Algorithm Analysis

Published by: Anil K. Panta

What is Algorithm Analysis?

Analysis of an algorithm means checking how much time and space (memory) it needs to solve a problem. We study its efficiency - how fast and how smart it works when given different amounts of data.

This helps us choose the best algorithm among many.

Why Do We Need to Analyze Algorithms?

To choose the most efficient algorithm
To save time when the input size is large
To use less memory, especially in low-storage systems
To understand how different algorithms behave for the same problem

Example: Sorting Numbers

We can sort numbers using different algorithms like Bubble Sort or Merge Sort.

Bubble Sort: Easy to understand, but slow
Merge Sort: Faster, but needs extra memory

If you're working on a system with limited memory, bubble sort might be better.

If you're working with lots of data, merge sort is a better choice because it's faster.

Types of Algorithm Analysis

Type	What it Means	Example Scenario
Best Case	Fastest time the algorithm can take	Sorting a list that is already sorted
Worst Case	Longest time the algorithm can take	Sorting a list that’s in reverse order
Average Case	Expected time in normal situations	Random order of numbers in a list

Time Complexity

It tells how fast an algorithm runs as the input size increases.
Measured in terms like O(n), O(n²), etc. (This is called "Big O notation")

Example:

O(n) → Time increases linearly with input
O(n²) → Time increases much faster

Space Complexity

It tells how much memory an algorithm needs while running.
Important for devices with limited memory.

Final Summary

Analysis of algorithms helps us find out how fast and efficient a solution is. We analyze both the time it takes and the space it needs to make better choices when coding.

Why It Matters for Students:

Helps you choose the right algorithm
Builds problem-solving skills
Makes your code faster and smarter