What is the time complexity of the Quick Sort algorithm in the worst case? Question 20Select one: O(n^2) O(n) O(n log n) O(2^n)

Breakdown of the Problem

1. Identify the algorithm in question (Quick Sort).
2. Understand the concept of time complexity and seek the worst-case scenario for Quick Sort.

Relevant Concepts

3. Quick Sort is a divide-and-conquer algorithm that sorts an array or a list by selecting a 'pivot' element and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot.

Analysis and Detail

4. In the worst-case scenario for Quick Sort, the pivot selected is always either the smallest or the largest element. This leads to unbalanced partitions:
   • For instance, if the pivot is the smallest element, then one partition will have $n - 1$ elements and the other partition will have $0$ elements.
   • This results in recursive calls that take $n + (n - 1) + (n - 2) + ... + 1$ which simplifies to $O(n^2)$.

Verify and Summarize

5. The time complexity of Quick Sort in the worst case is verified to be $O(n^2)$. This can be consistently observed through the worst-case analysis.

Final Answer

The time complexity of the Quick Sort algorithm in the worst case is O(n²).