Recursion in Programming Fundamentals, Study Guides, Projects, Research of Computer Programming

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Recursion

Programming Fundamentals

Informatics Engineering

Gunadarma University

Introduction to Recursion: Recursion is a programming technique where a function calls itself directly or indirectly. It is used to solve problems that can be divided into smaller, similar sub- problems. Recursion can simplify code and make it more readable when used correctly, but it can also lead to performance issues if not implemented properly. Key Concepts in Recursion

1. Base Case: o The condition under which the recursive function stops calling itself. This prevents infinite recursion. o Example: In a factorial function, the base case is when n equals 1 or 0.
2. Recursive Case: o The part of the function where the function calls itself with a modified argument, moving towards the base case. o Example: In a factorial function, the recursive case calls the function with n- 1.
3. Stack Overflow: o A potential problem where the recursive calls exceed the stack size, leading to a program crash. o Ensure there is a base case and the problem size reduces with each call.
4. Direct vs. Indirect Recursion: o Direct Recursion: A function calls itself directly. o Indirect Recursion: A function calls another function, which in turn calls the first function.

Advanced Concepts

1. Tail Recursion: o A form of recursion where the recursive call is the last operation in the function. o Some languages optimize tail-recursive functions to prevent stack overflow. o Example:
2. Memoization: o An optimization technique to store the results of expensive function calls and reuse them when the same inputs occur again. o Example (Fibonacci with Memoization):

3. Recursion vs. Iteration: o Recursion can sometimes be less efficient than iteration due to function call overhead and stack usage. o Convert recursive solutions to iterative ones when performance is critical. Conclusion Recursion is a powerful tool in a programmer's toolkit, useful for solving problems that have a natural recursive structure. By understanding base cases and recursive cases, and being aware of potential pitfalls like stack overflow, you can effectively leverage recursion to write elegant and concise code. Practice with various recursive problems to strengthen your understanding and ability to apply recursion effectively. Practice Exercises
4. Fibonacci Sequence: o Write a recursive function fibonacci(n) to find the n-th Fibonacci number. o Example:
5. Sum of Array: o Write a recursive function sum_array(arr) to find the sum of elements in an array. o Example: