---
title: "Why use asymptotic notations"
subject: "Data Structure and Algorithm"
chapter: 9
key: "semester_4/data_structure_and_algorithm:why-asymptotic-notations"
source: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/why-asymptotic-notations
site: BCT Engineering
---

# Why use asymptotic notations

Data Structure and Algorithm · Chapter 9: Growth Functions

- Asked in: 2071 Bhadra, 1 marks; 2071 Magh, 1 marks (asked 2 times)
- Video: [Analyzing algorithms in 7 minutes — Asymptotic Notation](https://www.youtube.com/watch?v=u8AprTUkJjM) — Michael Sambol
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/why-asymptotic-notations
- Whole chapter: https://www.bctengineer.com/md/semester_4/data_structure_and_algorithm/chapter-9

## Question

Why do we use asymptotic notations during algorithm analysis?

## Short answer

Asymptotic notations (O, Ω, Θ) provide a machine-independent way to compare algorithms by describing growth rates as input size n becomes large, ignoring constants and lower-order terms. They simplify analysis (e.g., 5n²+3n+7 is Θ(n²)) and predict scalability.

## Answer

Exact running time depends on the computer, compiler, language and input, so it cannot be used to compare algorithms fairly. **Asymptotic notations** (O, Ω, Θ) describe how running time or space **grows with the input size n** when n becomes large, ignoring constants and lower-order terms.

Reasons:
- They are machine independent: we compare growth rates, not seconds.
- They simplify analysis: 5n² + 3n + 7 is just Θ(n²).
- They show how an algorithm scales: O(n log n) beats O(n²) for large inputs.
- They express best (Ω), worst (O) and tight (Θ) behaviour, helping to choose the right algorithm before writing code.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is exact running time not used to compare algorithms?
   A. It is always infinite
   B. It cannot be measured at all
   C. It depends on machine, compiler, language and input
   D. It is always the same
   Answer: C. Asymptotic notation instead compares growth with n. (Key point: Reason for asymptotics)

2. What is 5n^2 + 3n + 7 in asymptotic terms?
   A. Theta(n)
   B. Theta(n^3)
   C. Theta(15)
   D. Theta(n^2)
   Answer: D. Constants and lower-order terms are ignored. (Key point: Dropping terms)

3. Which notation describes worst-case (upper) behaviour?
   A. O
   B. Omega
   C. Theta
   D. small omega
   Answer: A. O is upper bound, Omega lower, Theta tight. (Key point: Notation roles)

## Related in Data Structure and Algorithm

- [Small o vs small omega](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Asmall-o-vs-small-omega) — Data Structure and Algorithm, chapter 9
- [Sentinel in sequential search](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Asentinel-sequential-search-importance) — Data Structure and Algorithm, chapter 8

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