# Merge Sort – Data Structure and Algorithms

Functioning as an advanced sorting technique, much like systematically combining well-arranged puzzle pieces, merge sort employs a divide-and-conquer strategy to sort an array efficiently. It shines particularly in effectively managing large datasets while maintaining the stability of equal elements’ relative order.

## Merge Sort Algorithm

The crux of merge sort algorithm involves breaking the array into smaller sub-arrays, sorting each sub-array, and then merging them back together. This merging step is where merge sort’s power lies.

## Working of Merge Sort

To understand the process, let’s dig into an example array: arr[] = {38, 27, 43, 3, 9, 82, 10}

Pass 1: Divide

Array: 38    27    43    3    9    82    10

Divide: Firstly, Split array into smaller sub-arrays.

•                         

Pass 2: Merge

Array:                         

Merge: Then, Combine and sort pairs of sub-arrays.

• [27, 38]    [3, 43]    [9, 82]    

Pass 3: Merge

Array: [27, 38]    [3, 43]    [9, 82]    

Merge: To preceed, Combine and sort larger sub-arrays.

• [3, 27, 38, 43]    [9, 10, 82]

Pass 4 (Final Pass): Merge

Array: [3, 27, 38, 43]    [9, 10, 82]

Merge: Combine the last remaining sub-arrays.

• [3, 9, 10, 27, 38, 43, 82]

Finally, The array is now fully sorted.

## Code in C++

This table explains each step of the Merge Sort algorithm implementation in C++ along with relevant code snippets.

## Complexity Analysis

### Time Complexity:

• Worst-case time complexity: O(n log n)
• Average-case time complexity: O(n log n)
• Best-case time complexity: O(n log n)

### Space Complexity:

In conclusion, merge sort emerges as a potent sorting solution, adept at handling substantial datasets while preserving stability. Furthermore, Its division, sorting, and merging steps epitomize the elegance of divide-and-conquer strategies, delivering consistent and efficient sorting across a variety of scenarios. Hence, understanding merge sort enriches insights into algorithmic complexities and efficient data organization.

Moreover, Quick Sort also uses the same divide and conquer technique for sorting.