1. What is Time Complexity?

Time complexity is a computational concept that describes the amount of time an algorithm takes to run as a function of the length of the input. It provides a way to analyze and compare the efficiency of different algorithms.

2. Big O Notation Explained

Big O notation is a mathematical notation used to describe the upper bound of an algorithm's time complexity. It expresses the worst-case scenario of how long an algorithm will take to complete:

Where:

• \( T(n) \) — Time taken by the algorithm
• \( O \) — Big O notation (order of magnitude)
• \( f(n) \) — Function describing growth rate
• \( n \) — Input size

3. Common Time Complexities

O(1) - Constant Time: Execution time doesn't depend on input size
O(log n) - Logarithmic Time: Execution time grows logarithmically with input size
O(n) - Linear Time: Execution time grows linearly with input size
O(n log n) - Linearithmic Time: Common in efficient sorting algorithms
O(n²) - Quadratic Time: Common in nested loops
O(2ⁿ) - Exponential Time: Execution time doubles with each additional input element
O(n!) - Factorial Time: Extremely slow, common in brute-force algorithms

4. How to Use This Calculator

Steps: Select the algorithm type from the dropdown menu, enter the input size (n), and click Calculate. The calculator will show the Big O notation and estimated number of operations.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between time and space complexity?
A: Time complexity measures how long an algorithm takes to run, while space complexity measures how much memory it uses.

Q2: Why is Big O notation important?
A: It helps developers choose the most efficient algorithm for their specific use case and predict performance at scale.

Q3: What does "worst-case scenario" mean in Big O?
A: It describes the maximum time an algorithm could take for any input of size n, providing a performance guarantee.

Q4: Can an algorithm have multiple time complexities?
A: Yes, algorithms can have different best-case, average-case, and worst-case time complexities.

Q5: How accurate are these complexity estimates?
A: Big O provides asymptotic analysis - it describes behavior as n approaches infinity, not exact operation counts.