How Merge Sort Is Implemented in Data Structure?

How Merge Sort Is Implemented in Data Structure?

Merge sort is a popular sorting algorithm used in the field of data structure. It is known for its efficiency and ability to handle large datasets.

In this tutorial, we will explore how merge sort works and how it can be implemented using various data structures.

Understanding Merge Sort

Merge sort follows the divide-and-conquer approach to sorting. It breaks down the input array into smaller subarrays until each subarray contains only one element.

Then, it merges these subarrays into larger sorted arrays until the entire array is sorted.

The process can be summarized in three steps:

• Divide the array into smaller subarrays.
• Recursively sort each subarray.
• Merge the sorted subarrays back into one array.

Implementation of Merge Sort

Let’s take a look at how merge sort can be implemented using a Python program and an array data structure.

Step 1: Divide the Array

To divide the array, we need to find the middle index and split it into two halves. We can use recursion to continue dividing each half until we reach subarrays with only one element.

def merge_sort(arr):
    if len(arr) > 1:
        mid = len(arr) // 2
        left_half = arr[:mid]
        right_half = arr[mid:]
        
        # Recursively divide each half
        merge_sort(left_half)
        merge_sort(right_half)
        
        # Perform merging operation
        merge(arr, left_half, right_half)

Step 2: Merge the Subarrays

Once we have the divided subarrays, we can start merging them. The merging operation compares the elements from both subarrays and places them in the correct order in the original array.

def merge(arr, left_half, right_half):
    i = j = k = 0
    
    while i < len(left_half) and j < len(right_half):
        if left_half[i] < right_half[j]:
            arr[k] = left_half[i]
            i += 1
        else:
            arr[k] = right_half[j]
            j += 1
        k += 1
        
    # Copy remaining elements from left_half (if any)
    while i < len(left_half):
        arr[k] = left_half[i]
        i += 1
        k += 1
        
    # Copy remaining elements from right_half (if any)
    while j < len(right_half):
        arr[k] = right_half[j]
        j += 1
        k += 1

Testing Merge Sort

Now that we have implemented merge sort, let's test it with an example array.

arr = [5, 2, 8, 3, 9, 1]
print("Original Array:", arr)

merge_sort(arr)
print("Sorted Array:", arr)

The output will be:

Original Array: [5, 2, 8, 3, 9, 1]
Sorted Array: [1, 2, 3, 5, 8 ,9]

Conclusion

Merge sort is an efficient sorting algorithm that utilizes the divide-and-conquer approach. By dividing the array into smaller subarrays and merging them back together, merge sort can efficiently sort large datasets.

Understanding how merge sort works and implementing it using appropriate data structures is essential for any programmer dealing with sorting algorithms.

By following the steps outlined in this tutorial, you should now have a clear understanding of how merge sort is implemented in data structure.