The term Recursion can be defined as the process of defining something in terms of itself. In simple words, it is a process in which a function calls itself directly or indirectly.
Advantages of using recursion
- A complicated function can be split down into smaller sub-problems utilizing recursion.
- Sequence creation is simpler through recursion than utilizing any nested iteration.
- Recursive functions render the code look simple and effective.
Disadvantages of using recursion
- A lot of memory and time is taken through recursive calls which makes it expensive for use.
- Recursive functions are challenging to debug.
- The reasoning behind recursion can sometimes be tough to think through.
Syntax:
def func(): <--
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| (recursive call)
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func() ----
Example 1: A Fibonacci sequence is the integer sequence of 0, 1, 1, 2, 3, 5, 8….
Python3
# Program to print the fibonacci series upto n_terms# Recursive functiondef recursive_fibonacci(n): if n <= 1: return n else: return(recursive_fibonacci(n-1) + recursive_fibonacci(n-2))n_terms = 10# check if the number of terms is validif n_terms <= 0: print("Invalid input ! Please input a positive value")else: print("Fibonacci series:")for i in range(n_terms): print(recursive_fibonacci(i)) |
Fibonacci series: 0 1 1 2 3 5 8 13 21 34
Example 2: The factorial of 6 is denoted as 6! = 1*2*3*4*5*6 = 720.
Python3
# Program to print factorial of a number# recursively.# Recursive functiondef recursive_factorial(n): if n == 1: return n else: return n * recursive_factorial(n-1)# user inputnum = 6# check if the input is valid or notif num < 0: print("Invalid input ! Please enter a positive number.")elif num == 0: print("Factorial of number 0 is 1")else: print("Factorial of number", num, "=", recursive_factorial(num)) |
Factorial of number 6 = 720
What is Tail-Recursion?
A unique type of recursion where the last procedure of a function is a recursive call. The recursion may be automated away by performing the request in the current stack frame and returning the output instead of generating a new stack frame. The tail-recursion may be optimized by the compiler which makes it better than non-tail recursive functions.
Is it possible to optimize a program by making use of a tail-recursive function instead of non-tail recursive function?
Considering the function given below in order to calculate the factorial of n, we can observe that the function looks like a tail-recursive at first but it is a non-tail-recursive function. If we observe closely, we can see that the value returned by Recur_facto(n-1) is used in Recur_facto(n), so the call to Recur_facto(n-1) is not the last thing done by Recur_facto(n).
Python3
# Program to calculate factorial of a number# using a Non-Tail-Recursive function.# non-tail recursive functiondef Recur_facto(n): if (n == 0): return 1 return n * Recur_facto(n-1) # print the resultprint(Recur_facto(6)) |
720
We can write the given function Recur_facto as a tail-recursive function. The idea is to use one more argument and in the second argument, we accommodate the value of the factorial. When n reaches 0, return the final value of the factorial of the desired number.
Python3
# Program to calculate factorial of a number# using a Tail-Recursive function.# A tail recursive functiondef Recur_facto(n, a = 1): if (n == 0): return a return Recur_facto(n - 1, n * a) # print the resultprint(Recur_facto(6)) |
720
