What is the time complexity of a binary search algorithm on a sorted array?

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Question: What is the time complexity of a binary search algorithm on a sorted array?

Options:

Correct Answer: O(log n)

Solution:

The time complexity of binary search on a sorted array is O(log n) because it repeatedly divides the search interval in half.

What is the time complexity of a binary search algorithm on a sorted array?

What is the time complexity of a binary search algorithm on a sorted array?

Step 1: Understand that binary search is used on a sorted array.
Step 2: Start with the entire array as the search interval.
Step 3: Find the middle element of the current search interval.
Step 4: Compare the middle element with the target value you are searching for.
Step 5: If the middle element is equal to the target, you found it! If not, decide which half of the array to search next.
Step 6: If the target is less than the middle element, narrow the search to the left half. If it's greater, narrow it to the right half.
Step 7: Repeat steps 3 to 6 until you find the target or the search interval is empty.
Step 8: Each time you narrow the search interval, you are effectively dividing the number of elements to search by 2.
Step 9: This division by 2 leads to a logarithmic time complexity, which is expressed as O(log n).

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