An algorithm iterates 10 times for an input of size n. What is the best-case time complexity?Group of answer choicesO(n)O(1)O(n^10)O(log n)

Break Down the Problem

1. Identify the key components of the algorithm: the number of iterations (10) and the input size (n).
2. Determine how these components affect the algorithm's performance.

Relevant Concepts

1. Time complexity generally describes how the runtime of an algorithm grows relative to the input size.
2. The best-case time complexity reflects the scenario where the algorithm performs the least amount of work.

Analysis and Detail

Since the algorithm iterates a constant number of times (10) regardless of the input size $n$, this indicates a fixed overhead. The time taken does not depend on $n$, which means that in the best case, the algorithm operates in constant time. Thus, the time complexity can be expressed as:

$T(n) = O(1)$

Verify and Summarize

The choices provided are as follows:

• $O(n)$
• $O(1)$
• $O(n^{10})$
• $O(\log n)$

Given that the time complexity is $O(1)$, this aligns with our analysis that the number of iterations does not change with varying input sizes.

Final Answer

The best-case time complexity is $O(1)$.