Algorithm Time Complexity in Big Theta: Solving an Asymptotic Analysis Problem

[GeorgeCostanz]

Homework Statement

i've been asked to find the asymptotic time complexity of an algorithm in Big Theta

78045522000 + n$^{2}$log$^{3}$n + n$^{3}$logn + 200n + 45$^{n}$

Homework Equations

The Attempt at a Solution

from my understanding Big Theta is a tight/exact bound, but I'm not sure how to write the proper answer.

i came to the conclusion it's = Big Theta(n$^{2}$log$^{3}$n + n$^{3}$logn + 200n + 45$^{n}$) (removing constants, including both upper and lower bounds)

i'd appreciate it if someone could let me kno how wrong I am and set me on the right track

 

[KataKoniK]

.



it is important to provide a clear and accurate response to this forum post. Firstly, you are correct in your understanding that Big Theta is a tight or exact bound for the time complexity of an algorithm. In this case, the asymptotic time complexity can be written as Big Theta of the highest order term, which in this case is 45^{n}. This means that the algorithm has a time complexity of O(45^{n}), where n is the size of the input. It is important to note that this is an exponential time complexity, which means that as the input size increases, the time taken by the algorithm will increase at a much faster rate. This can lead to long processing times and is something to consider when analyzing the efficiency of the algorithm. Additionally, it is important to mention that constants and lower order terms are typically ignored when determining the time complexity in Big Theta notation, so the final answer would be Big Theta(45^{n}). I hope this helps to clarify the concept of asymptotic time complexity and how it applies to the given algorithm.