Recursion Algorithms

Last Updated : 03 Apr, 2024

Recursion is technique used in computer science to solve big problems by breaking them into smaller, similar problems. The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. Using a recursive algorithm, certain problems can be solved quite easily.

What is Recursion?

Recursion is a programming technique where a function calls itself within its own definition. This allows a function to break down a problem into smaller subproblems, which are then solved recursively.

How Does Recursion Work?

Recursion works by creating a stack of function calls. When a function calls itself, a new instance of the function is created and pushed onto the stack. This process continues until a base case is reached, which is a condition that stops the recursion. Once the base case is reached, the function calls start popping off the stack and returning their results.

What is a Recursive Algorithm?

A recursive algorithm is an algorithm that uses recursion to solve a problem. Recursive algorithms typically have two parts:

Base case: Which is a condition that stops the recursion.
Recursive case: Which is a call to the function itself with a smaller version of the problem.

Types of Recursion

There are several different recursion types and terms. These include:

Direct recursion: This is typified by the factorial implementation where the methods call itself.
In-Direct recursion: This happens where one method, say method A, calls another method B, which then calls method A. This involves two or more methods that eventually create a circular call sequence.
Head recursion: The recursive call is made at the beginning of the method.
Tail recursion: The recursive call is the last statement.

When to Use Recursion?

Recursion is a powerful technique that can be used to solve a wide variety of problems. However, it is important to use recursion carefully, as it can lead to stack overflows if not used properly.

Recursion should be used when:

The problem can be broken down into smaller subproblems that can be solved recursively.
The base case is easy to identify.
The recursive calls are tail recursive.

Examples of Recursion

Here are some common examples of recursion:

Example 1: Factorial: The factorial of a number n is the product of all the integers from 1 to n. The factorial of n can be defined recursively as:

factorial(n) = n * factorial(n-1)

Example 2: Fibonacci sequence: The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers. The Fibonacci sequence can be defined recursively as:

fib(n) = fib(n-1) + fib(n-2)

Applications of Recursion Algorithms:

Here are some common applications of recursion:

Tree and Graph Traversal: Depth-first search (DFS) and breadth-first search (BFS)
Dynamic Programming: Solving optimization problems by breaking them into smaller subproblems
Divide-and-Conquer: Solving problems by dividing them into smaller parts, solving each part recursively, and combining the results
Backtracking: Exploring all possible solutions to a problem by recursively trying different options
Combinatorics: Counting or generating all possible combinations or permutations of a set

Learn Basics of Recursion Algorithms:

Recursion in Different Languages:

Easy Problems on Recursion

Medium Problems on Recursion

Hard Problems on Recursion

Practice Sets on Recursion

Quiz based on Recursion:

Top MCQs on Recursion Algorithm with Answers

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