What is the time complexity of the quicksort algorithm in the worst case?

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Question: What is the time complexity of the quicksort algorithm in the worst case?

Options:

Correct Answer: O(n^2)

Solution:

In the worst case, quicksort can degrade to O(n^2) time complexity, typically when the pivot is the smallest or largest element.

What is the time complexity of the quicksort algorithm in the worst case?

What is the time complexity of the quicksort algorithm in the worst case?

Step 1: Understand what quicksort is. It is a sorting algorithm that works by selecting a 'pivot' element and partitioning the array into two parts: elements less than the pivot and elements greater than the pivot.
Step 2: Know that the efficiency of quicksort depends on how well the pivot divides the array. Ideally, the pivot should split the array into two equal halves.
Step 3: Recognize the worst-case scenario. This happens when the pivot chosen is either the smallest or largest element in the array, leading to unbalanced partitions.
Step 4: In the worst case, one partition will have n-1 elements and the other will have 0 elements, causing the algorithm to perform n comparisons for the first partition, n-1 for the second, and so on.
Step 5: Calculate the total number of comparisons. This results in a series of comparisons that add up to n + (n-1) + (n-2) + ... + 1, which equals n(n-1)/2.
Step 6: Simplify the expression. The dominant term is n^2, so we express the time complexity as O(n^2).
Step 7: Conclude that the worst-case time complexity of quicksort is O(n^2).

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