Merge Sort Variant
The Merge Sort algorithm can be applied to a variety of problems on LeetCode. Below are a few examples:
Sorting Lists or Arrays: Problems that involve sorting a list or array can be solved using Merge Sort. For example:
Finding the Inversion Count: The concept of Merge Sort can be used to find the number of inversion pairs in an array. An inversion count indicates how far the array is from being sorted. For instance:
Merge k Sorted Lists: This problem can be efficiently solved by modifying the standard merge sort algorithm to merge k lists instead of 2.
External Sorting: While not a common category in LeetCode, external sorting refers to sorting data that is too large to fit into a computer’s main memory at one time. It uses Merge Sortlike algorithms.
Multiple solutions could exist for these problems, and the choice of algorithm often depends on the specific constraints and requirements of the problem.
In some problems, we do not need the full merge sort algorithm. Instead, we might use a variation that solves the specific problem more efficiently. However, you are correct in that a simplified example of merge sort doesn’t necessarily represent a variant.
A common variant of merge sort is the inversion count or count of reverse pairs, which is a modification of the merge sort algorithm that, besides sorting the input array, also counts the number of inversions in the array. This variant is used in problems like LeetCode 493. Reverse Pairs.
Here is a simplified Python code for the inversion count variant:


The function merge_and_count
performs both the merge operation and counts the inversions. The function count_inversions
recursively applies itself to left and right halves of the input, and the reverse_pairs
function provides the entry point. This variant leverages the divideandconquer nature of merge sort but modifies the merge step to count inversions.
Claude Explanation
Merge sort is often modified and adapted for different use cases. Some variants include:
Topdown vs bottomup: Topdown is recursive, bottomup iterative using subarrays.
Inplace merge: Saves memory by merging inplace instead of extra space.
Threeway merge: Splits array into three parts for each merge.
Hybrid merge: Uses insertion sort on small chunks instead of recursion.
Java topdown merge sort:


C++ bottomup merge sort:


Python inplace merge sort:


Merge sort is very adaptable and allows optimizations for different situations.