What is the time complexity (worst case) of a binary search in an array of size n?O(n^2)O(log(n))O(1)O(n!)

1. ### Break Down the Problem

The question requires us to determine the worst-case time complexity of a binary search algorithm in an array of size $n$.

2. ### Relevant Concepts

• The binary search algorithm works by dividing the search interval in half. It compares the target value to the middle element of the array and eliminates half of the search space with each comparison.
• The time complexity of binary search can be expressed as $O(\log n)$ since each step reduces the problem size by half.

3. ### Analysis and Detail

1. The number of times we can divide $n$ by 2 until we reach 1 is expressed as $\log_2(n)$.
2. Thus, the worst-case scenario occurs when we need to continue comparing through multiple iterations until we locate the target or conclude its absence.

4. ### Verify and Summarize

• Other options were: $O(n^2)$, $O(1)$, and $O(n!)$, all of which are not applicable to binary search.
• The verified time complexity of binary search in the worst case is consistently $O(\log n)$.

Final Answer

The time complexity (worst case) of a binary search in an array of size $n$ is $O(\log n)$.