Asymptotic Analysis
Given two algorithms for a task, how do we find out which one is better?
One naive way of doing this is – to implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach for the analysis of algorithms.
- It might be possible that for some inputs, the first algorithm performs better than the second. And for some inputs second performs better.
- It might also be possible that for some inputs, the first algorithm performs better on one machine, and the second works better on another machine for some other inputs.
Asymptotic Analysis is the big idea that handles the above issues in analyzing algorithms. In Asymptotic Analysis, we evaluate the performance of an algorithm in terms of input size (we don’t measure the actual running time). We calculate, how the time (or space) taken by an algorithm increases with the input size.
Asymptotic Analysis of Algorithms Notes for GATE Exam [2024]Asymptotic Notations
This Asymptotic Analysis of Algorithms is a critical topic for the GATE (Graduate Aptitude Test in Engineering) exam, especially for candidates in computer science and related fields. This set of notes provides an in-depth understanding of how algorithms behave as input sizes grow and is fundamental for assessing their efficiency. Let’s delve into an introduction for these notes:
Table of Content
- Introduction of Algorithms
- Asymptotic Analysis
- Worst, Best and Average Case
- How to Analyse Loops for Complexity Analysis of Algorithms?
- How to combine the time complexities of consecutive loops?
- Algorithms Cheat Sheet for Complexity Analysis:
- Runtime Analysis of Algorithms:
- Little o and Little omega notations
- What does ‘Space Complexity’ mean?
- Previous Year GATE Questions
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