# Two Way Merge Sort

**Two Way Merge Sort** : When it comes to sorting algorithms, *Merge Sort* is one of the most popular and efficient ones out there. It is a divide and conquer algorithm that divides the input *array* into two halves, sorts each half separately, and then merges the two sorted halves back together. One variant of this algorithm is the *Two-Way Merge Sort*, which is also known as Binary Merge Sort.

The Two-Way Merge Sort algorithm takes two sorted lists and merges them into one list in sorted order. It is widely used in Merge Sort to output the minimum item in each step given list in sorted order and builds a sorted list with all items in any of the input lists in proportion to the total of the lengths of the input lists. As opposed to K-Way Merge Sort, which merges K sorted lists, Two-Way Merge Sort merges only two sorted lists.

In this article, we will explore the Two Way Merge Sort algorithm in detail, including its steps, time complexity, advantages, and disadvantages. We will also compare it to other sorting algorithms such as *insertion sort*, *heap sort*, *bubble sort*, *radix sort*, *counting sort*, and discuss its practical applications. By the end of this article, you will have a thorough understanding of the Two-Way Merge Sort algorithm and its usefulness in sorting large datasets efficiently.

## Overview of Merge Sort

When it comes to sorting algorithms, Merge Sort is a popular choice because of its efficiency and ease of implementation. It follows the divide and conquer approach, which involves breaking down the problem into smaller sub-problems and solving them individually before combining the results to get the final solution.

In Merge Sort, the divide step involves splitting the array into two halves, and recursively sorting each half. The conquer step involves merging the sorted sub-arrays back together to get the final sorted array.

The most time-consuming part of Merge Sort is the merging step, where two sorted sub-arrays are combined into a single sorted array. However, this step can be optimized using a two-way merge sort, which sorts and merges pairs of adjacent sub-arrays, and then merges the resulting pairs together until the final sorted array is obtained.

Overall, Merge Sort is an efficient and reliable sorting algorithm that is widely used in computer science and programming. Its divide and conquer approach makes it easy to understand and implement, and its runtime complexity of O(nlogn) makes it suitable for sorting large datasets.

## Two Way Merge Sort

In this section, we will discuss the *Two Way Merge Sort* algorithm, which is an efficient sorting algorithm that uses the divide and conquer approach. It is a variation of the Merge Sort algorithm, which involves dividing the input array into two halves, sorting them recursively, and then merging them back together.

### How it Works

The Two Way Merge Sort algorithm works by dividing the input array into two halves, sorting each half recursively, and then merging them back together. The merging process involves comparing the first element of each half and selecting the smaller one to be placed in the output array. This process is repeated until all elements have been placed in the output array.

### Pseudocode

Here is the pseudocode for the Two Way Merge Sort algorithm:

```
function mergeSort(arr):
if length of arr is less than or equal to 1:
return arr
middle = length of arr divided by 2
left = mergeSort(arr[0:middle])
right = mergeSort(arr[middle:])
return merge(left, right)
function merge(left, right):
result = []
while length of left and length of right is greater than 0:
if first element of left is less than or equal to first element of right:
append first element of left to result
remove first element of left from left
else:
append first element of right to result
remove first element of right from right
if length of left is greater than 0:
append left to result
if length of right is greater than 0:
append right to result
return result
```

Plaintext### Time and Space Complexity

The time complexity of the Two Way Merge Sort algorithm is O(n log n), which is the same as the standard Merge Sort algorithm. The space complexity is O(n), which is the same as the standard Merge Sort algorithm as well. This means that the algorithm is efficient and can handle large input sizes without running out of memory.

### Implementation of Two Way Merge Sort

*Recursive Implementation*

One way to implement two way merge sort is through a recursive approach. This involves dividing the list into two halves, sorting each half recursively, and then merging the two sorted halves back together. The base case for the recursion is when the list has only one element, in which case it is already sorted.

Here are the steps for the recursive implementation of two way merge sort:

- Divide the list into two halves
- Recursively sort each half
- Merge the two sorted halves back together

The merge step involves comparing the first element of each half and selecting the smaller one to add to a new list. This process is repeated until one of the halves is empty, at which point the remaining elements from the other half are simply added to the new list.

*Iterative Implementation*

Another way to implement two way merge sort is through an iterative approach. This involves using a loop to repeatedly merge adjacent pairs of elements until the entire list is sorted.

Here are the steps for the iterative implementation of two way merge sort:

- Set the chunk size to 1
- Loop over the list in chunks of the current size
- Merge adjacent pairs of chunks together
- Increase the chunk size by a factor of 2
- Repeat until the chunk size is greater than or equal to the length of the list

The merge step in the iterative implementation is similar to that in the recursive implementation, except that it involves merging adjacent pairs of chunks instead of halves of the list.

### Advantages and Disadvantages of Two Way Merge Sort

**Advantages**

Two way merge sort is a popular sorting algorithm that has several advantages. One of the main advantages is that it has a time complexity of O(n log n), which means it can sort large arrays relatively quickly. This makes it a popular choice for sorting large datasets

Another advantage of two way merge sort is that it is a stable sort. This means that the order of elements with equal values is preserved during the sort. This can be important in some applications where maintaining the original order of equal elements is necessary.

Two way merge sort is also a great choice for sorting data that is stored on external storage devices, such as hard drives or solid-state drives. This is because the algorithm minimizes the number of times data needs to be read from or written to the external storage device, which can be a slow operation.

### Disadvantages

While two way merge sort has several advantages, it also has some disadvantages. One of the main disadvantages is that it requires additional memory to store the temporary arrays used during the sorting process. This can be a problem when sorting very large datasets, as it may not be possible to allocate enough memory to hold all the temporary arrays.

Another disadvantage of two way merge sort is that it can be slower than other sorting algorithms when sorting small datasets. This is because the overhead of creating and merging temporary arrays can be significant when the number of elements being sorted is small.

Finally, two way merge sort is not an in-place sorting algorithm. This means that it requires additional memory to store the sorted array, which can be a problem when working with limited memory resources.