# Difference between bubble sort and merge sort

## Bubble Sort

A bubble sort is a simple and basic system for sorting the elements of a list or array in a specific order, usually in ascending or descending order. Bubble sort steps through the list repeatedly, comparing adjacent items and replacing them if they are in the wrong order. This process continues until no more modifications are required, indicating that the list is sorted.

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## Merge Sort

Merge sorting is a common and efficient comparison-based sorting algorithm classified as divide-and-conquer. It works by dividing a list or array into smaller sublists, repeatedly sorting those sublists, and then recombining them to produce a sorted list. Merge sorting is well-known for its consistency and efficiency, particularly when working with big data sets.

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## Difference between bubble sort and merge sort

Parameters Bubble sort Merge sort
Sorting approach Bubble Sort is a sorting algorithm that compares and swaps neighbouring components if they are out of order. Merge Sort is a divide-and-conquer sorting algorithm that splits a large list into smaller sublists, sorts them, and then combines the sorted sublists.
Time complexity Best case: O(n)
Worst case: O(n^2)
Average case: O(n^2)
Best case: O(nlogn)
Worst case: O(nlogn)
Average case: O(nlogn)
Stability Stable Stable
Adaptivity Bubble Sort is an adaptable sorting method. When the input data is virtually sorted, its performance can be optimized. Merge Sort is not intrinsically adaptive and functions consistently regardless of the supplied data.
In-place sorting Bubble Sort is an in-place sorting algorithm, which means it sorts the items of the original array without needing extra memory allocation. Merge Sort often requires more memory for temporary sublist storage during the merging process, making it less appropriate for in-place sorting.
Efficiency Bubble Sort is inefficient for big datasets because of its O(n^2) time complexity. Merge Sort is scalable and efficient, making it suited for huge datasets.
Algorithm complexity Bubble Sort is fundamentally basic and straightforward. Merge Sort's divide-and-conquer approach makes it more difficult to learn and use.
Use cases Bubble Sort is mostly used for instructional purposes or on tiny datasets when simplicity trumps speed. Merge Sort is utilised in practical applications where efficiency and consistency are critical, such as sorting big databases.
Space complexity Bubble Sort has a space complexity of O (1) since it generally sorts in place. Merge Sort has an O(n) space complexity due to the temporary storing required for sublists during merging.

## Conclusion

In conclusion, Bubble Sort and Merge Sort are sorting algorithms with different characteristics and performance issues.

Although conceptually simple and adequate for educational purposes, bubble sort could be more efficient for large data sets. It has worse time complexity than O(n^2), making it less practical for real-world applications where efficiency is essential.

On the other hand, Merge Sort is a powerful sorting system known for its continuous operation. It uses a divide-and-conquer approach and has a time complexity of O(n log n) for all cases, making it more efficient, especially in sorting large datasets. A robust and flexible Merge Sort enhances its usefulness in various applications.

The decision when choosing between these two programs depends largely on the specific requirements of the job at hand. For small, simple sorting tasks, or when simplicity is prioritized over efficiency, Bubble Sort can be the right choice. However, Merge Sort is the best choice for large data and critical applications where speed and efficiency need to be organized.