Welcome, aspiring programmer! Today's topic is Merge Sort. Merge Sort is a sorting technique reminiscent of organizing a shuffled deck of cards in order. For large-scale data, Merge Sort can outperform typical techniques. Today, we'll explore Merge Sort, code it in Ruby, and analyze its efficiency. Ready? Let's get started!

In computer science, Merge Sort is a popular method to sort elements. Merge Sort uses the 'divide-and-conquer' strategy similar to the Quick Sort algorithm. The three main steps of Merge Sort are:

1. Split the array into halves.
2. Sort each half separately.
3. Merge the sorted halves back together.

We will begin by building code for merging two sorted parts. The merge process involves comparing elements from two halves and merging them so the resulting list is sorted.

Let's code a merge function in Ruby to achieve this. We will make use of Ruby's Array operations and slice capabilities.

Ruby
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1def merge(arr, left, mid, right)
2  # Split the array into a left and a right part
3  left_array = arr[left..mid]
4  right_array = arr[mid+1..right]
5
6  # Initialize indices for merging
7  i, j, k = 0, 0, left
8
9  # Merge left and right arrays
10  while i < left_array.size && j < right_array.size
11    # Compare and pick smaller element
12    if left_array[i] <= right_array[j]
13      arr[k] = left_array[i] # Copy from left part
14      i += 1
15    else
16      arr[k] = right_array[j] # Copy from right part
17      j += 1
18    end
19    k += 1 # Move to next index
20  end

Here, we've divided our original list into two halves, left_array and right_array.

Now, we'll sort and merge these halves:

Ruby
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1  while i < left_array.size
2    arr[k] = left_array[i]
3    i += 1
4    k += 1
5  end
6
7  while j < right_array.size
8    arr[k] = right_array[j]
9    j += 1
10    k += 1
11  end
12end

This code places two pointers, i and j, at the beginning of the left_array and right_array. It selects the smaller element, places it in the final array arr, and moves the corresponding pointer onward. This continues until all elements are merged.

Once one of the pointers reaches the end of its array, some elements might be left in the other array. To handle this, let's copy the remaining elements of both arrays (if any) to the end of the resulting arr array.

Now, let's implement the method to divide the array into two halves. Coding-wise, we'll define a sort method that will recursively split the array and manage the merge process. We will split the array into smaller arrays until they contain only one element, which is naturally sorted, and then merge them back together.

Let's start creating the sort method. Initially, we'll handle the splitting part:

Ruby
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1def sort(arr, left, right)
2  if left < right
3    mid = (left + right) / 2
4    
5    # Sorting the first and second halves
6    sort(arr, left, mid)
7    sort(arr, mid + 1, right)
8
9    # Merging the sorted halves
10    merge(arr, left, mid, right)
11  end
12end

The above code will split our list into two halves, sort them, and then merge them together.

Here is the full implementation of the Merge Sort algorithm in Ruby:

Ruby
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1def sort(arr, left, right)
2  if left < right
3    mid = (left + right) / 2
4
5    # Recursively sort the first and second halves
6    sort(arr, left, mid)
7    sort(arr, mid + 1, right)
8
9    # Merge the sorted halves
10    merge(arr, left, mid, right)
11  end
12end
13
14def merge(arr, left, mid, right)
15  left_array = arr[left..mid]
16  right_array = arr[mid+1..right]
17
18  i, j, k = 0, 0, left
19
20  while i < left_array.size && j < right_array.size
21    if left_array[i] <= right_array[j]
22      arr[k] = left_array[i]
23      i += 1
24    else
25      arr[k] = right_array[j]
26      j += 1
27    end
28    k += 1
29  end
30
31  while i < left_array.size
32    arr[k] = left_array[i]
33    i += 1
34    k += 1
35  end
36
37  while j < right_array.size
38    arr[k] = right_array[j]
39    j += 1
40    k += 1
41  end
42end
43
44# Example to demonstrate merge sort
45arr = [38, 27, 43, 3, 9, 82, 10]
46sort(arr, 0, arr.length - 1)
47puts "Sorted array: #{arr}" # Output: Sorted array: [3, 9, 10, 27, 38, 43, 82]

In the computing world, performance is vital. Faster sorting means a more efficient algorithm. Merge Sort boasts a time complexity of O(n log n), making it ideal for sorting huge data sets quickly.

Merge Sort is consistent. It offers stable and predictable performance, which is crucial when dealing with large and unordered datasets. However, its memory usage can be a downside, as it creates new arrays during the merge process.

Great job! We've broken down Merge Sort and coded it in Ruby. Next up, we have some exciting hands-on exercises for you. Ready to put what you've learned into practice? Let's dive into the fun part! Let's get coding!