Recursion

In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.

Need of Recursion

Recursion is an amazing technique with the help of which we can reduce the length of our code and make it easier to read and write. It has certain advantages over the iteration technique which will be discussed later. A task that can be defined with its similar subtask, recursion is one of the best solutions for it. For example; The Factorial of a number.

Properties of Recursion:

Performing the same operations multiple times with different inputs.
In every step, we try smaller inputs to make the problem smaller.
Base condition is needed to stop the recursion otherwise infinite loop will occur.

How are recursive functions stored in memory?

Recursion uses more memory, because the recursive function adds to the stack with each recursive call, and keeps the values there until the call is finished. The recursive function uses LIFO (LAST IN FIRST OUT) Structure just like the stack data structure.

A Mathematical Interpretation Let us consider a problem that a programmer has to determine the sum of first n natural numbers, there are several ways of doing that but the simplest approach is simply to add the numbers starting from 1 to n. So the function simply looks like this,

approach(1) – Simply adding one by one

f(n) = 1 + 2 + 3 +……..+ n

but there is another mathematical approach of representing this,

approach(2) – Recursive adding 

f(n) = 1                  n=1

f(n) = n + f(n-1)    n>1

There is a simple difference between the approach (1) and approach(2) and that is in approach(2) the function “ f( ) ” itself is being called inside the function, so this phenomenon is named recursion, and the function containing recursion is called recursive function, at the end, this is a great tool in the hand of the programmers to code some problems in a lot easier and efficient way.

What is the base condition in recursion? In the recursive program, the solution to the base case is provided and the solution to the bigger problem is expressed in terms of smaller problems.

int fact(int n)
{
    if (n < = 1) // base case
        return 1;
    else    
        return n*fact(n-1);    
}

In the above example, the base case for n < = 1 is defined and the larger value of a number can be solved by converting to a smaller one till the base case is reached.

Types of recursion

Single recursion and multiple recursion: Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion include tree traversal, such as in a depth-first search.
Indirect recursion: Most basic examples of recursion, and most of the examples presented here, demonstrate direct recursion, in which a function calls itself. Indirect recursion occurs when a function is called not by itself but by another function that it called (either directly or indirectly). For example, if f calls f, that is direct recursion, but if f calls g which calls f, then that is indirect recursion of f. Chains of three or more functions are possible; for example, function 1 calls function 2, function 2 calls function 3, and function 3 calls function 1 again.
Anonymous recursion: Recursion is usually done by explicitly calling a function by name. However, recursion can also be done via implicitly calling a function based on the current context, which is particularly useful for anonymous functions, and is known as anonymous recursion.

recursion (1).jpg

A classic example of a recursive procedure is the function used to calculate the factorial of a natural number:

function factorial is:

input: integer n such that n >= 0

output: [n × (n-1) × (n-2) × ... × 1]


    1. if n is 0, return 1
    2. otherwise, return [ n × factorial(n-1) ]


end factorial

Note: You can go Here to read more about recursion. (Give it a try ;))

Fun Fact: If you'll google "Recursion" the page will demonstrate the recursive phenomenon with the "Did you mean: recursion", just below the search bar.

Hope it helps!! Keep learning :)

Recursion

The recursive blog on recursion.

Recursion