The document discusses recursion, which is defining something in terms of itself. It provides examples of recursion in computer programming, such as calculating factorials recursively. Recursion involves a function calling itself and requires a base case and changing state to terminate. Advantages are clean code and breaking problems into sub-problems, while disadvantages are complexity, inefficiency, and difficulty debugging.

1. Chapter 25
Recursion
WITH MRSAEM
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Recursion
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What is recursion?
Recursion is the process of defining something
in terms of itself.
A physical world example would be to place
two parallel mirrors facing each other. Any
object in between them would be reflected
recursively.
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3. A Level
Recursion
Chapter
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4. A Level
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def factorial(x):
if x == 1:
return 1
else:
return (x * factorial(x-1))
x = 3
print("The factorial of", x, "is",
factorial(x))

5. A Level
Recursion
Chapter
25
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Recursion
Chapter
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A very efficient way of programming is to make the same function work over and over
again in order to complete a task.
Recursion is a very powerful technique that can be used when programming an algorithm in
which there is a variable number of iterations. Recursive routines have two important
features:
•a recursive routine calls itself
•it must have a terminating condition.
As a recursive routine calls itself there must be a way of stopping it or it will continue to call
itself for ever in a continuous loop.
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Another Defination
One way of doing this is to use 'Recursion'.
Recursion is where a function or sub-routine calls itself as part of the overall process.
Some kind of limit is built in to the function so that recursion ends when a certain
condition is met.
A classic computer programming problem that make clever use of recursion is to find the
factorial of a number. i.e. 4 factorial is 4! = 4 x 3 x 2 x 1
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Now go back and see if you can understand the code. In particular, see if you can
identify the three laws of recursion :
•A recursive algorithm must have a base case.
•A recursive algorithm must change its state and move toward the base case.
•A recursive algorithm must call itself, recursively.
The base case above is n <= 0. Without a base case and movement towards it at
each repeated function call, the program would never end – similar to what
happens when you write a while loop with a condition which never becomes true.

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In terms of a basic intuitive understanding, the third
law is probably the most important:
A recursive function is a function which calls itself.
Now you have seen a recursive function and got some
understanding of what they involve, it’s time for some
practice. Following are two exercises to help you
develop your skill and understanding with recursion.
Make sure you give each one a really good try on your
own before looking at the solution, in order to get the
most out of the exercises.
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def greet():
print("Hello")
greet()
greet()

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To start it off the following
statement is written
p = fct(3)
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Recursion
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def fact(n):
if(n==0):
return 1
return n*fact(n-1)
result =fact(5)
print(result)

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Advantages of Recursion
1.Recursive functions make the code look clean and elegant.
2.A complex task can be broken down into simpler sub-problems using recursion.
3.Sequence generation is easier with recursion than using some nested iteration.
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Disadvantages of Recursion
1.Sometimes the logic behind recursion is hard to follow through.
2.Recursive calls are expensive (inefficient) as they take up a lot of memory and time.
3.Recursive functions are hard to debug.
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