Recursion is characterized as the process of describing something in terms of itself; in other words, it is the process of naming the function by itself. Recursion is the mechanism of a function calling itself directly or implicitly, and the resulting function is known as a Recursive function.
Advantages:
- Code reusability
- Easily understandable
- Time complexity sometimes low
- Less number of code
Disadvantages:
- Causes overflow if condition exceeds
- More memory
- It is difficult to understand
- It is difficult to debug
- Terminating conditions in Recursion is a must
Syntax:
def function_name():Â
       ……………..
       |(recursive call)
       ………………….
  function_name()Â
Recursion calls the function which is already called and will call many times till the condition will become false. After that, it will return the value
Applications:
- Tower of Hanoi
- Stack implementation
- Fibonacci implementation
- Round Robin problem in Operating System.
Apart from the above applications below are some examples that depict how to use recursive functions in a program.
Example 1:
Python program to print Fibonacci series up to given terms.
Fibonacci:
Number=sum of two previous numbers
0,1
0+1=1
0+1=2
2+1=3
3+2=5
5+3=8
So the Fibonacci numbers are 0,1,1,2,3,5,8…….
In this program, the values are defined in till_range variables and then we are passing that variable into an argument, then calling the recursive function.
recursive_function(a-1) + recursive_function(a-2)
Implementation:
Python3
# Recursive functiondef recursive_function(a):       # Check number    if a <= 1:        return a    else:                 # Get next term        return(recursive_function(a-1) + recursive_function(a-2))Â
     # Display first fibonacci numberprint("\nFibonacci series upto 1 number:")for i in range(1):    print(recursive_function(i),          end=" ")        # Display first 5 fibonacci numbersprint("\nFibonacci series upto 5 numbers:")for i in range(5):    print(recursive_function(i),          end=" ")     # Display first 10 fibonacci numbersprint("\nFibonacci series upto 10 numbers:")for i in range(10):    print(recursive_function(i),          end=" ")   |
Output:Â
Fibonacci series upto 1 number: 0 Fibonacci series upto 5 numbers: 0 1 1 2 3 Fibonacci series upto 10 numbers: 0 1 1 2 3 5 8 13 21 34
Example 2:Â
Python program to find factorial of a number.
Factorial
Number=Number*(Number-1)*(Number-2)…*(Number-(Number+1))
Factorial of 3= 3*2*1
Factorial of 5= 5*4*3*2*1
Factorial of 7 = 7*6*5*4*3*2*1
In this python program, we are going to return the factorial of an integer. We are passing the variable n value to an argument, then we are calling the function.
a* recursion_factorial(a-1)
Implementation:
Python3
# recursive functiondef recursion_factorial(a):       # check number    if a == 1:        return 1    else:                 # multiply with next number        return (a * recursion_factorial(a-1))Â
Â
# factorial of 7n = 7print("Factorial of", n, "is", recursion_factorial(n))Â
# factorial of 2n = 2print("Factorial of", n, "is", recursion_factorial(n))Â
# factorial of 4n = 4print("Factorial of", n, "is", recursion_factorial(n))Â
# factorial of 9n = 9print("Factorial of", n, "is", recursion_factorial(n))Â
# factorial of 10n = 10print("Factorial of", n, "is", recursion_factorial(n)) |
Output:
Factorial of 7 is 5040 Factorial of 2 is 2 Factorial of 4 is 24 Factorial of 9 is 362880 Factorial of 10 is 3628800
