# Data Structures - Asymptotic Analysis

Asymptotic analysis of an algorithm refers to defining the mathematical framing of its run-time performance. Using asymptotic analysis, we can very well conclude the best case, average case, and worst case scenario of an algorithm.

Asymptotic notations are mathematical tools to represent the time complexity of algorithms for asymptotic analysis.

Usually, the time required by an algorithm falls under three types −

**Best Case**− Minimum time required for program execution.**Average Case**− Average time required for program execution.**Worst Case**− Maximum time required for program execution.

### Asymptotic Notations

Following are the commonly used asymptotic notations to calculate the running time complexity of an algorithm.

- Ο Notation
- Ω Notation
- θ Notation

### Big Oh Notation, Ο

The notation Ο(n) is the formal way to express the upper bound of an algorithm's running time. It measures the worst case time complexity or the longest amount of time an algorithm can possibly take to complete.

For example, consider the case of Insertion Sort. It takes linear time in best case and quadratic time in worst case. We can safely say that the time complexity of Insertion sort is O(n^2). Note that O(n^2) also covers linear time.

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