Introduction to Recursion

Recursion is one of the most fundamental concepts in Data Structures and Algorithms (DSA) and is widely used to solve complex problems by breaking them into smaller subproblems. If you are enrolled in a DSA course in Jaipur, understanding recursion is essential for mastering advanced topics like trees, graphs, and backtracking.

Recursion is heavily used in coding interviews and problem-solving.

What is Recursion?

Recursion is a technique where a function calls itself to solve a problem.

A recursive function has two main parts:

• Base Case (stopping condition)
• Recursive Case (function calling itself)

Example of Recursion

Factorial of a number:

n! = n × (n-1)!

Base Case:
0! = 1

Recursive Case:
5! = 5 × 4 × 3 × 2 × 1

Structure of Recursive Function

• Check base case
• Call function recursively
• Combine results

How Recursion Works

Recursion uses the call stack to store function calls.

Each function call:

• Gets added to stack
• Executes
• Returns result
• Removed from stack

Time Complexity of Recursion

T(n)=T(n−1)+O(1)

Time complexity depends on number of recursive calls.

Types of Recursion

• Direct Recursion
  Function calls itself directly
• Indirect Recursion
  Function calls another function which calls it back
• Tail Recursion
  Recursive call is the last operation
• Non-Tail Recursion
  Recursive call is not the last operation

Advantages of Recursion

• Simplifies complex problems
• Easy to understand
• Useful for divide and conquer
• Essential for tree and graph problems

Disadvantages of Recursion

• Uses extra memory (call stack)
• Risk of stack overflow
• Slower than iterative solutions

Real-World Applications

• Tree traversal
• Graph algorithms
• Backtracking problems
• Dynamic programming
• Mathematical computations

Common Interview Questions

• Factorial using recursion
• Fibonacci series
• Reverse array using recursion
• Power of number
• Sum of digits

Best Practices

• Always define base case
• Avoid infinite recursion
• Optimize using memoization
• Convert to iteration if needed

Summary

• Recursion is function calling itself
• Requires base case and recursive case
• Uses call stack
• Important for advanced DSA concepts

FAQs

Q1. What is recursion in DSA?
Recursion is a method where a function calls itself.

Q2. What is base case?
It is the condition where recursion stops.

Q3. What is stack overflow?
It occurs when too many recursive calls are made.

Q4. Is recursion important for interviews?
Yes, it is a fundamental concept.

Q5. What is difference between recursion and iteration?
Recursion uses function calls, iteration uses loops.

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