Question

Define a recursive function merge, which takes two sorted lists of numbers, and returns one merged list where all numbers are sorted in decreasing order. Assume that all elements are sorted in decreasing order

Answer 1

A recursive function to merge two sorted lists in decreasing order adds the larger of the leading elements from each list to a new list, then recursively calls itself with the remainder of the list. This process repeats until one list is empty, returning the non-empty list as the result.

Step-by-step explanation:

To define a recursive function named merge that takes two sorted lists of numbers and returns a single merged list in decreasing order, we consider the following steps:

• Check if any of the lists are empty. If so, return the non-empty list, as it is already sorted in decreasing order.
• Compare the first elements (which are the largest due to decreasing order sorting) of each list.
• Add the larger element to the merged list and proceed recursively with the rest of that list and the other list unchanged.
• Continue until all elements are merged into one list, which will be sorted in decreasing order.

Here is a Python function exemplifying the above logic:

def merge(list1, list2):
if not list1: # if first list is empty
return list2
if not list2: # if second list is empty
return list1
if list1[0] > list2[0]:
return [list1[0]] + merge(list1[1:], list2)
else:
return [list2[0]] + merge(list1, list2[1:])

The recursive function will continually reduce the size of one list until all elements have been merged into the resulting list, which will be sorted in decreasing order.