Recursive Algorithms: Factorial, GCD, Modular Exponent | Lecture 35 | Discrete Structures | CSIT, TU

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In this video, we introduce some important recursive algorithms, along with their pseudocode. We start by explaining the relationship between a recursive definition and a recursive algorithm, and the general guidelines for building recursive algorithms. We then dive into a few specific algorithms, providing background and reasoning for the process, and finally compiling the observations into a pseudocode. We first look into the exponentiation algorithm to compute a raised to the power n. The next recursive implementation is for n!, the factorial of n. We then look into a recursive definition of GCD that’s based on the Euclidean algorithm, and provide an algorithm for computing the gcd of two numbers.
The last algorithm that we provide is the recursive modular exponentiation algorithm, for which we first explain two recursive definitions, and use the optimal definition to complete the algorithm.

This video belongs to the playlist: Discrete Structures Full Course for Tribhuwan University, under the BSc CSIT programme.

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Chapters:
0:00 Scope of the Video
1:25 Recursive Algorithms: Overview
3:48 Recursive Exponentiaion: Concepts
6:28 Recursive Exponentiation: Pseudocode
9:51 Recursive Factorial: Concepts
10:30 Recursive Factorial: Pseudocode
11:23 Recursive GCD: Concepts
14:10 Recursive GCD: Pseudocode
14:35 Recursive Modular Exponentiation: Concept
18:49 Recursive Modular Exponentiation: Pseudocode

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Credits:
Text-Book:
Kenneth H. Rosen | Discrete Mathematics and its Applications
Kolman | Discrete Mathematical Structures
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References:

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Keywords:
discrete structures, discrete mathematics, csit, course series, computer science, induction and recursion, induction, recursion, recursive defintions, recursive functions, recursive sets, recursive sequences, recursive structures, recursive algorithms, recursive exponentiation, recursive factorial, recursive gcd, recursive euclidean algorithm, recursive modular exponentiation