Randomized binary search tree with rank support. More...

#include <tpl_rand_tree.H>

Inheritance diagram for Aleph::Gen_Rand_Tree< NodeType, Key, Compare >:

Classes
struct	Iterator
	Iterator on nodes of the tree. More...

Public Types
using	Node = NodeType< Key >

Public Member Functions
	Gen_Rand_Tree (const Gen_Rand_Tree &)=delete

Gen_Rand_Tree &	operator= (const Gen_Rand_Tree &)=delete

Compare &	key_comp () noexcept
	return the comparison criteria

const Compare &	key_comp () const noexcept

Compare &	get_compare () noexcept

const Compare &	get_compare () const noexcept

gsl_rng *	gsl_rng_object () noexcept
	Get a pointer to gsl random number generator.

void	set_seed (const unsigned long seed) noexcept
	Set the random number generator seed.

	Gen_Rand_Tree (const unsigned int seed, const Compare &__cmp=Compare())
	Initialize a random tree with random `seed` and comparison criteria `__cmp`

	Gen_Rand_Tree (const Compare &cmp=Compare()) noexcept
	Initialize a random tree with random seed from system time and comparison criteria `cmp`

void	swap (Gen_Rand_Tree &tree) noexcept
	Swap in constant time all the nodes of `this` with `tree`

	Gen_Rand_Tree (Gen_Rand_Tree &&other) noexcept
	Move constructor - transfers ownership of tree and RNG.

Gen_Rand_Tree &	operator= (Gen_Rand_Tree &&other) noexcept
	Move assignment - transfers ownership of tree and RNG.

virtual	~Gen_Rand_Tree () noexcept

Node *	insert (Node *p) noexcept
	Insert a node in the tree.

Node *	insert_dup (Node *p) noexcept
	Insert a node in the tree.

Node *	remove (const Key &key) noexcept
	Remove a key from the tree.

Node *	search (const Key &key) const noexcept
	Search a key.

Node *	search_or_insert (Node *p) noexcept
	Search or insert a key.

bool	verify () const
	Return `true` if this is a consistent randomized tree.

Node *&	getRoot () noexcept
	Return the tree's root.

Node *	select (const size_t i) const
	Return the i-th node in inorder sense.

size_t	size () const noexcept
	Return the number of nodes that have the tree.

bool	is_empty () const noexcept
	Return true if the tree is empty.

std::pair< long, Node * >	position (const Key &key) const noexcept
	Compute the inorder position of a key.

std::pair< long, Node * >	find_position (const Key &key) const noexcept
	Find the inorder position of a key in the tree.

Node *	remove_pos (const size_t i)
	Remove the key at inorder position `i`

bool	split_key (const Key &key, Gen_Rand_Tree &t1, Gen_Rand_Tree &t2) noexcept
	Split the tree according to a key.

void	split_key_dup (const Key &key, Gen_Rand_Tree &t1, Gen_Rand_Tree &t2) noexcept
	Split the tree according to a key that could be in the tree.

void	split_pos (size_t pos, Gen_Rand_Tree &t1, Gen_Rand_Tree &t2) noexcept
	Split a extended binary tree according to a position.

void	join (Gen_Rand_Tree &t, Gen_Rand_Tree &dup) noexcept
	Join `this` with `t` filtering the duplicated keys.

void	join_dup (Gen_Rand_Tree &t) noexcept
	Join `this` with `t` independently of the presence of duplicated keys.

void	join_exclusive (Gen_Rand_Tree &t) noexcept
	Join exclusive of `this` with `t`

Private Member Functions
Node *	random_insert (Node root, Node p) noexcept

Node *	random_insert_dup (Node root, Node p) noexcept

Node *	random_search_or_insert (Node &root, Node p) noexcept

void	init (const unsigned long seed)

Node *	random_join_exclusive (Node tl, Node tr) noexcept

Node *	random_remove (Node *&root, const Key &key) noexcept

Node *	remove_pos (Node *&root, const size_t pos) noexcept

Node *	random_join (Node t1, Node t2, Node *&dup)

Node *	random_join (Node t1, Node t2)

Private Attributes
Node *	tree_root
	The type of node.

gsl_rng *	r

Compare	cmp

Detailed Description

template<template< typename > class NodeType, typename Key, class Compare>
requires StrictWeakOrder<Compare, Key>
class Aleph::Gen_Rand_Tree< NodeType, Key, Compare >

Randomized binary search tree with rank support.

This class implements a randomized binary search tree where random decisions during insertion and deletion ensure that the tree has the same expected properties as if it were built from a random permutation of keys, regardless of actual insertion order.

Key Insight:: At each insertion, a random "raffle" determines whether the new node becomes the root (and existing nodes are split around it) or is inserted recursively into a subtree. This ensures that every node has an equal probability of being at any position, producing expected O(log n) height.

Ranked Operations:

Unlike basic BSTs, randomized trees maintain subtree sizes (COUNT), enabling O(log n) access by rank (inorder position):

select(i): Get the i-th smallest element
position(key): Get the rank of a key
remove_pos(i): Remove the i-th element

This allows treating the tree like a sorted dynamic array with O(log n) indexed access, insertion, and deletion.

Split and Join:: Randomized trees excel at split/join operations, which take O(log(max(n,m))) time. This is dramatically better than other balanced trees that require O(n log m) for joining two trees of sizes n and m.

Template Parameters

NodeType	Node template (RandNode or RandNodeVtl).
Key	The type of keys stored in the tree.
Compare	Comparison functor for ordering keys.

Complexity:

Search: O(log n) expected
Insert: O(log n) expected
Delete: O(log n) expected
Select (by rank): O(log n) expected
Position (get rank): O(log n) expected
Split: O(log n) expected
Join: O(log(max(n,m))) expected - much better than other trees
Space: O(n) + O(1) per node for COUNT

Random Number Generator:: Uses GSL (GNU Scientific Library) Mersenne Twister (mt19937) by default. Seed can be set via set_seed() for reproducible behavior.

Example:: Rand_Tree<int> tree;

// Insert nodes

tree.insert(new Rand_Tree<int>::Node(42));

tree.insert(new Rand_Tree<int>::Node(17));

tree.insert(new Rand_Tree<int>::Node(99));

tree.insert(new Rand_Tree<int>::Node(8));

// Ranked access (treat as sorted array)

auto smallest = tree.select(0); // Get 0th element (8)

auto median = tree.select(tree.size() / 2); // Get median

// Find position/rank of a key

size_t pos = tree.position(42); // Returns 2 (0-indexed)

// Remove by position

auto removed = tree.remove_pos(1); // Remove 2nd smallest

delete removed;

// Efficient split at key

Rand_Tree<int> left, right;

tree.split_key(50, left, right); // All <= 50 go to left, > 50 to right

// Efficient join (O(log(max(n,m))))

tree.join(left, right);

Aleph::Gen_Rand_Tree::Node
NodeType< Key > Node
Definition tpl_rand_tree.H:156

Aleph::Gen_Rand_Tree::split_key
bool split_key(const Key &key, Gen_Rand_Tree &t1, Gen_Rand_Tree &t2) noexcept
Split the tree according to a key.
Definition tpl_rand_tree.H:624

Aleph::Gen_Rand_Tree::insert
Node * insert(Node *p) noexcept
Insert a node in the tree.
Definition tpl_rand_tree.H:374

Aleph::Gen_Rand_Tree::size
size_t size() const noexcept
Return the number of nodes that have the tree.
Definition tpl_rand_tree.H:525

Aleph::Gen_Rand_Tree::select
Node * select(const size_t i) const
Return the i-th node in inorder sense.
Definition tpl_rand_tree.H:519

Aleph::Gen_Rand_Tree::join
void join(Gen_Rand_Tree &t, Gen_Rand_Tree &dup) noexcept
Join this with t filtering the duplicated keys.
Definition tpl_rand_tree.H:760

Aleph::Gen_Rand_Tree::remove_pos
Node * remove_pos(Node *&root, const size_t pos) noexcept
Definition tpl_rand_tree.H:585

Aleph::Gen_Rand_Tree::position
std::pair< long, Node * > position(const Key &key) const noexcept
Compute the inorder position of a key.
Definition tpl_rand_tree.H:539

Aleph::median
const T * median(const T &a, const T &b, const T &c, const Compare &cmp=Compare())
Return a pointer to the median value among three elements.
Definition ahUtils.H:84

Aleph::divide_and_conquer_partition_dp
Divide_Conquer_DP_Result< Cost > divide_and_conquer_partition_dp(const size_t groups, const size_t n, Transition_Cost_Fn transition_cost, const Cost inf=dp_optimization_detail::default_inf< Cost >())
Optimize partition DP using divide-and-conquer optimization.
Definition DP_Optimizations.H:133

Aleph::Rand_Tree
Randomized binary search tree.
Definition tpl_rand_tree.H:846

Note: This is a low-level implementation managing raw nodes. For automatic memory management, use DynSetRandTree.; All operations maintain COUNT values for ranked operations.; Best choice when frequent split/join operations are needed.

See also: Rand_Tree Convenient typedef for Rand_Tree<Key, Compare>.; Treap Alternative randomized tree (often faster by constant factor).; TreapRk Treap with rank support.; DynSetRandTree High-level wrapper with automatic memory management.

Definition at line 153 of file tpl_rand_tree.H.

Member Typedef Documentation

◆ Node

template<template< typename > class NodeType, typename Key , class Compare >

using Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::Node = NodeType<Key>

Definition at line 156 of file tpl_rand_tree.H.

Constructor & Destructor Documentation

◆ Gen_Rand_Tree() [1/4]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::Gen_Rand_Tree ( const Gen_Rand_Tree< NodeType, Key, Compare > & )

delete

◆ Gen_Rand_Tree() [2/4]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::Gen_Rand_Tree	(	const unsigned int	seed,
		const Compare &	__cmp = `Compare()`
	)

inline

Initialize a random tree with random seed and comparison criteria __cmp

Definition at line 309 of file tpl_rand_tree.H.

References Aleph::init, and seed.

◆ Gen_Rand_Tree() [3/4]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::Gen_Rand_Tree ( const Compare & cmp = Compare() )

inlinenoexcept

Initialize a random tree with random seed from system time and comparison criteria cmp

Definition at line 317 of file tpl_rand_tree.H.

◆ Gen_Rand_Tree() [4/4]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::Gen_Rand_Tree ( Gen_Rand_Tree< NodeType, Key, Compare > && other )

inlinenoexcept

Move constructor - transfers ownership of tree and RNG.

Definition at line 331 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp().

◆ ~Gen_Rand_Tree()

template<template< typename > class NodeType, typename Key , class Compare >

virtual Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::~Gen_Rand_Tree ( )

inlinevirtualnoexcept

Definition at line 360 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r.

Member Function Documentation

◆ find_position()

template<template< typename > class NodeType, typename Key , class Compare >

std::pair< long, Node * > Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::find_position ( const Key & key ) const

inlinenoexcept

Find the inorder position of a key in the tree.

find_position(key) determines the inorder position that has or had key in the tree. Themethod return a tuple with a position and a node pointer.

If key is found then its inorder position is returned along with a pointer to the node containing it.

Otherwise, the tuple returns the position that would have key if this was in the tree and the parent node that the key should be. At this regard, there are three cases:

if key is lesser than the minimum key of tree, then first is -1 and the node is one with the smallest key.
If key is greater than the maximum key in the tree, then first is the number of keys and the node is one with the maximum key in the tree.
For any other case, first is the inorder position that would have key if this was in the tree and second is the node whose key is immediately greater than key.

Parameters

[in] key to be searched

Returns: a pair with the inorder position and related node

Definition at line 574 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::find_position(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::find_position().

◆ get_compare() [1/2]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::get_compare ( ) const

inlinenoexcept

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 296 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp.

◆ get_compare() [2/2]

template<template< typename > class NodeType, typename Key , class Compare >

Compare & Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::get_compare ( )

inlinenoexcept

Definition at line 293 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::key_comp().

◆ getRoot()

template<template< typename > class NodeType, typename Key , class Compare >

Node *& Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::getRoot ( )

inlinenoexcept

Return the tree's root.

Definition at line 510 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Referenced by main(), and write_rand().

◆ gsl_rng_object()

template<template< typename > class NodeType, typename Key , class Compare >

gsl_rng * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::gsl_rng_object ( )

inlinenoexcept

Get a pointer to gsl random number generator.

Definition at line 299 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r.

◆ init()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::init ( const unsigned long seed )

inlineprivate

Definition at line 276 of file tpl_rand_tree.H.

References ah_bad_alloc_if, Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, and seed.

◆ insert()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::insert ( Node * p )

inlinenoexcept

Insert a node in the tree.

Parameters

[in] p pointer to the node to insert

Returns: if p->get_key() is not in the tree, then the pointer p is returned (it was inserted); otherwise, nullptr is returned

Definition at line 374 of file tpl_rand_tree.H.

References Aleph::and, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert(), RLINK, and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Referenced by main(), and write_rand().

◆ insert_dup()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::insert_dup ( Node * p )

inlinenoexcept

Insert a node in the tree.

This method does not fail. It always inserts.

Parameters

[in] p pointer to the node to insert

Returns: the p pointer

Definition at line 394 of file tpl_rand_tree.H.

References Aleph::and, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert_dup(), RLINK, and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ is_empty()

template<template< typename > class NodeType, typename Key , class Compare >

bool Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::is_empty ( ) const

inlinenoexcept

Return true if the tree is empty.

Definition at line 528 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ join()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join	(	Gen_Rand_Tree< NodeType, Key, Compare > &	t,
		Gen_Rand_Tree< NodeType, Key, Compare > &	dup
	)

inlinenoexcept

Join this with t filtering the duplicated keys.

join(t, dup) produces a random tree result of join of this and t. The resulting tree is stored in this.

Nodes containing duplicated keys are inserted in the randomized tree dup. The nodes could belong to any of two trees

Parameters

[in]	t	randomized tree to join with `this`
[out]	dup	randomized tree where nodes containing duplicated keys are inserted

Definition at line 760 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ join_dup()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join_dup ( Gen_Rand_Tree< NodeType, Key, Compare > & t )

inlinenoexcept

Join this with t independently of the presence of duplicated keys.

join(t) produces a random tree result of join of this and t. The resulting tree is stored in this.

Parameters

[in] t randomized tree to join with this keys are inserted

Definition at line 774 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ join_exclusive()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join_exclusive ( Gen_Rand_Tree< NodeType, Key, Compare > & t )

inlinenoexcept

Join exclusive of this with t

Exclusive means that all the keys of this are lesser than all the keys of t. This knowledge allows a more efficient way for joining that when the keys ranks are overlapped. However, use very carefully because the algorithm does not perform any check and the result would be incorrect.

Parameters

[in] t randomized tree to exclusively join with this keys are inserted

Definition at line 791 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ key_comp() [1/2]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::key_comp ( ) const

inlinenoexcept

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 290 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp.

◆ key_comp() [2/2]

template<template< typename > class NodeType, typename Key , class Compare >

Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::key_comp ( )

inlinenoexcept

return the comparison criteria

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 287 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp.

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::get_compare().

◆ operator=() [1/2]

template<template< typename > class NodeType, typename Key , class Compare >

Gen_Rand_Tree & Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::operator= ( const Gen_Rand_Tree< NodeType, Key, Compare > & )

delete

◆ operator=() [2/2]

template<template< typename > class NodeType, typename Key , class Compare >

Gen_Rand_Tree & Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::operator= ( Gen_Rand_Tree< NodeType, Key, Compare > && other )

inlinenoexcept

Move assignment - transfers ownership of tree and RNG.

Definition at line 339 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::destroyRec(), Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ random_insert()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert	(	Node *	root,
		Node *	p
	)

inlineprivatenoexcept

Definition at line 163 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::BinTreeXt_Operation< Node, Cmp >::insert_root(), KEY, LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert(), RLINK, and root().

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::insert(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert().

◆ random_insert_dup()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert_dup	(	Node *	root,
		Node *	p
	)

inlineprivatenoexcept

Definition at line 203 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::BinTreeXt_Operation< Node, Cmp >::insert_dup_root(), KEY, LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert_dup(), RLINK, and root().

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::insert_dup(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert_dup(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join().

◆ random_join() [1/2]

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join	(	Node *	t1,
		Node *	t2
	)

inlineprivate

Definition at line 714 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::insert_dup_root_xt(), l, LLINK, m, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), and RLINK.

◆ random_join() [2/2]

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join	(	Node *	t1,
		Node *	t2,
		Node *&	dup
	)

inlineprivate

Definition at line 663 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::insert_root_xt(), KEY, l, LLINK, m, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_insert_dup(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove(), and RLINK.

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join_dup(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join().

◆ random_join_exclusive()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive	(	Node *	tl,
		Node *	tr
	)

inlineprivatenoexcept

Definition at line 404 of file tpl_rand_tree.H.

References Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), LLINK, m, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive(), and RLINK.

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::join_exclusive(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos().

◆ random_remove()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove	(	Node *&	root,
		const Key &	key
	)

inlineprivatenoexcept

Definition at line 425 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), KEY, LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove(), RLINK, and root().

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove().

◆ random_search_or_insert()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_search_or_insert	(	Node *&	root,
		Node *	p
	)

inlineprivatenoexcept

Definition at line 228 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::insert_root(), KEY, LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_search_or_insert(), RLINK, and root().

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_search_or_insert(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::search_or_insert().

◆ remove()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove ( const Key & key )

inlinenoexcept

Remove a key from the tree.

Parameters

[in] key to remove

Returns: a valid pointer to the removed node if key was found in the tree, nullptr otherwise

Definition at line 464 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_remove(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ remove_pos() [1/2]

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos ( const size_t i )

inline

Remove the key at inorder position i

Parameters

[in] i inorder position to be removed

Returns: a valid pointer to the removed node

Exceptions

out_of_range if i is greater or equal than the number of nodes of tree

Definition at line 609 of file tpl_rand_tree.H.

References ah_out_of_range_error_if, Aleph::COUNT(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ remove_pos() [2/2]

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos	(	Node *&	root,
		const size_t	pos
	)

inlineprivatenoexcept

Definition at line 585 of file tpl_rand_tree.H.

References Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), LLINK, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_join_exclusive(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos(), RLINK, and root().

Referenced by Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::remove_pos().

◆ search()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::search ( const Key & key ) const

inlinenoexcept

Search a key.

Parameters

[in] key to be searched

Returns: a pointer to the containing key if this was found; otherwise nullptr

Definition at line 477 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::divide_and_conquer_partition_dp(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Referenced by main(), and write_rand().

◆ search_or_insert()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::search_or_insert ( Node * p )

inlinenoexcept

Search or insert a key.

search_or_insert(p) searches in the tree the key KEY(p). If this key is found, then a pointer to the node containing it is returned. Otherwise, p is inserted.

Parameters

[in] p node containing a key to be searched and eventually inserted

Returns: if the key contained in p is found, then a pointer to the containing key in the tree is returned. Otherwise, p is inserted and returned

Definition at line 495 of file tpl_rand_tree.H.

References Aleph::COUNT(), Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::random_search_or_insert(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ select()

template<template< typename > class NodeType, typename Key , class Compare >

Node * Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::select ( const size_t i ) const

inline

Return the i-th node in inorder sense.

Parameters

[in] i inorder position to be located

Returns: a valid pointer to the i-th node inorder sense

Exceptions

out_of_range if i is greater or equal that the number of nodes

Definition at line 519 of file tpl_rand_tree.H.

References Aleph::select(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ set_seed()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::set_seed ( const unsigned long seed )

inlinenoexcept

Set the random number generator seed.

Definition at line 302 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, and seed.

◆ size()

template<template< typename > class NodeType, typename Key , class Compare >

size_t Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::size ( ) const

inlinenoexcept

Return the number of nodes that have the tree.

Definition at line 525 of file tpl_rand_tree.H.

References Aleph::COUNT(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Referenced by write_rand().

◆ split_key()

template<template< typename > class NodeType, typename Key , class Compare >

bool Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::split_key	(	const Key &	key,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t1,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t2
	)

inlinenoexcept

Split the tree according to a key.

Parameters

[in]	key	for splitting
[out]	t1	tree with keys lesser than `key`
[out]	t2	tree with keys greater than `key`

Returns: true if tree was split; that is if key is not in the tree. Otherwise, if key is in the tree, false is returned

Definition at line 624 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::split_key_rec_xt(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ split_key_dup()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::split_key_dup	(	const Key &	key,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t1,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t2
	)

inlinenoexcept

Split the tree according to a key that could be in the tree.

split_dup(key, t1, t2) splits the tree according to key in two trees t1 which contains the key lesser than key and t2 which contains the keys greater or equal than key.

Parameters

[in]	key	for splitting
[out]	t1	resulting tree with the keys lesser than `key`
[out]	t2	resulting tree with the keys greater or equal than `key`

Definition at line 640 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::split_key_dup_rec_xt(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ split_pos()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::split_pos	(	size_t	pos,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t1,
		Gen_Rand_Tree< NodeType, Key, Compare > &	t2
	)

inlinenoexcept

Split a extended binary tree according to a position.

split_pos(pos, ts, tg) splits the tree two trees t1 and t2 according to a position pos. t1 contains the keys from 0 to pos - 1 inorder sense and tg the keys from pos to n -

After completion this becames empty.

Parameters

[in]	pos	position for splitting
[out]	t1	tree where the rank of keys \([0, i)\) will be put
[out]	t2	tree where the rank of keys \([i, n]\) will be put

Definition at line 657 of file tpl_rand_tree.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::split_pos_rec(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ swap()

template<template< typename > class NodeType, typename Key , class Compare >

void Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::swap ( Gen_Rand_Tree< NodeType, Key, Compare > & tree )

inlinenoexcept

Swap in constant time all the nodes of this with tree

Definition at line 323 of file tpl_rand_tree.H.

References Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp, Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r, and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

◆ verify()

template<template< typename > class NodeType, typename Key , class Compare >

bool Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::verify ( ) const

inline

Return true if this is a consistent randomized tree.

Definition at line 504 of file tpl_rand_tree.H.

References Aleph::check_rank_tree(), and Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root.

Member Data Documentation

◆ cmp

template<template< typename > class NodeType, typename Key , class Compare >

Compare Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::cmp

private

Definition at line 161 of file tpl_rand_tree.H.

◆ r

template<template< typename > class NodeType, typename Key , class Compare >

gsl_rng* Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::r

private

Definition at line 160 of file tpl_rand_tree.H.

◆ tree_root

template<template< typename > class NodeType, typename Key , class Compare >

Node* Aleph::Gen_Rand_Tree< NodeType, Key, Compare >::tree_root

private

The type of node.

Definition at line 159 of file tpl_rand_tree.H.

The documentation for this class was generated from the following file:

tpl_rand_tree.H

Classes

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Node

Constructor & Destructor Documentation

◆ Gen_Rand_Tree() [1/4]

◆ Gen_Rand_Tree() [2/4]

◆ Gen_Rand_Tree() [3/4]

◆ Gen_Rand_Tree() [4/4]

◆ ~Gen_Rand_Tree()

Member Function Documentation

◆ find_position()

◆ get_compare() [1/2]

◆ get_compare() [2/2]

◆ getRoot()

◆ gsl_rng_object()

◆ init()

◆ insert()

◆ insert_dup()

◆ is_empty()

◆ join()

◆ join_dup()

◆ join_exclusive()

◆ key_comp() [1/2]

◆ key_comp() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ random_insert()

◆ random_insert_dup()

◆ random_join() [1/2]

◆ random_join() [2/2]

◆ random_join_exclusive()

◆ random_remove()

◆ random_search_or_insert()

◆ remove()

◆ remove_pos() [1/2]

◆ remove_pos() [2/2]

◆ search()

◆ search_or_insert()

◆ select()

◆ set_seed()

◆ size()

◆ split_key()

◆ split_key_dup()

◆ split_pos()

◆ swap()

◆ verify()

Member Data Documentation

◆ cmp

◆ r

◆ tree_root