Question

Write a program that merges two ordered list objects of integers into a single ordered-list object of integers. Method merge of class ListMerge should receive references to each of the list objects to be merged and return a reference to the merged list object.

Short answer

Merge the lists using a function that compares elements with two index pointers, then append remaining elements.

Step-by-step solution

Initialize the Lists

Start by creating two predetermined sorted lists of integers. For example, let's have the lists `list1 = [1, 3, 5, 7]` and `list2 = [2, 4, 6, 8]`. These lists must be sorted prior to the merging process.

Define the Merge Function

Define a new function `merge_lists` that will take two input lists as parameters. The purpose of this function is to merge the two lists while maintaining order.

Prepare for Merging

Inside `merge_lists`, initialize an empty list `merged_list` to store the result of the merge. Also, create two pointers or indices, `i` and `j`, both starting at 0. These pointers will help track positions in `list1` and `list2` respectively.

Iterative Merging Process

Use a `while` loop to iterate through both lists until one of the indices, `i` or `j`, reaches the end of its corresponding list. Inside the loop, compare the current elements from `list1` and `list2`. Append the smaller element to `merged_list` and increment its corresponding index (`i` or `j`).

Append Remaining Elements

After one list is completely traversed, there may be remaining elements left in the other list. Append these remaining elements to `merged_list`. You can do this using slicing, such as `merged_list.extend(list1[i:])` or `merged_list.extend(list2[j:])`.

Return the Merged List

Finally, return `merged_list` from the function `merge_lists`. This list is the merged version of the original input lists.

Test the Function

Call the function `merge_lists(list1, list2)` and store the result. For our example lists, the output should be `[1, 2, 3, 4, 5, 6, 7, 8]`. Print the result to verify correctness.

Key concepts

list merging

List merging is an essential concept in Java programming, especially when dealing with sorted arrays or lists. It involves creating a new list from two or more existing lists, ensuring that the resulting list maintains a specific order, often ascending or descending. To merge lists in an efficient manner, we generally keep track of current positions in each of the lists with pointers or indices.

During the merging process, we compare current elements pointed to by each index and append the smaller element to the new list. This step-by-step comparison ensures that the final merged list retains the sorted order of the input lists. Once we've finished the initial merging loop, any remaining elements in the lists can be appended directly as they are already in order.

When implementing list merging in Java, it's advantageous to utilize methods that automatically handle basic list operations, such as appending elements, which simplifies the task and enhances readability.

algorithm design

Designing an algorithm for list merging involves piecing together a clear, step-by-step method to reach an effective solution. The first step in designing such an algorithm is to identify the problem, which in this context is merging two ordered lists into a single ordered list. A good algorithm design ensures that your solution is both correct and efficient.

Here, our algorithm follows a structured approach:

• Begin with initializing the two lists you want to merge.
• Create a function to handle the merging logic.
• Implement pointers to track positions in the lists.
• Run a loop to compare and merge elements until one list is exhausted.
• Finally, append any remaining elements from the other list.

In this case, the algorithm is particularly efficient due to its linear time complexity, denoted as \(O(n + m)\) where \(n\) and \(m\) are the lengths of the lists. This is because each element from both lists is processed exactly once.

Java methods

In Java, methods are blocks of code that perform specific tasks and can be executed when called upon. They help in organizing code into reusable blocks, making the program easier to read, debug, and maintain. When writing a program to merge lists, defining a Java method is an efficient way to encapsulate the merging logic.

The `merge_lists` method in our context takes two arguments, namely the lists that need merging. It returns the result, which is the merged list, back to the caller. This encapsulation allows for the reusability of the merge operation whenever it's needed without rewriting the logic each time.

In practice, Java methods are defined using the `public`, `private`, `protected`, or `default` access modifiers depending on their intended visibility scope. Here, the merging method might be designed as a `public static` method if it doesn't rely on instantiating any class objects.

ordered lists

Ordered lists are collections of elements that maintain a specific sequence, usually numerical or alphabetical. In Java programming, ordered lists can be implemented using arrays or Java's List interface. The main characteristic of an ordered list is that its elements are arranged based on a defined ordering criterion.

When merging ordered lists, it's crucial to maintain the sort order to ensure the integrity of the data structure. This ordered property allows for the efficient merging using the two-pointer technique as previously discussed. Since the individual lists are already sorted, inserting elements into the merged list only involves comparing elements from the heads of each remaining sublist, ensuring the least element is picked next.

Understanding ordered lists is fundamental for operations such as binary search or efficient data retrieval and manipulation, making it an essential topic when learning about data structures in Java.