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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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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