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/LighterSternBrocot.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 LighterSternBrocot< TInteger, TQuotient, TMap >	Self

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

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

	~LighterSternBrocot ()

bool	isValid () const

Static Public Member Functions
static LighterSternBrocot &	instance ()

static Fraction	zeroOverOne ()

static Fraction	oneOverZero ()

static Fraction	oneOverOne ()

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

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
	LighterSternBrocot ()

	LighterSternBrocot (const LighterSternBrocot &other)

LighterSternBrocot &	operator= (const LighterSternBrocot &other)

Private Attributes
Node *	myOneOverZero

Node *	myOneOverOne

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

Detailed Description

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

Description of template class 'LighterSternBrocot'

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[]. This representation is also different from LightSternBrocot in the sense that nodes have only one set of child nodes and that only fractions greater than 1/1 are stored.

In this representation, the fraction 1/1 has depth 0, like 2/1, 3/1, etc. Furthermore, each fraction [u_0,...,u_n] has an origin which is the fraction [u_0,...,u_{n-1},1]. It is the top extremity of this branch. The origin has depth n-1 since [u_0,...,u_{n-1},1] = [u_0,...,u_{n-1}+1]. Inversely a k-child of [u_0,...,u_n], for k >= 2, is the fraction [u_0,...,u_n - 1, k]. A 1-child of a fraction f is itself, except for the fraction 1/0 where its 1-child is 1/1 by convention.

In practice, also 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 7 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 LighterSternBrocot::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.

Examples: arithmetic/approximation.cpp, arithmetic/convergents-biginteger.cpp, arithmetic/convergents.cpp, arithmetic/fraction.cpp, and arithmetic/pattern.cpp.

Definition at line 108 of file LighterSternBrocot.h.

Member Typedef Documentation

◆ Integer

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

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

Definition at line 111 of file LighterSternBrocot.h.

◆ Map

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

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

Definition at line 113 of file LighterSternBrocot.h.

◆ MapQuotientToNode

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

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

Definition at line 119 of file LighterSternBrocot.h.

◆ Quotient

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

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

Definition at line 112 of file LighterSternBrocot.h.

◆ Self

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

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

Definition at line 114 of file LighterSternBrocot.h.

Constructor & Destructor Documentation

◆ ~LighterSternBrocot()

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

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

Destructor.

◆ LighterSternBrocot() [1/2]

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

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

private

Constructor. Hidden since singleton class.

◆ LighterSternBrocot() [2/2]

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

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

◆ display()

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

static void DGtal::LighterSternBrocot< 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::LighterSternBrocot< TInteger, TQuotient, TMap >::fraction	(	Integer	p,
		Integer	q,
		Fraction	ancestor = `oneOverZero()`
	)

static

Any fraction p/q. Complexity is in O(n) where n is the depth of continued fraction of 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.

◆ instance()

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

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

static

Returns: the (only) instance of LighterSternBrocot.

◆ isValid()

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

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

Checks the validity/consistency of the object.

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

◆ oneOverOne()

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

static Fraction DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::oneOverOne ( )

static

The fraction 1/1

◆ oneOverZero()

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

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

static

The fraction 1/0

◆ operator=()

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

LighterSternBrocot & DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::operator= ( const LighterSternBrocot< 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::LighterSternBrocot< TInteger, TQuotient, TMap >::zeroOverOne ( )

static

The fraction 0/1

Field Documentation

◆ myOneOverOne

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

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

private

Definition at line 551 of file LighterSternBrocot.h.

◆ myOneOverZero

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

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

private

Definition at line 550 of file LighterSternBrocot.h.

◆ nbFractions

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

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

The total number of fractions in the current tree.

Definition at line 540 of file LighterSternBrocot.h.

◆ singleton

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

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

staticprivate

Singleton class.

Definition at line 548 of file LighterSternBrocot.h.

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

LighterSternBrocot.h

Data Structures

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ Integer

◆ Map

◆ MapQuotientToNode

◆ Quotient

◆ Self

Constructor & Destructor Documentation

◆ ~LighterSternBrocot()

◆ LighterSternBrocot() [1/2]

◆ LighterSternBrocot() [2/2]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

◆ display()

◆ fraction()

◆ instance()

◆ isValid()

◆ oneOverOne()

◆ oneOverZero()

◆ operator=()

◆ zeroOverOne()

Field Documentation

◆ myOneOverOne

◆ myOneOverZero

◆ nbFractions

◆ singleton