If the size of the array is doubled, how does the time complexity of binary sear

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Question: If the size of the array is doubled, how does the time complexity of binary search change?

Options:

Correct Answer: It remains the same

Solution:

The time complexity of binary search is O(log n), which does not change with the size of the array.

If the size of the array is doubled, how does the time complexity of binary search change?

If the size of the array is doubled, how does the time complexity of binary search change?

Step 1: Understand what binary search is. It is a method to find an item in a sorted array by repeatedly dividing the search interval in half.
Step 2: Know the time complexity of binary search. It is O(log n), where n is the number of elements in the array.
Step 3: Recognize that 'doubling the size of the array' means if the original array has n elements, the new array will have 2n elements.
Step 4: Calculate the new time complexity. For the new array size of 2n, the time complexity will be O(log(2n)).
Step 5: Simplify O(log(2n)). This can be rewritten as O(log 2 + log n). Since log 2 is a constant, it does not affect the overall complexity.
Step 6: Conclude that the time complexity remains O(log n) because adding a constant does not change the big O notation.

Time Complexity – Understanding how the time complexity of algorithms, such as binary search, is affected by the size of the input data.
Binary Search – A search algorithm that finds the position of a target value within a sorted array, operating in logarithmic time.