Question

Write a program that merges two ordered list objects of integers into a single ordered list object of integers. Function merge should receive references to each of the list objects to be merged and reference to a list object into which the merged elements will be placed.

Short answer

Merge by comparing elements and use pointers to form a single ordered list.

Step-by-step solution

Understanding the Problem

We need to merge two sorted lists of integers into a single sorted list. The function will take three arguments: two references to the original lists and one reference to the list where the merged result will be stored.

Initialize Pointers

Initialize two pointers to track the current elements of each list. Start both pointers at the first element of each list.

Compare Elements

Compare the elements pointed to by the pointers from both lists. Since both lists are ordered, add the smaller element to the merged list and move the pointer of that list forward.

Handle Remaining Elements

When the end of one list is reached, append all remaining elements from the other list to the merged list. This is necessary to ensure all elements are included in the merged list.

Code Implementation

Implement the above steps in a programming language like Python. For example: ```python def merge(list1, list2, merged_list): i, j = 0, 0 while i < len(list1) and j < len(list2): if list1[i] < list2[j]: merged_list.append(list1[i]) i += 1 else: merged_list.append(list2[j]) j += 1 while i < len(list1): merged_list.append(list1[i]) i += 1 while j < len(list2): merged_list.append(list2[j]) j += 1 ``` This code will merge two ordered lists and store the result in the third list.

Test the Function

Test the function with different ordered input lists to ensure correctness. For example, merge([1, 3, 5], [2, 4, 6], []) should output [1, 2, 3, 4, 5, 6].

Key concepts

List Merging

List merging is a common task in computer science. It involves combining two or more ordered lists into a single ordered list. In this context, ordered means the list elements are sorted in a particular sequence, usually ascending or descending.

When merging:

• Start with two sorted lists, such as [1, 3, 5] and [2, 4, 6].
• Compare the smallest (or largest, depending on sorting order) elements of each list.
• Add the smaller element from the two lists to the new merged list.
• Advance in the list where the element was taken from, and repeat the comparison.

Continue this process until one of the lists is completely added to the merged list. After that, simply append the remaining elements of the other list.

This approach efficiently utilizes the fact that both input lists are already sorted, which minimizes the number of required comparisons.

Algorithm Design

Algorithm design refers to the methodical approach of solving problems using a sequence of computational steps. An effective algorithm should be clear, efficient, and easy to implement. The merging algorithm is a classical example of careful algorithm design.

Here's how an algorithm for merging works:

• Define what input is needed: two ordered lists and a third list to hold the output.
• Set up initial conditions: use variables (or pointers) to track which element is considered in each list.
• Iteratively perform operations: repeatedly compare and place elements into the result list.
• Ensure completion: handle any remaining elements after one list is finished.

This process emphasizes efficiency, ensuring the ordered nature of the input lists speeds up the merging operation significantly, compared to starting from two unordered lists. Good algorithm design like this keeps operations minimal and leverages existing order to optimize performance.

Pointers

Pointers are fundamental in algorithm design, especially when dealing with lists and arrays. Rather than simply elements in lists, pointers are variables that "point" to the location of data in memory.

In the context of list merging:

• Pointers are used to track the current position in both lists being merged.
• Each pointer starts at the beginning (first element) of a list.
• As elements are merged, the pointer for that list moves to the next element.

This is efficient because pointers replace the "brute-force" method of checking all elements at every step. Instead, they maintain only necessary information about the list’s position, naturally leading to a reduction in the computational complexity.

In advanced data structures or languages, pointers might also be used as actual memory address references, which can significantly affect how data is accessed and manipulated, though in high-level languages such as Python, this is abstracted into index-tracking.