Fundamental Algorithms

Euclid's algorithm
Extended Euclid's algorithm
Fibonacci Sequence
Factorial
Collatz
Pascal's Triangle
Goldbach's conjecture
Primes (test isPrime, Fundamental Theorem of Arithmetic, display N primes and till N, Sieve of Eratosthenes)
Modular Exponentiation
Eq degree 1
Eq degree 2
Nature roots x1,x2 quadratic equations
Derivative Polynomial
Towers of Hanoi
Babylonian Square Root
PI
Euler's number
Natural Logarithm
Euler's totient
Series Farey
Gen Permutations
Gen Subsets
Kadane's algoritm -Maximum Subarray Sum
Prefix Sum
Sliding Window Algorithm
Z-Algorithm

The distinction between the design and analysis of algorithms is a fundamental concept in computer science, encompassing how algorithms are created and evaluated. Let's explore these differences:

Design of Algorithms:

Purpose: The goal of design is to create algorithms that solve specific problems efficiently and correctly.
Process:
- Problem Definition: Clearly defining the problem requirements and constraints.
- Approach Selection: Choosing an appropriate strategy or paradigm (e.g., divide and conquer, dynamic programming, greedy algorithms) to tackle the problem.
- Algorithm Development: Constructing a step-by-step procedure that translates the chosen approach into a clear and concise form, such as pseudocode or a flowchart.
- Optimization: Refining the algorithm to improve its efficiency, either in terms of time or space complexity, without compromising correctness.
Creativity and Innovation: Involves significant amounts of creativity to invent novel solutions or adapt existing solutions to new problems.

Analysis of Algorithms:

Purpose: The goal of analysis is to determine the efficiency and effectiveness of an algorithm. This includes understanding its behavior and resource utilization.
Process:
- Complexity Analysis: Determining the time and space complexity of an algorithm by evaluating how these resources scale with input size. This often involves using Big O notation.
- Correctness Proof: Ensuring that the algorithm correctly solves the prescribed problem, often through formal verification or logical proofs.
- Performance Evaluation: Empirically testing the algorithm with various inputs to understand its average, best, and worst-case performance.
- Comparison: Assessing the algorithm against others to determine its relative efficiency and suitability for specific applications.
Theoretical and Empirical: Combines theoretical analysis, which involves mathematical rigor, with empirical evaluation through implementation and testing.

Complementary Nature:

Interdependence: Design and analysis are deeply interconnected. Effective design is informed by insights gained from analysis, and rigorous analysis depends on a well-constructed design.
Iterative Enhancement: Often, analysis will reveal limitations or inefficiencies in an algorithm, prompting a redesign to optimize these aspects, thereby improving both the design and the final product.

In summary, algorithm design is about creating efficient and correct solutions, while analysis is about understanding and evaluating those solutions in terms of performance and correctness. Both are essential for developing robust and efficient software.

References

https://github.com/manjunath5496/Algorithm-Books

CS Open CourseWare

Algorithms and Data Structures: Fall 2023 https://www2.cs.uh.edu/~panruowu/2023f_cosc3320/course.html
MIT Introduction to Algorithms, Fall 2011 https://www.youtube.com/playlist?list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb
Curriculum of Top Universities in CS https://learncs.me/curriculum/
Fall 2010 Algorithm Design and Analysis https://www.cs.ucdavis.edu/~gusfield/cs122f10/videolist.html
https://nixdell.com/teaching.html
CSE373: Data Structures and Algorithms https://courses.cs.washington.edu/courses/cse373/
DSA w3 https://www.w3schools.com/dsa/index.php
Computability and Complexity https://plato.stanford.edu/entries/computability/