Analysis of Algorithms

Introduction

Analysis of algorithms is crucial in computer science for evaluating the performance of algorithms and programs.
Efficiency is measured in terms of time and space.

Purpose: Understand why analysis is important to evaluate algorithm performance.
Order of Growth: Measures how the algorithm's resource consumption increases with input size.
Asymptotic Analysis: Evaluates the algorithm's efficiency by focusing on input size.
Worst, Average, and Best Cases: Different scenarios for analyzing algorithm performance.

Big-O Notation: Describes the upper limit of the algorithm's running time, focusing on the worst-case scenario.
Theta (Θ) Notation: Provides tight bounds on algorithm performance by specifying both upper and lower bounds.
Big Omega (Ω) Notation: Describes the lower bound of the algorithm's running time.
Time Complexity: Evaluates the time an algorithm takes to complete as a function of input size.
Space Complexity: Evaluates the memory space an algorithm requires as a function of input size.
Differences Among Notations: Understanding when to use Big-O, Θ, and Ω.
Examples and Practice Questions: Apply knowledge through examples and questions on time complexity analysis.

Analyzing Loops: Understanding complexity in iterative loops.
Analyzing Recursive Functions: Evaluating the complexity of recursive functions using recurrence relations.
Amortized Analysis: Technique to assess the average performance of each operation in a worst-case sequence of operations.

Complexity Classes: Discusses P, NP, CoNP, NP-hard, and NP-complete.
NP-Complete Problems: Understanding proofs and examples, including the Clique decision problem and Independent Set problem.

Explore additional tutorials and articles for deeper understanding of algorithms, complexity analysis, and specific asymptotic notations.
Practice problems and examples are available for hands-on learning.