Question

Give two instances for which Quicksort algorithm is the most appropriate choice.

Short answer

Quicksort is most appropriate when data is in memory, as it has good cache performance and when average-case performance is more important than worst-case performance, specifically for numeric data that has a random order.

Step-by-step solution

Understanding Quicksort Algorithm

Quicksort is a divide and conquer algorithm, which involves partitioning an array of data into smaller arrays. A 'pivot' element is chosen from the array. The remaining elements are split into two subsets, according to whether they are less than or greater than the pivot. The process is recursively applied to the smaller arrays.

Performance of Quicksort Algorithm

The average and best case time complexity of Quicksort is \(O(n log n)\), where 'n' is the number of elements. This makes Quicksort one of the fastest sorting algorithms, especially for large datasets. However, the worst-case scenario for Quicksort is \(O(n^2)\), which can happen when the pivot is the smallest or the largest element in the array.

First Instance for Choosing Quicksort

Quicksort is best suited when the data is in memory. This is because Quicksort has a good cache performance due to the locality of reference. For example, when sorting a large array that fits into memory, Quicksort would be an appropriate choice.

Second Instance for Choosing Quicksort

Quicksort is also a good choice when average-case performance matters more than the worst-case performance, and when it's important that the original ordering of equal elements is not preserved (i.e., Quicksort is not a stable sort). For instance, in practice, Quicksort is often the algorithm of choice for numeric datatypes that have a random order.