DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node Struct Reference

#include <DGtal/arithmetic/LighterSternBrocot.h>

Public Member Functions
	Node (Integer p1, Integer q1, Quotient u1, Quotient k1, Node *anOrigin)
Node *	child (Quotient v)
Node *	origin () const
Node *	ancestor () const
Node *	father () const
bool	even () const
bool	odd () const
bool	isSameDepthLeft () const

Data Fields
Integer	p
	the numerator;
Integer	q
	the denominator;
Quotient	u
	the quotient (last coefficient of its continued fraction).
Quotient	k
	the depth (1+number of coefficients of its continued fraction).
Node *	myOrigin
	A pointer to the origin node [u_0,...,u_{n-1},1].
MapQuotientToNode	myChildren

Detailed Description

template<typename TInteger, typename TQuotient, typename TMap = StdMapRebinder>
struct DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node

Represents a node in the Stern-Brocot. The node stores information on the irreducible fraction itself (p/q, the partial quotient u, the depth k), but also pointers to ascendant and descendants in the Stern-Brocot tree. Nodes are constructed on demand, when the user ask for a descendant or for a specific fraction.

The LighterSternBrocot instances only fractions greater than or equal to 1/1. The node 0/1 does not exist. It is the inverse of 1/0. Given a fraction [u_0,...,u_n], for u_n >= 2, its origin is [u_0,...,u_{n-1},1]. The k-th son, k >= 2, of [u_0,...,u_n] is the fraction [u_0,...,u_n - 1, k].

See also

LighterSternBrocot::fraction

Definition at line 139 of file LighterSternBrocot.h.

Constructor & Destructor Documentation

Node()

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

DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::Node	(	Integer	p1,
		Integer	q1,
		Quotient	u1,
		Quotient	k1,
		Node *	anOrigin )

Constructor for node.

Parameters

p1	the numerator.
q1	the denominator.
u1	the quotient (last coefficient of its continued fraction).
k1	the depth (1+number of coefficients of its continued fraction).
anOrigin	A pointer to the origin node [u_0,...,u_{n-1},1].

Member Function Documentation

ancestor()

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

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

(

)

const

Returns

the ancestor of this fraction in O(1), ie [u0,...,u_{k-1},uk] => [u0,...,u_{k-1}] if u_{k-1} > 1, => [u0,...,u_{k-2}] otherwise. Equivalent to reduced( 1 ).

child()

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

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

(

Quotient

v

)

Returns

the node [u_0, ..., u_n - 1, v] if [u_0, ..., u_n] is the current node. Construct it if it does not exist yet.

even()

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

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

inline

Returns

'true' iff this node has an even depth.

Definition at line 193 of file LighterSternBrocot.h.

                               {
        return NumberTraits<Quotient>::even( k );
      }

References DGtal::NumberTraitsImpl< std::decay< T >::type >::even(), and DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::k.

father()

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

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

(

)

const

Returns

the father of this fraction in O(1), ie [u0,...,uk] => [u0,.. .,uk - 1]

isSameDepthLeft()

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

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

inline

Returns

'true' iff the descendant with the same depth is to the left.

Definition at line 201 of file LighterSternBrocot.h.

                                          {
        return odd();
      }

References DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::odd().

odd()

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

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

inline

Returns

'true' iff this node has an odd depth.

Definition at line 197 of file LighterSternBrocot.h.

                              {
        return NumberTraits<Quotient>::odd( k );
      }

References DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::k, and DGtal::NumberTraitsImpl< std::decay< T >::type >::odd().

Referenced by DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::isSameDepthLeft().

origin()

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

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

(

)

const

Returns

the origin of this node in O(1), ie [u0,...,uk] => [u0,...,u_{k-1},1], i.e. [u0,...,u_{k-1}+1].

Field Documentation

k

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

Quotient DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::k

the depth (1+number of coefficients of its continued fraction).

Definition at line 183 of file LighterSternBrocot.h.

Referenced by DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::even(), DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::odd(), and DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Fraction::trueK().

myChildren

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

MapQuotientToNode DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::myChildren

a map which gives the descendant [u_0,...,u_n - 1, k] if k is the key. Note that they are left or right descendant according to the parity of the depth. (odd=left, even=right).

Definition at line 189 of file LighterSternBrocot.h.

myOrigin

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

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

A pointer to the origin node [u_0,...,u_{n-1},1].

Definition at line 185 of file LighterSternBrocot.h.

p

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

Integer DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::p

the numerator;

Definition at line 177 of file LighterSternBrocot.h.

q

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

Integer DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::q

the denominator;

Definition at line 179 of file LighterSternBrocot.h.

u

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

Quotient DGtal::LighterSternBrocot< TInteger, TQuotient, TMap >::Node::u

the quotient (last coefficient of its continued fraction).

Definition at line 181 of file LighterSternBrocot.h.

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

• LighterSternBrocot.h