What is the time complexity of quicksort in the average case?

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

Options:

Correct Answer: O(n log n)

Solution:

Quicksort has an average-case time complexity of O(n log n) due to the divide-and-conquer approach.

What is the time complexity of quicksort in the average case?

What is the time complexity of quicksort in the average case?

Step 1: Understand what quicksort is. Quicksort is a sorting algorithm that sorts an array or list by dividing it into smaller parts.
Step 2: Learn about the divide-and-conquer approach. This means quicksort divides the list into two smaller lists based on a 'pivot' element.
Step 3: Know that in the average case, quicksort divides the list into two roughly equal parts. This helps in balancing the work done.
Step 4: Realize that each division takes linear time, O(n), because you have to look at each element to place it in the correct part.
Step 5: Understand that the number of times you can divide the list is logarithmic, O(log n), because you keep halving the size of the list.
Step 6: Combine the two parts: Since you do O(n) work for each of the O(log n) divisions, you multiply them together.
Step 7: Conclude that the average-case time complexity of quicksort is O(n log n).

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