What is the time complexity of merging two sorted lists?

Merging two sorted lists is an efficient operation that combines both lists into a single sorted list. To understand why the time complexity is O(n + m), consider what happens during the merge process.

When merging, you start from the beginning of both sorted lists and compare the first elements of each list. You then add the smaller of the two elements to the new merged list and advance the pointer in that list. This process continues until you reach the end of one of the lists, at which point you can append the remainder of the other list (which is already sorted) to the merged list.

Let's break this down:

• If the first list has 'n' elements and the second list has 'm' elements, you will make a total of 'n + m' comparisons and data moves in the worst case. This is because, in the worst case, you may need to examine every element from both lists to create a fully merged list.

• Each comparison and element move is done in constant time, O(1), making the overall time for the merging operation proportional to the size of the input lists combined.

Thus, the time complexity of merging two sorted lists is O(n + m), as it accounts for each element being processed once