Python Coding Test Course, Merge Sort

Hello! Today, we will take an in-depth look at the Merge Sort algorithm, which is frequently asked in Python coding tests. Merge Sort is one of the sorting algorithms that uses the divide and conquer method to sort data. Since sorting is a crucial process in data processing, understanding and implementing this algorithm will greatly help in coding tests as well as in actual development.

What is Merge Sort?

Merge Sort works by recursively dividing the list, sorting the divided lists, and then merging them back together. The process for Merge Sort is as follows:

  1. Divide the list into halves.
  2. Recursively perform merge sort on each sublist.
  3. Merge the two sorted sublists into one sorted list.

The characteristic of Merge Sort is that it is a stable sort algorithm, and its time complexity is O(n log n), making it very efficient. Furthermore, it guarantees a performance of O(n log n) even in the worst case, making it useful for sorting large datasets.

Time Complexity of Merge Sort

Analyzing the time complexity of Merge Sort gives us the following results:

  • When the size of the input array is n, the time required to divide the array into two parts is O(1).
  • Since merge sort is called recursively on each part, the depth will be log n.
  • The merging stage requires O(n) time to combine the two sublists into one.

Thus, the overall time complexity is O(n log n). Additionally, Merge Sort requires O(n) of memory space.

Implementing Merge Sort

Now let’s implement Merge Sort in Python. The code below implements Merge Sort:

def merge_sort(array):
    if len(array) <= 1:
        return array

    mid = len(array) // 2
    left_half = merge_sort(array[:mid])
    right_half = merge_sort(array[mid:])

    return merge(left_half, right_half)

def merge(left, right):
    result = []
    left_index, right_index = 0, 0

    while left_index < len(left) and right_index < len(right):
        if left[left_index] <= right[right_index]:
            result.append(left[left_index])
            left_index += 1
        else:
            result.append(right[right_index])
            right_index += 1

    result.extend(left[left_index:])
    result.extend(right[right_index:])
    
    return result

# Example usage
array = [38, 27, 43, 3, 9, 82, 10]
sorted_array = merge_sort(array)
print(sorted_array)  # [3, 9, 10, 27, 38, 43, 82]

The code above consists of two functions. The merge_sort function recursively divides the array, and the merge function merges two sorted lists. To briefly explain this code, it first returns the array if its length is 1 or less. Then, it divides the array at the midpoint and calls merge_sort on each sublist again. Finally, it merges the two sublists into one sorted list using the merge function.

Checking the Result

You can sort an input array using the merge_sort function defined above, as shown below. The output will be the sorted list.

array = [38, 27, 43, 3, 9, 82, 10]
sorted_array = merge_sort(array)
print(sorted_array)  # [3, 9, 10, 27, 38, 43, 82]

Applications of Merge Sort

Merge Sort is used in many applications that require large data processing or stability. For instance, the usefulness of Merge Sort can be found in database sorting, large-scale data analysis, and data sorting in distributed systems.

Comparison of Sorting Algorithms

Merge Sort has several pros and cons compared to Quick Sort and Insertion Sort:

  • Quick Sort tends to perform faster on average, but it could have a performance of O(n2) in the worst case.
  • Insertion Sort performs well on small datasets, but it is inefficient for large data processing.
  • Merge Sort guarantees a performance of O(n log n) at all times, making it suitable for specific problems where stability is required.

Conclusion

In this lesson, we have delved deeply into Merge Sort. Understanding Merge Sort plays an important role in grasping the basic concepts of data sorting and serves as a foundation for learning other sorting algorithms. Knowing these algorithms will greatly assist not only in preparing for coding tests but also in actual development.

I hope this lesson helps you effectively understand and utilize Merge Sort, and next time we will explore other sorting algorithms. If you have any questions, feel free to leave a comment!