Question

quick sort is an unstable sorting method. give a simple example of input array to demonstrate that the partition() function in our textbook does not perserve the original order of equal keys

Answer 1

Quick Sort is an unstable sorting method that does not always preserve the original order of equal keys. An example with an array [2, 9, 3, 5, 3] can demonstrate that, depending on pivot selection, the order of equal keys such as '3' may change after sorting.

Step-by-step explanation:

The Quick Sort algorithm is indeed an unstable sorting method, which means that it does not always preserve the relative order of equal elements. An example that illustrates this behavior involves the partition function of Quick Sort.

Let's consider an input array of integers: [2, 9, 3, 5, 3]. If we select the first element as a pivot, Quick Sort could rearrange the elements into [2, 3, 3, 9, 5]. Notice that the two '3's maintain their original order.

However, if we select '5' as the pivot (the choice of pivot can vary), the array might be rearranged to [3, 2, 3, 5, 9], where the original order of the '3's has been altered during partitioning. This change in their order shows that Quick Sort does not guarantee the stability of sorting equal keys.