Sorting Algorithm Efficiency Quiz: Big-O Showdown! Quiz

Challenge your understanding of sorting algorithms and their Big-O time complexities with this focused quiz. Explore key differences between popular sorting methods, efficiency in common scenarios, and foundational Big-O concepts useful for computer science and coding interviews.

1. Quick Sort Average Case Complexity

   What is the average-case time complexity of Quick Sort when sorting an unsorted array of distinct integers, such as [3, 1, 4, 2, 5]?

   1. O(n log n)
   2. O(log n)
   3. O(n^2)
   4. O(n^3)

   Explanation: Quick Sort has an average-case time complexity of O(n log n) due to recursive partitioning, which divides the problem efficiently. O(n^2) represents its worst-case, which happens rarely when pivots are chosen poorly; O(log n) does not account for all element comparisons; and O(n^3) is overly pessimistic and not applicable to Quick Sort's design.

2. Best Case for Insertion Sort

   When sorting an already sorted array (like [1, 2, 3, 4, 5]) using Insertion Sort, what is the best-case time complexity?

   1. O(n log n)
   2. O(n^2)
   3. O(log n)
   4. O(n)

   Explanation: Insertion Sort achieves O(n) time complexity in the best case when the array is already sorted, making only one pass through without shifting elements. O(n^2) is its general or worst-case time, O(log n) is too optimistic and only applicable to certain cases like binary search, and O(n log n) is not attainable for Insertion Sort.

3. Merge Sort Efficiency

   Which sorting algorithm guarantees O(n log n) time complexity in both the best and worst cases, regardless of the initial order of elements?

   1. Bubble Sort
   2. Stooge Sort
   3. Selection Sort
   4. Merge Sort

   Explanation: Merge Sort reliably provides O(n log n) time in any scenario due to its divide-and-conquer approach. Bubble Sort and Selection Sort have O(n^2) worst-case times, making them slower as the dataset grows. Stooge Sort is an intentionally inefficient algorithm with much worse complexity, not practical for real use.

4. Space Complexity of Merge Sort

   What is the auxiliary space complexity of Merge Sort when sorting an array like [8, 4, 7, 3] in standard implementations?

   1. O(log n)
   2. O(1)
   3. O(n)
   4. O(n^2)

   Explanation: Merge Sort needs O(n) extra space because it requires temporary arrays during the merge process. O(1) would indicate an in-place algorithm, which standard Merge Sort is not; O(log n) corresponds to the recursion depth but not the space for data; O(n^2) overestimates the space Merge Sort requires.

5. Efficient Choice for Nearly Sorted Data

   For an input array that is almost sorted, such as [1, 2, 4, 3, 5], which algorithm generally sorts the data most efficiently in practice?

   1. Insertion Sort
   2. Shell Sort
   3. Bubble Sorted
   4. Heap Sort

   Explanation: Insertion Sort is particularly efficient for nearly sorted data, performing close to linear time. Heap Sort maintains O(n log n) regardless and doesn't take advantage of existing order. 'Bubble Sorted' is not the correct name for the algorithm (the term should be Bubble Sort), and Bubble Sort is still less efficient than Insertion Sort in this case. Shell Sort improves on Insertion but isn't as efficient for small deviations.