Asymptotic Notations for Algorithm Analysis summary

Asymptotic Notations for Algorithm Analysis

Comparing Algorithm Efficiency using Asymptotic Notations

Definition and Importance of Big O, Big Ω and Big Θ

 Big O (O): Upper bound of an algorithm's time complexity in the worst-case scenario.

 Example: O(n) for linear search

 Big Ω (Ω): Lower bound of an algorithm's time complexity in the best-case scenario.

 Example: Ω(n) for linear search

 Big Θ (Θ): Tight bound of an algorithm's time complexity when both upper and lower bounds
are the same function.

 Example: Θ(n) for linear search

Importance of Big Theta (Θ)

 Provides a tighter bound from above and below

 Gives a better picture of an algorithm's runtime

 Θ-notation is preferred in interviews or tests when reporting an algorithm's efficiency

Graphical illustration

 Visualizing big-O, big-Θ, and big-Ω through graphs can provide insights into selecting the best
asymptotic notation for a given function

Asymptotic notation properties

 Understanding the properties of the three notations is crucial for efficient problem-solving
during technical interviews

Time complexity

 Analyzing the time complexity of algorithms helps determine the best big-Θ answer