I have a large array of integers containing millions of elements, and I need to sort it in ascending order. However, the standard sorting algorithms like Bubble Sort and Selection Sort are too slow for this large dataset. Can anyone suggest an efficient sorting algorithm or technique that can handle such a large array effectively? Additionally, I would appreciate any implementation examples or code snippets in a popular programming language like Python or Java.
I've tried implementing Bubble Sort and Selection Sort algorithms to sort the large array of integers. However, due to the size of the dataset, these algorithms are taking an extremely long time to complete, which is not practical for my use case. I expected the sorting process to finish within a reasonable time frame, but it's currently impractical for the size of the dataset I'm working with.
I have also explored the possibility of using built-in sorting functions provided by my programming language's standard library, such as sort() in Python or Arrays.sort() in Java. While these functions work well for smaller arrays, they are not optimized for handling large datasets efficiently.
To overcome this issue, I'm seeking advice on alternative sorting algorithms or techniques that are more suitable for sorting large arrays of integers effectively. I would greatly appreciate any suggestions, code examples, or pointers in the right direction to efficiently sort such large datasets.
Bubble sort and selection sort are known to be very slow for lots of elements, both being O(n^2). Merge sort O(nlog n) is a fast general purpose stable sorting algorithm, with typically log_2(n) passes required, but radix sort O(n) a.k.a. pigeon hole or bucket sort, can be faster, with typically k passes required where k is the key length. Radix sort is not a stable sort though that shouldn't matter if you are only sorting keys. With millions of elements to sort, multi-threading is an option. You can sort subsets, then merge them at the end. If the range of integers to sort is materially less than the number of elements, you could compress the data to (key, frequency) pairs before sorting by key, then uncompress the sorted elements.