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An overview of recursion and recursive algorithms from an object-oriented perspective.

Recursive data structures

A recursive data structure is an object or class that contains an abstraction of itself.

In mathematical terms, we say that the object is "isomorphic" to itself. The basic embodiment of a recursive data structure is the Composite Design pattern . Recursive data structures enable us to represent repetitive abstract patterns. In such, they enable us to generate or represent complexity from simplicity.

Characteristics of a recursive data structure:

  • Abstract representation : Since the actual total structure of the data is not known until run-time, the data must be represented by an abstraction, such as an abstract class or interface.
  • Base case(s) : These represent the "end" of the pattern. They are the termination point(s) of the data structure.
  • Inductive case(s) : These represent the on-going, "interior" portion of the repetitive pattern. They embody the ability to represent the data structure as a a simple connection between abstractly equivalent entities.

Recursive data structures are arguably the most important data structure in computer science as they are able to represent arbitrarily complex data. Indeed, if one looks across all the sciences, one sees that one of the fundamental modeling tools used is to attempt to

Recursive algorithms

In order to process a recursive data structure, it makes sense that any such algorithm should reflect the recursive nature of the data structure:

A recursive algorithm is a process that accomplishes its task, in part, by calling an abstraction of itself

Recursion is thus a special case of delegation.

In light of the above definition, it is not surprising that recursive algorithms and recursive data structures share common characteristics:

Characteristics of a recursive algorithm:

  • Abstract representation : Since the actual total process needed to process the recursive dataastructure of the data is not known until run-time, the algorithm must be represented by an abstraction, such as an abstract method (this is not the only way).
  • Base case(s) : These represent the "end" of the algorithm. They are the termination point(s) of the algorithm.
  • Inductive case(s) : These represent the on-going, "interior" portion of the algorithm. They embody the ability to process the recursive data structure by calling the same abstract process on the composed elements of the structure.

The similarity between recursive algorithms and recursive data structures is because in an OO system, the structure drives the algorithm . That is, it is the form of the data structure that determines the form if the algorithm. In an OO system, objects are asked to perform algorithms as they pertain to that object--that is, an algorithm on an object is a method of that object. The data has the behavior. The data is intelligent. This is in contrast to procedural or functional programming, where data is handed to the behavior. That is, stand-alone functions are used to process non-intelligent data. (Caveat: With all that said, in more advanced designs, we will show the algorithm can be decoupled from its data structure and thus be removed as a method of the data. This will not change the above principles however.)

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Principles of object-oriented programming. OpenStax CNX. May 10, 2013 Download for free at http://legacy.cnx.org/content/col10213/1.37
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