Difference between Big O vs Big Theta Θ vs Big Omega Ω Notations

Big O, Big Theta, and Big Omega are notations used in computer science to describe the performance or complexity of an algorithm. Here's how they differ:

1. Big O Notation (O): This notation describes an upper bound of an algorithm in the worst-case scenario. It provides an upper limit on the time complexity of an algorithm, which means the algorithm will not take more time to complete than the time represented by Big O notation. For example, if we say that the time complexity of an algorithm is O(n), it means that in the worst-case scenario, the algorithm will take linear time to complete.

2. Big Theta Notation (Θ): This notation represents the average complexity of an algorithm. It provides both an upper and lower bound on the time complexity of an algorithm. This means that the running time of an algorithm will neither be better than its Big Theta notation nor worse. For example, if we say that the time complexity of an algorithm is Θ(n), it means that on average, the algorithm will take linear time to complete.

3. Big Omega Notation (Ω): This notation describes a lower bound of an algorithm in the best-case scenario. It provides a lower limit on the time complexity of an algorithm, which means the algorithm will not complete in less time than the time represented by Big Omega notation. For example, if we say that the time complexity of an algorithm is Ω(n), it means that in the best-case scenario, the algorithm will take linear time to complete.

In summary, Big O provides an upper limit (worst-case), Big Omega provides a lower limit (best-case), and Big Theta provides both an upper and lower limit (average-case) on the time complexity of an algorithm.