This document discusses recursion, which refers to a programming technique where a function calls itself, either directly or indirectly. It provides examples of direct and indirect recursion and explains that for recursion to be usable, it needs to have a base case or exit condition to make it finite. The base case is a condition whose result is already known, like a factorial function where factorial(1) = 1. The document compares recursion to iteration, noting that recursion uses more memory due to allocating new memory for each call, while iteration repeats the same code and variables. It provides some guidelines on when to use recursion vs iteration based on code length, complexity, time, and efficiency considerations. Finally, it provides some practice problems to write programs recursively.

1. Recursion
Intro, Recursive functions
Recursion vs Iteration
-> By Apni Kaksha <-

2. Recursion
A function can call other functions.
But a function calling itself seems logically wrong.
Recursion refers to a programming technique in which a function calls itself
directly or indirectly.

3. Direct/Indirect Recursions
def A( ):
A( )
def A( ):
B( )
def B( ):
A( )
Direct
Calling Itself
Indirect
Calling Itself

4. Recursive Function
def func1( ) :
print( ‘Hello World’ )
func1( )
This is a recursive function calling itself.

5. Recursion is Infinite...
To make it usable we need to make it finite.
We will make a case which will break the recursion.
def a(i):
if(i>0):
print(i)
i=i-1
a(i)
else:
return
Recursive Condition
Exit Condition

6. Base Case
We make a case whose result is already known. We use this case as the exit
case.
e.g. recursive code for factorial.
factorial(1) = 1 We know it already.
BASE CASE

7. Function to compute : an
Iterative definition : an
= a * a * a . . . a
n
Recursive definition : an
= a * an-1
Further an-1
= a * an-2
Recursive Definition

8. Practice Time
Q1. Find the output:
def binod(n):
if n==0:
print(‘Finally’)
else:
print(n)
binod(n-3)
binod(15)
Q2. Find the output:
def val(n):
if(n<=1):
return True
elif(n%2==0):
return val(n/2)
else:
return val(n/1)

9. Recursion & Loops are related, one thing can be done by both methods.
Sometimes Recursion is better, sometimes loop is better.
Recursion vs Iteration
When a loop runs, it repeats the same variables
and the same unit of code.
In Recursion for each recursive call, new memory
is allocated for the function.

10. ● Recursion makes a program look shorter and easily
understandable in terms of mathematics also.
● Recursion is heavy on memory due to allocation of new memory
with each recursive call.
● When the code length & complexity matters, Recursion is
recommended.
● When the time & efficiency of the code matters, Iteration is
recommended.
Important Points

11. Practice Time
Q1. Write a program to print the string backwards (by both methods).
Do the following questions recursively.
Q2. Write a program to calculate ab
.
Q3. Write a program to calculate HCF.
Q4. Write a program to print fibonacci series.