Which sorting algorithm is known as a partition and exchange sort?
a) Selection Sort
b) Merge Sort
c) Quick Sort
d) Bubble Sort
The correct answer and explanation is :
The correct answer is c) Quick Sort.
Explanation:
Quick Sort is a well-known “partition and exchange” sorting algorithm, often celebrated for its efficiency in sorting large datasets. It is based on the divide-and-conquer principle, where the problem is recursively divided into smaller subproblems, sorted independently, and then combined to yield the final sorted list.
Here’s how Quick Sort works and why it’s considered a partition and exchange sort:
- Partitioning: Quick Sort begins by selecting a ‘pivot’ element from the array. The choice of pivot can vary (it could be the first, last, or middle element, or even a random element). Once the pivot is chosen, the array is partitioned into two subarrays: one containing elements smaller than the pivot and the other containing elements larger than the pivot. The pivot itself is then placed in its correct position in the sorted array, as every element on the left side is smaller and every element on the right side is larger.
- Exchanging: The partitioning step involves exchanging elements to place them in the correct relative order with respect to the pivot. The idea is to “exchange” elements so that elements less than the pivot end up on the left side, and elements greater than the pivot end up on the right. The pivot element is not exchanged during the partition step; it simply ends up in its correct position after all elements have been rearranged.
- Recursion: After partitioning the array around the pivot, Quick Sort recursively sorts the subarrays to the left and right of the pivot. This recursive process continues until the entire array is sorted.
Quick Sort is considered efficient because, on average, its time complexity is $O(n \log n)$. In the worst-case scenario (when the pivot always ends up being the smallest or largest element), its time complexity can degrade to $O(n^2)$, but this can be mitigated by using randomized or median-of-three pivot selection strategies.
Thus, Quick Sort’s partitioning and exchanging mechanism is the key reason it is often referred to as a “partition and exchange” sort.