Merge Sort in Data Structure

Introduction

Sorting is also one of the most addressed problem in Data Structure and Algorithms.

It is whenever we require data in sorted order (ascending or descending), we apply sorting. One of the Best and Most Efficient sorting methods are Merge Sort.

SORTING: Merge Sort in Data Structure Merge Sort is a division and conquer algorithm. It is much used that, it has consistency of performance and even it’s good for large data too. Being predictable, these printable sheets are very useful for BTech, CSE, AI, ML’s exam preparation.

Merge sort is commonly compared to these other quadratic time sorting algorithms as it’s significantly more efficient. This post is about Merge Sort, in very simple words so that anyone can understand and remember it for exams.

What is Merge Sort?

Merge Sort is an algorithm in the sorting category; it selects two halves of a declared array and then again divides those sub-arrays. After that, a comparison will be made between each element.

It is based on the Divide and Conquer approach:

Split the array in two halves

Sort each half

Merge the sorted halves

Merge Sort performs consistently regardless of what the input data actually is.

Why is Merge Sort significant?

• Merge Sort is important because:
• It is one of the faster elementary sorting algorithms.
• It is super-efficient to handle Big data
• It has guaranteed time complexity
• It has been used in systems such as databases and file systems
• It comes as a standard question in exams and interviews

Due to these factors, Merge Sort in Data Structure becomes a mandatory topic to learn.

Divide and Conquer Concept

• Merge Sort is an application of the divide and conquer method.
• There are three key steps to this method:
• Break the problem down into sub-problems.
• Solve each sub-problem
• Combine the results
• In Merge Sort:
• The array is partitioned until all subarrays have single element.
• Single elements are already sorted
• Sorted parts are merged together
• This is what makes Merge Sort so efficient.
• Working of Merge Sort(Step by Step) H2: Can pots and pans go in a dishwasher?

The functioning of Merge Sort can be easily summarised in the following sequence:

Step 1: Consider the unsorted array.

Step 2: Split the array into two halves

Step 3: Repeat step two until each sub-array has only a single element

Step 4: Begin merging the sub-arrays

Step 5: Compare and sort elements.

Continue merging until the complete array is sorted.

This procedure guarantees that final array is exactaneously sorted.

Example of Merge Sort

• Say, we have a an array like below:
• 20, 10, 40, 30
• (X) Divide the array into two parts
• Left: 20, 10
• Right: 40, 30
• Divide again
• 20 | 10
• 40 | 30
• Now merge and sort
• 10, 20
• 30, 40
• Final merge
• 10, 20, 30, 40
• So, this is the process of Merge Sort step by step.

Implementation of Merge Sort (Simple Explanation)

• Here are the rules of Mergesort:

If there’s only a single element in the array, return it if (sizeof($values) === 1) { return $values[0]; }

Split the array into two parts

Perform Merge Sort on both the halves

Merge the two sorted halves

The crucial step of this algorithm is the merging step.

Time Required by Merge Sort

• A measure of how fast an algorithm performs its tasks is its time complexity.
• Merge Sort has:
• Best Case Time Complexity: O(n log n)
• Time Complexity in average case: O(n log n)

Time Complexity: O(n log n) in worst-case time, where n is the number of elements-editorial.

This is to say, Merge Sort has guaranteed performance even when inputs are nebulous.

Merge Sort is O(n) space stable 3.1.3.

• Merge Sort needs temporary arrays in a place where extra storage is available.
• Space Complexity: O(n)

This additional memory means that Merge Sort is not appropriate for a constrained sized system.

Advantages of Merge Sort

• Merge Sort has many advantages:
• Very fast for large data
• Predictable performance
• Stable sorting algorithm
• Works well with linked lists
• Suitable for external sorting
• For these advantages merge sort is widely employed in practice.

Disadvantages of Merge Sort

• In addition to those benefits, Merge Sort does have some disadvantages:
• Requires extra memory
• Not an in-place sorting algorithm
• Slower for small data sets
• More on the advanced side, as opposed to basic sorting algorithms
• Yet for big data, its merits outweigh the limitations.

Applications of Merge Sort

• In the real world Merge Sort is used in:
• Sorting large files
• Database sorting operations
• External sorting
• File systems
• Data processing systems
• It is good for professional use in reliability.

Merge Sort versus simple sorting algorithms

• As against Bubble Sort or Selection Sort:-
• Merge Sort is much faster

Favorable conditions for merge-sort: Merge Sort runs more efficiently than Quick Sort at the high end.

Easy to sort but too Slow Fast or Bubble or Handshake Sort is slow but easy for everyone.

That’s why Merge Sort is more practical for real-world use.

Exam Tips for Merge Sort

• For exams, remember these points:
• Merge Sort follows Divide and Conquer.
• Its time complexity will be O(nlogn) always.
• Requires extra memory
• Stable sorting algorithm
• Used for large datasets
• Here I m giving these points which can easily bring full marks.

Conclusion

Merge Sort in Data Structure is the easiest and efficient sorting algorithm. It is procedure-based, which is effective as well as efficient. It is not memory efficient, however it is useful because of its relatively high speed and stability, for large data sets and real applications.

Merge Sort is also very important for students studying how to program, as it serves a great purpose in academic exams and interviews. Knowing reactive, its pros and cons and how it works will make your data structure as beautiful.

def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2
left = arr[:mid]
right = arr[mid:]

    merge_sort(left)
    merge_sort(right)

    i = j = k = 0

    while i < len(left) and j < len(right):
        if left[i] < right[j]:
            arr[k] = left[i]
            i += 1
        else:
            arr[k] = right[j]
            j += 1
        k += 1

    while i < len(left):
        arr[k] = left[i]
        i += 1
        k += 1

    while j < len(right):
        arr[k] = right[j]
        j += 1
        k += 1

data = [20, 10, 40, 30]
merge_sort(data)
print(data)