Recursive Algorithms

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.

Basics

• Introduction
• What is Tail Recursion
• Tail Recursion Elimination

In Different Languages

• Recursion in Python
• Recursion in Java
• Recursion in C#
• Recursion in JavaScript

Easy Problems

• Factorial
• Print 1 to n
• Print n to 1
• Sum of array
• Reverse a string
• Decimal to binary
• Sum of digit
• Array Min and Max
• Palindrome Check

Medium Problems

• Mean of Array
• Adjacent duplicates
• Coin Change
• Binary to Gray
• Longest palindromic substring
• Tower of Hanoi
• Compute nCr
• Permutations
• Subsets
• Possible paths in matrix
• Combinations of Parentheses

Hard Problems

• Sort a Queue
• Sort a Stack
• Palindromic Partitions
• Scrambled Strings
• Word Break Problem
• N Queen Problem
• Sudoku Solver
• Knight's Tour

Practice Sets on Recursion

• Recursive Practice Problems with Solutions
• Practice Questions for Recursion | Set 1
• Practice Questions for Recursion | Set 2
• Practice Questions for Recursion | Set 3
• Practice Questions for Recursion | Set 4
• Practice Questions for Recursion | Set 5
• Practice Questions for Recursion | Set 6
• Practice Questions for Recursion | Set 7
• Practice questions for Linked List and Recursion

Quiz based on Recursion:

• Top MCQs on Recursion Algorithm with Answers

What is a Recursive Algorithm?

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

1. Base case: Which is a condition that stops the recursion.
2. 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

Introduction of Recursion

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Introduction of Recursion

Application's of Recursion

Writing base case in Recursion