Question

Big-O Notation of: f(n) = n^2 + 100n + log(n) + 1000

a. O(n)
b. O(n log n)
c. O(n^2)
d. O(log n)

Answer 1

The Big-O Notation of the function f(n) = n^2 + 100n + log(n) + 1000 is O(n^2), which is determined by the term with the highest growth rate, n^2, ignoring lower-order terms and constants.

Step-by-step explanation:

The Big-O Notation of the function f(n) = n^2 + 100n + log(n) + 1000 is used to describe the upper bound of the complexity of an algorithm in terms of the size of the input, n. To determine the Big-O Notation, we look for the term with the highest growth rate as n approaches infinity. In this case, the term n^2 grows faster than n, log(n), or any constant like 1000.

Therefore, we can disregard the lower-order terms and the constant, focusing only on the term with the highest growth rate, which is n^2. The Big-O Notation for f(n) = n^2 + 100n + log(n) + 1000 is O(n^2), which represents the function's time complexity as n grows large.