prevleaf << " next " << leafnode->nextleaf << std::endl;
for(unsigned int i = 0; i < depth; i++) os << " ";
for (unsigned int slot = 0; slot < leafnode->slotuse; ++slot)
{
os << leafnode->slotkey[slot] << " "; // << "(data: " << leafnode->slotdata[slot] << ") ";
}
os << std::endl;
}
else
{
const inner_node *innernode = static_cast<const inner_node*>(node);
for(unsigned int i = 0; i < depth; i++) os << " ";
for (unsigned short slot = 0; slot < innernode->slotuse; ++slot)
{
os << "(" << innernode->childid[slot] << ") " << innernode->slotkey[slot] << " ";
}
os << "(" << innernode->childid[innernode->slotuse] << ")" << std::endl;
if (recursive)
{
for (unsigned short slot = 0; slot < innernode->slotuse + 1; ++slot)
{
print_node(os, innernode->childid[slot], depth + 1, recursive);
}
}
}
}
#endif
public:
// *** Verification of B+ Tree Invariants
/// Run a thorough verification of all B+ tree invariants. The program
/// aborts via assert() if something is wrong.
void verify() const
{
key_type minkey, maxkey;
tree_stats vstats;
if (root)
{
verify_node(root, &minkey, &maxkey, vstats);
assert( vstats.itemcount == stats.itemcount );
assert( vstats.leaves == stats.leaves );
assert( vstats.innernodes == stats.innernodes );
}
verify_leaflinks();
}
private:
/// Recursively descend down the tree and verify each node
void verify_node(const node* n, key_type* minkey, key_type* maxkey, tree_stats &vstats) const
{
BTREE_PRINT("verifynode " << n << std::endl);
if (n->isleafnode())
{
const leaf_node *leaf = static_cast<const leaf_node*>(n);
assert(leaf == root || !leaf->isunderflow());
for(unsigned short slot = 0; slot < leaf->slotuse - 1; ++slot)
{
assert(key_lessequal(leaf->slotkey[slot], leaf->slotkey[slot + 1]));
}
*minkey = leaf->slotkey[0];
*maxkey = leaf->slotkey[leaf->slotuse - 1];
vstats.leaves++;
vstats.itemcount += leaf->slotuse;
}
else // !n->isleafnode()
{
const inner_node *inner = static_cast<const inner_node*>(n);
vstats.innernodes++;
assert(inner == root || !inner->isunderflow());
for(unsigned short slot = 0; slot < inner->slotuse - 1; ++slot)
{
assert(key_lessequal(inner->slotkey[slot], inner->slotkey[slot + 1]));
}
for(unsigned short slot = 0; slot <= inner->slotuse; ++slot)
{
const node *subnode = inner->childid[slot];
key_type subminkey = key_type();
key_type submaxkey = key_type();
assert(subnode->level + 1 == inner->level);
verify_node(subnode, &subminkey, &submaxkey, vstats);
BTREE_PRINT("verify subnode " << subnode << ": " << subminkey << " - " << submaxkey << std::endl);
if (slot == 0)
*minkey = subminkey;
else
assert(key_greaterequal(subminkey, inner->slotkey[slot-1]));
if (slot == inner->slotuse)
*maxkey = submaxkey;
else
assert(key_equal(inner->slotkey[slot], submaxkey));
if (inner->level == 1 && slot < inner->slotuse)
{
// children are leaves and must be linked together in the
// correct order
const leaf_node *leafa = static_cast<const leaf_node*>(inner->childid[slot]);
const leaf_node *leafb = static_cast<const leaf_node*>(inner->childid[slot + 1]);
assert(leafa->nextleaf == leafb);
assert(leafa == leafb->prevleaf);
(void)leafa; (void)leafb;
}
if (inner->level == 2 && slot < inner->slotuse)
{
// verify leaf links between the adjacent inner nodes
const inner_node *parenta = static_cast<const inner_node*>(inner->childid[slot]);
const inner_node *parentb = static_cast<const inner_node*>(inner->childid[slot+1]);
const leaf_node *leafa = static_cast<const leaf_node*>(parenta->childid[parenta->slotuse]);
const leaf_node *leafb = static_cast<const leaf_node*>(parentb->childid[0]);
assert(leafa->nextleaf == leafb);
assert(leafa == leafb->prevleaf);
(void)leafa; (void)leafb;
}
}
}
}
/// Verify the double linked list of leaves.
void verify_leaflinks() const
{
const leaf_node *n = headleaf;
assert(n->level == 0);
assert(!n || n->prevleaf == NULL);
unsigned int testcount = 0;
while(n)
{
assert(n->level == 0);
for(unsigned short slot = 0; slot < n->slotuse - 1; ++slot)
{
assert(key_lessequal(n->slotkey[slot], n->slotkey[slot + 1]));
}
testcount += n->slotuse;
if (n->nextleaf)
{
assert(key_lessequal(n->slotkey[n->slotuse-1], n->nextleaf->slotkey[0]));
assert(n == n->nextleaf->prevleaf);
}
else
{
assert(tailleaf == n);
}
n = n->nextleaf;
}
assert(testcount == size());
}
private:
// *** Dump and Restore of B+ Trees
/// \internal A header for the binary image containing the base properties
/// of the B+ tree. These properties have to match the current template
/// instantiation.
struct dump_header
{
/// "stx-btree", just to stop the restore() function from loading garbage
char signature[12];
/// Currently 0
unsigned short version;
/// sizeof(key_type)
unsigned short key_type_size;
/// sizeof(data_type)
unsigned short data_type_size;
/// Number of slots in the leaves
unsigned short leafslots;
/// Number of slots in the inner nodes
unsigned short innerslots;
/// Allow duplicates
bool allow_duplicates;
/// The item count of the tree
size_type itemcount;
/// Fill the struct with the current B+ tree's properties, itemcount is
/// not filled.
inline void fill()
{
// don't want to include string.h just for this signature
*reinterpret_cast<unsigned int*>(signature+0) = 0x2d787473;
*reinterpret_cast<unsigned int*>(signature+4) = 0x65727462;
*reinterpret_cast<unsigned int*>(signature+8) = 0x00000065;
version = 0;
key_type_size = sizeof(typename btree_self::key_type);
data_type_size = sizeof(typename btree_self::data_type);
leafslots = btree_self::leafslotmax;
innerslots = btree_self::innerslotmax;
allow_duplicates = btree_self::allow_duplicates;
}
/// Returns true if the headers have the same vital properties
inline bool same(const struct dump_header &o) const
{
return (*reinterpret_cast<const unsigned int*>(signature+0) ==
*reinterpret_cast<const unsigned int*>(o.signature+0))
&& (*reinterpret_cast<const unsigned int*>(signature+4) ==
*reinterpret_cast<const unsigned int*>(o.signature+4))
&& (*reinterpret_cast<const unsigned int*>(signature+8) ==
*reinterpret_cast<const unsigned int*>(o.signature+8))
&& (version == o.version)
&& (key_type_size == o.key_type_size)
&& (data_type_size == o.data_type_size)
&& (leafslots == o.leafslots)
&& (innerslots == o.innerslots)
&& (allow_duplicates == o.allow_duplicates);
}
};
public:
/// Dump the contents of the B+ tree out onto an ostream as a binary
/// image. The image contains memory pointers which will be fixed when the
/// image is restored. For this to work your key_type and data_type must be
/// integral types and contain no pointers or references.
void dump(std::ostream &os) const
{
struct dump_header header;
header.fill();
header.itemcount = size();
os.write(reinterpret_cast<char*>(&header), sizeof(header));
if (root)
dump_node(os, root);
}
/// Restore a binary image of a dumped B+ tree from an istream. The B+ tree
/// pointers are fixed using the dump order. For dump and restore to work
/// your key_type and data_type must be integral types and contain no
/// pointers or references. Returns true if the restore was successful.
bool restore(std::istream &is)
{
struct dump_header fileheader;
is.read(reinterpret_cast<char*>(&fileheader), sizeof(fileheader));
if (!is.good()) return false;
struct dump_header myheader;
myheader.fill();
myheader.itemcount = fileheader.itemcount;
if (!myheader.same(fileheader))
{
BTREE_PRINT("btree::restore: file header does not match instantiation signature." << std::endl);
return false;
}
clear();
if (fileheader.itemcount > 0)
{
root = restore_node(is);
if (root == NULL) return false;
stats.itemcount = fileheader.itemcount;
}
#ifdef BTREE_DEBUG
if (debug) print(std::cout);
#endif
if (selfverify) verify();
return true;
}
private:
/// Recursively descend down the tree and dump each node in a precise order
void dump_node(std::ostream &os, const node* n) const
{
BTREE_PRINT("dump_node " << n << std::endl);
if (n->isleafnode())
{
const leaf_node *leaf = static_cast<const leaf_node*>(n);
os.write(reinterpret_cast<const char*>(leaf), sizeof(*leaf));
}
else // !n->isleafnode()
{
const inner_node *inner = static_cast<const inner_node*>(n);
os.write(reinterpret_cast<const char*>(inner), sizeof(*inner));
for(unsigned short slot = 0; slot <= inner->slotuse; ++slot)
{
const node *subnode = inner->childid[slot];
dump_node(os, subnode);
}
}
}
/// Read the dump image and construct a tree from the node order in the
/// serialization.
node* restore_node(std::istream &is)
{
union {
node top;
leaf_node leaf;
inner_node inner;
} nu;
// first read only the top of the node
is.read(reinterpret_cast<char*>(&nu.top), sizeof(nu.top));
if (!is.good()) return NULL;
if (nu.top.isleafnode())
{
// read remaining data of leaf node
is.read(reinterpret_cast<char*>(&nu.leaf) + sizeof(nu.top), sizeof(nu.leaf) - sizeof(nu.top));
if (!is.good()) return NULL;
leaf_node *newleaf = allocate_leaf();
// copy over all data, the leaf nodes contain only their double linked list pointers
*newleaf = nu.leaf;
// reconstruct the linked list from the order in the file
if (headleaf == NULL) {
BTREE_ASSERT(newleaf->prevleaf == NULL);
headleaf = tailleaf = newleaf;
}
else {
newleaf->prevleaf = tailleaf;
tailleaf->nextleaf = newleaf;
tailleaf = newleaf;
}
return newleaf;
}
else
{
// read remaining data of inner node
is.read(reinterpret_cast<char*>(&nu.inner) + sizeof(nu.top), sizeof(nu.inner) - sizeof(nu.top));
if (!is.good()) return NULL;
inner_node *newinner = allocate_inner(0);
// copy over all data, the inner nodes contain only pointers to their children
*newinner = nu.inner;
for(unsigned short slot = 0; slot <= newinner->slotuse; ++slot)
{
newinner->childid[slot] = restore_node(is);
}
return newinner;
}
}
};
} // namespace stx
#endif // _STX_RA_BTREE_H_