Functions and recursion are programming concepts. A function is a block of code that performs a specific task. Functions have a prototype, call, and body. Recursion is a technique where a function calls itself to solve a problem. It breaks the problem into smaller subproblems until it reaches a base case. Recursion uses the call stack to remember the state each time the function calls itself. Tail recursion is when the recursive call is the last thing executed, while head recursion calls itself first.

1. FUNCTIONS AND RECURSION
Gaurav Prakash
(MCA/25006/18)
Roopak Bhama
(MCA/25003/18)
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, JAIPUR CAMPUS

2. FUNCTIONS
• A function is a set of statements that take inputs, do
some specific computation and produces output.
OR
A self contained block of statement performing a
specific task.
• Components
• Prototype
• Call
• Body

3. PROTOTYPE
• Tells compiler about
• return type of function
• function name
• number of parameters
• data types of parameters
rtype fnct_name(dtype para1,…);
rtype = return type of function
fnct_name = name of the function
dtype = data type of parameter
para1 = parameter one… to ‘n’
PROTOTYPE

4. FUNCTION CALL
1 -
#include<iostream.h>
2 - void prnt();
3 - void main(){
4 - prnt();
5 - }
6 - void prnt(){
7 - cout<<“Hello”;
8 - }
1 -
#include<iostream.h>
2 - void prnt();
3 - void main(){
4 - prnt();
5 - }
6 - void prnt(){
7 - cout<<“Hello”;
8 - }
1 -
#include<iostream.h>
2 - void prnt();
3 - void main(){
4 - prnt();
5 - }
6 - void prnt(){
7 - cout<<“Hello”;
8 - }
1 – Include header files as per requirements of program.
2 – Function declaration. Tells the program that a function named prnt() has been
used.
3 – Main function starts. Program execution starts here.
4 – Function Call. Calls prnt() which returns nothing and have no parameters,
program moves to line 6.
6 – Starts executing statements of prnt(). Returns back to main at line 5. Program

5. FUNCTION BODY
1. #include<iostream.h>
2. void times(int);
3. int main(){
1. void times(5);
4. }
5. void times(int a){
1. for(int i=0;i<a;i++){
1. cout<<“Hellon”;
2. }
6. }
Function
Body
OUTPUT:
Hello
Hello
Hello
Hello
Hello

6. FUNCTIONS TYPES
LIBRARY USER DEFINED
Header Functions
stdio printf(),scanf()
math pow(), sqrt()
string strrev(),strcpy()
Without Argument, Without Return-
type
Without Argument, With Return-type
With Argument, Without Return-type
With Argument, With Return-type

7. NO ARGUEMENT AND NO
RETURN VALUES
#include<iostream>
using namespace std;
void printgreet(){
cout<<"Hellon";
}
int main(){
printgreet();
return 0;
}
• The empty
parentheses in
printgreet();
indicates that no
argument is passed
to the function.
• The return type of
the function is void.
Hence, no value is
returned from the
function.

8. NO ARGUEMENT AND RETURN
VALUES
#include<iostream.h>
int printgreet(){
int i,a;
cout<<"Enter times to
greetn";
cin>>a;
for(i=0;i<a;i++)
cout<<"Hellon";
return i;
}
void main(){
int a;
cout<<"Greeted
"<<printgreet()<<" time"; }
• The empty
parentheses in
printgreet();
statement indicates
that no argument is
passed to the
function.
• Here, the
printgreet()
function takes
input from the user
and returns i to the
main().

9. ARGUEMENT AND NO RETURN
VALUES
#include<iostream.h>
void printgreet(int a){
for(int i=0;i<a;i++)
cout<<"Hellon";
}
int main(){
printgreet(5);
return 0;
}
• The integer value is
passed to
printgreet()
function.
• The program will
print hello the
number of times
which is passed to
it.
• that is ‘5’ in
the above
program.

10. ARGUEMENT AND RETURN
VALUES
#include<iostream.h>
int printgreet(int x){
for(i=0;i<x;i++)
cout<<"Hellon";
return x;
}
int main(){
int a;
cout<<"Enter numbern";
cin>>a;
cout<<"Greeted
"<<printgreet(a)<<" times";
return 0;
}
• The input from the
user is passed to
printgreet()
function.
• The printgreet()
function returns
the number of
times the greeting
message has been
printed.
• Then the program
returns ‘x’ to the
main().

11. ACTUAL VS FORMAL
PARAMETERS
#include<iostream.h>
int sum(int a, int b) //Formal Parameters
{
return a+b;
}
int main()
{
int x=10,y=20;
int s = sum(x,y); //Actual Parameters
return 0;
)

12. PARAMETER PASSING
Pass by Value Pass by Reference
• Values of actual parameters
are copied to formal
parameters.
• Actual and Formal refer to
different memory locations.
• Address of actual parameters
is passed.
• Actual and Formal refer to
same memory location.
#include <iostream.h>
void fun(int x)
{ x = 30; }
void main()
{ int x = 20; fun(x);
printf("x = %d", x); }
# include <iostream.h>
void fun(int *ptr)
{ *ptr = 30; }
void main()
{ int x = 20; fun(&x);
printf("x = %d", x); }
OUTPUT OUTPUT
x = 20 x = 30

13. RECURSION
• Recursion breaks a problem into smaller identical
problems.
• Technique in which a method can call itself to solve a
problem.
• The recursive function is
• a kind of function that calls itself, or
• a function that is part of a cycle in the sequence of function
calls.

14. ITERATION VS RECURSION
Iteration Recursion
iterative function is one that
loops to repeat some part
of the code
recursive function is one
that calls itself again to
repeat the code.
FACTORIAL FACTORIAL
factorial(n) = n*(n-1)*….*1
factorial(0) = 1
factorial(n) =
1 //(if n=0)
n * (factorial(n)) //(if n>0)

15. HOW RECURSION WORKS?
• Each call creates a new instance of all the parameters and
the local variables
• As always, when the method completes, control returns to
the method that invoked it (which might be another
invocation of the same method)
• factorial(3) = 3 * factorial(3-1)
• = 3 * 2 * factorial(2-1)
• = 3 * 2 * 1 * factorial(1-1)
• = 3 * 2 * 1 * 1
• = 6

16. MEMORY
Instructions of a
program are kept
here.
Variables/Data of
the function are
stored here.
Dynamic Allocation
of memory
Used to store
Global/Static
variables

17. TAIL RECURSION
• A recursive function is tail recursive when recursive call
is the last thing executed by the function.
void A(int n)
{
if(n>0)
{
cout<<n<<“n”;
A(n-1);
}
}
void main()
{
int x=3;
A(x);
}
1
3
5
76
4
2

18. HEAD RECURSION
• A call is head-recursive when the first statement of the
function is the recursive call.
void A(int n)
{
if(n>0)
{
A(n-1);
printf(“%dn”,n);
}
}
void main()
{
int x=3;
A(x);
}
1
2 7
63
4 5

19. DIFFERENCE
1
3
5
76
4
2
1
2 7
63
4 5
TAIL OUTPUT:
3
2
1
HEAD OUTPUT:
1
2
3

20. REFERENCES
• https://www.advanced-
ict.info/programming/recursion.html
• https://www.youtube.com/watch?v=ygK0YON10sQ
• https://stackoverflow.com/questions/105838/real-
world-examples-of-recursion
• https://stackoverflow.com/questions/21426688/the-
difference-between-head-tail-recursion
• https://www.geeksforgeeks.org/recursion/
• https://www.geeksforgeeks.org/tail-recursion/