Question

Modify the merge sort algorithm to sort a list in descending order.

Short answer

Sort sublists as normal, modify the merge to compare for larger values, ensuring descending order.

Step-by-step solution

Understand Merge Sort

Merge Sort is a divide-and-conquer algorithm that divides the list into smaller sublists, sorts these sublists, and then merges them back together to form the sorted list. The key steps are splitting the list, sorting each half recursively, and then merging the sorted halves.

Splitting the List

To modify merge sort for descending order, we start by continuing to split the list into two halves recursively until each sublist contains a single element. In the original algorithm, this splitting process is the same for both ascending and descending order sorts.

Modify the Merging Process

In the merging process of the original algorithm, two sorted halves are merged in ascending order by comparing the smallest elements of each half. To sort in descending order, compare the largest elements of each half instead. If the element from the first half is larger, place it in the result first, otherwise place the element from the second half.

Implement Recursive Sorting

Implement the recursive function that continues to call itself with each half of the list until reaching single-element sublists. Ensure that when the merge function is called at each level, it follows the modified descending order merging logic.

Execute and Verify

Run this modified merge sort on a test list. Verify each step, ensuring that the final list is sorted in descending order. Print intermediate steps if necessary to check the process is correctly implemented.

Key concepts

Descending Order

To sort a list in descending order means arranging the elements from the highest to the lowest. This is the reverse of ascending order, where elements are sorted from smallest to largest. When modifying merge sort for descending order, the key change happens during the merging process. Instead of placing smaller elements before larger ones, you place larger elements first.
This switch in priorities ensures that the result is ordered from largest to smallest.
The rest of the sorting logic, such as dividing the list and recursively sorting each part, remains the same regardless of whether you are sorting in ascending or descending order.

Divide-and-Conquer Algorithm

The divide-and-conquer algorithm is a fundamental strategy in computer science. It involves three main steps: dividing a problem into subproblems, solving each subproblem recursively, and combining their solutions to address the original problem.
Merge sort perfectly demonstrates this approach. It splits the list into smaller sublists until each contains a single element, which is inherently sorted.

• **Divide**: Break the list into two halves.
• **Conquer**: Recursively sort each half.
• **Combine**: Merge the sorted halves back together.

Using this strategy, complex problems like sorting can be more manageable and systematic to solve.

Recursive Function

A recursive function is a function that calls itself with a reduced version of the original problem as its argument. In merge sort, the recursive function repeatedly divides a list into two smaller sublists. This recursion continues until each sublist reaches the simplest case of a single element.
Recursive functions are pivotal as they allow complex problems to be broken into smaller, more manageable problems. In the modified merge sort for descending order, the recursive function must ensure each sublist is sorted before being merged back together in the correct order. Understanding how recursion works in dividing and handling each half of the list is crucial for implementing merge sort successfully.

Merging Process

The merging process is a critical step in merge sort, where two sorted lists are combined into a single sorted list. When sorting in descending order, the principle is to always select the larger element from the two lists for placement in the result.
Let's outline how this effectively works:

• Compare the first elements of each sorted sublist.
• Select the larger element to be added to the result list.
• Move to the next element in the list from where the larger element was selected.
• Repeat until all elements are merged into the result list.

This careful comparison and selection ensure that the merged list maintains the desired order, either descending or ascending, based on the logic applied.