Why use asymptotic notations

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.