Question

Which of the following sorting algorithms is the most efficient in the average case?

• A. Bubble Sort
• B. Selection Sort
• C. Quick Sort
• D. Insertion Sort

Hint:

When comparing algorithm efficiency, remember the hierarchy of common complexities (from best to worst): O(1) > O(log n) > O(n) > O(n log n) > O(n$^2$) > O(2$^n$). Algorithms with O(n log n) complexity are generally considered very efficient for sorting.

Answer 1

The Correct Option is C

Let's compare the average-case time complexities of the given sorting algorithms:
(A) Bubble Sort: Has an average-case time complexity of O(n$^2$). It is generally inefficient for large datasets.
(B) Selection Sort: Has an average-case time complexity of O(n$^2$). Its performance does not change significantly based on the initial order of the data.
(D) Insertion Sort: Has an average-case time complexity of O(n$^2$). However, it is very efficient for small or nearly sorted datasets, with a best-case complexity of O(n).
(C) Quick Sort: Has an average-case time complexity of O(n log n). This is significantly more efficient than O(n$^2$) for large datasets. Although it has a worst-case complexity of O(n$^2$), this is rare in practice with good pivot selection strategies.
Comparing the complexities, O(n log n) is much more efficient than O(n$^2$). Therefore, Quick Sort is the most efficient in the average case among the options provided.