Merge sort algorithm is a popular sorting algorithm that uses the divide and conquer strategy to sort an array of elements. It works by dividing the input array into smaller arrays until each small array has only one element, then merging the small arrays into larger arrays in a sorted order until the entire array is sorted. In this article, we will explain in detail what merge sort algorithm is, how it works, and provide examples of implementing the algorithm using Python code.

## How Merge Sort Algorithm Works

Merge sort algorithm follows the divide and conquer strategy, which involves the following steps:

1. Divide: The input array is divided into two halves recursively until each small array has only one element.
2. Conquer: The small arrays are merged into larger arrays in a sorted order.
3. Combine: The sorted arrays are combined until the entire array is sorted.

The merging step involves comparing the first element of each array and placing the smaller element in a new array. This process is repeated until all elements are merged into a single sorted array.

## Python Code Implementation

Here is an example of implementing merge sort algorithm in Python:

``````def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2
left_half = arr[:mid]
right_half = arr[mid:]

merge_sort(left_half)
merge_sort(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

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

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

The above code implements merge sort algorithm using the `merge_sort` function, which takes an array `arr` as input and sorts it in ascending order. The function first checks if the length of the array is greater than one. If it is, the array is divided into two halves, and the `merge_sort` function is recursively called on each half. Then, the function merges the two halves by comparing each element and placing the smaller element in a new array. Finally, the function combines the sorted arrays until the entire array is sorted.

Merge sort algorithm has the following advantages:

• Efficient for large data sets due to its time complexity of O(n log n)
• Stable, meaning that it preserves the order of equal elements in the array
• Suitable for sorting any data type as long as a comparison operator is defined

However, merge sort algorithm has the following disadvantages:

• Not an in-place sorting algorithm, meaning that it requires additional memory to sort the array
• Slower in practice than other sorting algorithms for small data sets due to its recursive nature

## Conclusion

Merge sort algorithm is a popular sorting algorithm that uses the divide and conquer strategy to sort an array of elements. It is efficient for sorting large data sets and is suitable for sorting any data type. In this article, we have explained in detail what merge sort algorithm is, how it works, and provided examples of implementing the algorithm using Python code.

## FAQs

1. What is the time complexity of merge sort algorithm?
• The time complexity of merge sort algorithm is O(n log n).
1. What is the space complexity of merge sort algorithm?
• The space complexity of merge sort algorithm is O(n).

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