DGtal: DGtal::LightSternBrocot< TInteger, TQuotient, TMap

Aim: The Stern-Brocot tree is the tree of irreducible fractions. This class allows to construct it progressively and to navigate within fractions in O(1) time for most operations. It is well known that the structure of this tree is a coding of the continued fraction representation of fractions. More...

#include <DGtal/arithmetic/LightSternBrocot.h>

Data Structures
class	Fraction
	This fraction is a model of CPositiveIrreducibleFraction. More...

struct	Node

Public Types
typedef TInteger	Integer

typedef TQuotient	Quotient

typedef TMap	Map

typedef LightSternBrocot< TInteger, TQuotient, TMap >	Self

typedef TMap::template Rebinder< Quotient, Node * >::Type	MapQuotientToNode

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< Integer >))

	~LightSternBrocot ()

bool	isValid () const

Static Public Member Functions
static LightSternBrocot &	instance ()

static Fraction	zeroOverOne ()

static Fraction	oneOverZero ()

static Fraction	fraction (Integer p, Integer q, Fraction ancestor=zeroOverOne())

static void	display (std::ostream &out, const Fraction &f)

Data Fields
Quotient	nbFractions
	The total number of fractions in the current tree. More...

Private Member Functions
	LightSternBrocot ()

	LightSternBrocot (const LightSternBrocot &other)

LightSternBrocot &	operator= (const LightSternBrocot &other)

Private Attributes
Node *	myZeroOverOne

Node *	myOneOverZero

Node *	myOneOverOne

Static Private Attributes
static LightSternBrocot *	singleton
	Singleton class. More...

Detailed Description

template<typename TInteger, typename TQuotient, typename TMap = StdMapRebinder>
class DGtal::LightSternBrocot< TInteger, TQuotient, TMap >

Description of template class 'LightSternBrocot'

There are two main differences with the class SternBrocot. The first one is that inverses are not stored. With this optimization, there are twice less nodes and each node is lighter. The second one lies in the access to the children of a node. Here, a map type M is provided so that a node [u_0; u_1, ..., u_n] can access its child node [u_0; u_1, ..., u_n, k] in the time of the operation M::operator[].

In this representation, the fraction 1/1 has depth 1, like 1/2, 1/3, etc. Furthermore, each fraction has an ancestor, which is the reduced partial of order 1 of the fraction. Be careful the ancestor of an ancestor is not the reduced of order 2. Each node [u_0; u_1, ..., u_n] has two sets of children: the nodes [u_0; u_1, ..., u_n, k], for k >= 2, and the nodes [u_0; u_1, ..., u_n - 1, 1, k], for k >= 2. A disadvantage of this representation is that to obtain the father of something like [...,u_k, 1, ..., 1, u_n ], one has to go up the tree till u_k, to go back down on the other side.

In practice, although this class has supposedly a better complexity than SternBrocot, it is 1% slower for integers smaller than 10^9 and 5% slower for integers smaller than 10^4. Note however that it takes like 6 times less memory (and asymptotically less when the number of computations tends toward infinity).

This class is not to be instantiated, since it is useless to duplicate it. Use static method LightSternBrocot::fraction to obtain your fractions.

Template Parameters

TInteger	the integral type chosen for the fractions.
TQuotient	the integral type chosen for the quotients/coefficients or depth (may be "smaller" than TInteger, since they are generally much smaller than the fraction itself).
TMap	the rebinder type for defining an association TQuotient -> LighterSternBrocot::Node*. For instance, StdMapRebinder is fine.

Definition at line 107 of file LightSternBrocot.h.

Member Typedef Documentation

◆ Integer

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

typedef TInteger DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::Integer

Definition at line 110 of file LightSternBrocot.h.

◆ Map

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

typedef TMap DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::Map

Definition at line 112 of file LightSternBrocot.h.

◆ MapQuotientToNode

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

typedef TMap:: template Rebinder<Quotient, Node*>::Type DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::MapQuotientToNode

Definition at line 118 of file LightSternBrocot.h.

◆ Quotient

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

typedef TQuotient DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::Quotient

Definition at line 111 of file LightSternBrocot.h.

◆ Self

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

typedef LightSternBrocot<TInteger,TQuotient,TMap> DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::Self

Definition at line 113 of file LightSternBrocot.h.

Constructor & Destructor Documentation

◆ ~LightSternBrocot()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::~LightSternBrocot ( )

Destructor.

◆ LightSternBrocot() [1/2]

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::LightSternBrocot ( )

private

Constructor. Hidden since singleton class.

◆ LightSternBrocot() [2/2]

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::LightSternBrocot ( const LightSternBrocot< TInteger, TQuotient, TMap > & other )

private

Copy constructor.

Parameters

other the object to clone. Forbidden by default.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< Integer >) )

◆ display()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

static void DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::display	(	std::ostream &	out,
		const Fraction &	f
	)

static

Writes/Displays the fraction on an output stream.

Parameters

out	the output stream where the object is written.
f	the fraction to display.

◆ fraction()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

static Fraction DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::fraction	(	Integer	p,
		Integer	q,
		Fraction	ancestor = `zeroOverOne()`
	)

static

Creates the fraction p/q.

Parameters

p	the numerator (>=0)
q	the denominator (>=0)
ancestor	(optional) unused in this representation.

Returns: the corresponding fraction in the Stern-Brocot tree.

NB: Complexity is bounded by n where n is the depth of the continued fraction of p/q.

◆ instance()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

static LightSternBrocot& DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::instance ( )

static

Returns: the (only) instance of LightSternBrocot.

◆ isValid()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

bool DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ oneOverZero()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

static Fraction DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::oneOverZero ( )

static

The fraction 1/0

◆ operator=()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

LightSternBrocot& DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::operator= ( const LightSternBrocot< TInteger, TQuotient, TMap > & other )

private

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'. Forbidden by default.

◆ zeroOverOne()

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

static Fraction DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::zeroOverOne ( )

static

The fraction 0/1

Field Documentation

◆ myOneOverOne

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

Node* DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::myOneOverOne

private

Definition at line 529 of file LightSternBrocot.h.

◆ myOneOverZero

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

Node* DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::myOneOverZero

private

Definition at line 528 of file LightSternBrocot.h.

◆ myZeroOverOne

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

Node* DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::myZeroOverOne

private

Definition at line 527 of file LightSternBrocot.h.

◆ nbFractions

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

Quotient DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::nbFractions

The total number of fractions in the current tree.

Definition at line 513 of file LightSternBrocot.h.

◆ singleton

template<typename TInteger , typename TQuotient , typename TMap = StdMapRebinder>

LightSternBrocot* DGtal::LightSternBrocot< TInteger, TQuotient, TMap >::singleton

staticprivate

Singleton class.

Definition at line 521 of file LightSternBrocot.h.

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

LightSternBrocot.h

Data Structures

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

template<typename TInteger, typename TQuotient, typename TMap = StdMapRebinder> class DGtal::LightSternBrocot< TInteger, TQuotient, TMap >

Member Typedef Documentation

◆ Integer

◆ Map

◆ MapQuotientToNode

◆ Quotient

◆ Self

Constructor & Destructor Documentation

◆ ~LightSternBrocot()

◆ LightSternBrocot() [1/2]

◆ LightSternBrocot() [2/2]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

◆ display()

◆ fraction()

◆ instance()

◆ isValid()

◆ oneOverZero()

◆ operator=()

◆ zeroOverOne()

Field Documentation

◆ myOneOverOne

◆ myOneOverZero

◆ myZeroOverOne

◆ nbFractions

◆ singleton

template<typename TInteger, typename TQuotient, typename TMap = StdMapRebinder>
class DGtal::LightSternBrocot< TInteger, TQuotient, TMap >