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px2 = px1;

return 1;

}

else if (del>0.0)

{

px1 = (-b + sqrt(del))/(2*a);

px2 = (-b – sqrt(del))/(2*a);

return 2;

}

else

return 3;

}

Note: The called-by-value parameters a, b, and c are used to passed the data from the calling function to the called function, and the two reference parameters px1 and px2 are used to pass the results from the called function to the calling function.

Recursion

In C++, it’s possible for a function to call itself. Functions that do so are called seft-referential or recursive functions.

Example: To compute factorial of an integer

1! = 1

n! = n*(n-1)!

Example

// Recursive factorial function

#include<iostream.h>

#include<iomanip.h>

unsigned long factorial( unsigned long );

int main()

{

for ( int i = 0; i<= 10; i++ )

cout<<setw( 2 )<<i<<"! = "<<factorial( i )<<endl;

return 0;

}

// Recursive definition of function factorial

unsigned long factorial( unsigned long number )

{

if (number<1) // base case

return 1;

else // recursive case

return number * factorial( number - 1 );

}

The output of the above program:

0! = 1

1! = 1

2! = 2

3! = 6

4! = 24

5! = 120

6! = 720

7! = 5040

8! = 40320

9! = 362880

10! = 3628800

How the computation is performed

The mechanism that makes it possible for a C++ function to call itself is that C++ allocates new memory locations for all function parameters and local variables as each function is called. There is a dynamic data area for each execution of a function. This allocation is made dynamically, as a program is executed, in a memory area referred as the stack.

A memory stack is an area of memory used for rapidly storing and retrieving data areas for active functions. Each function call reserves memory locations on the stack for its parameters, its local variables, a return value, and the address where execution is to resume in the calling program when the function has completed execution (return address). Inserting and removing items from a stack are based on last-in/first-out mechanism.

Thus, when the function call factorial(n) is made, a data area for the execution of this function call is pushed on top of the stack. This data area is shown as figure below.

The data area for the first call to factorial

The progress of execution for the recursive function factorial applied with n = 3 is as follows:

Progress of execution for the recursive function

During the execution of the function call factorial(3), the memory stack evolves as shown in the figure below. Whenever the recursive function calls itself, a new data area is pushed on top of the stack for that function call. When the execution of the recursive function at a given level is finished, the corresponding data area is popped from the stack and the return value is passed back to its calling function.

The memory stack for execution of function call factorial(3)

Example: Fibonacci numbers:

F(N) = F(N-1) + F(N-2) for N>= 2

F(0) = F(1) = 1

#include<iostream.h>

int fibonacci(int);

int main()

{

int m;

cout<<"Enter a number: ";

cin>>m;

cout<<"The fibonacci of "<<m<<" is: "

<<fibonacci(m)<<endl;

return 0;

}

int fibonacci(int n)

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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Source:  OpenStax, Programming fundamentals in c++. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10788/1.1
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