Merge Sort vs Heap Sort
Both guarantee O(n log n) in every case, making them safer bets than Quick Sort when worst-case behavior matters — but they differ in memory usage and stability.
An efficient, stable, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in the input and output. Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945. The algorithm splits the array into two halves, recursively sorts them, and then merges the two sorted halves.
When to use it
Use Merge Sort when stability is required (e.g. sorting objects by one field while preserving order of another) or when sorting external/linked data.
A comparison-based sorting technique based on a Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for the remaining elements.
When to use it
Use Heap Sort when memory is tight — it sorts in-place with O(1) extra space — and stability is not a requirement, such as implementing a priority queue or bounded top-k selection.
Key Differences
- Merge Sort needs O(n) extra space; Heap Sort sorts in-place with O(1) extra space.
- Merge Sort is stable; Heap Sort is not stable.
- Heap Sort has poor cache locality due to jumping around the heap; Merge Sort has more sequential memory access.
- Both guarantee O(n log n) worst-case time, unlike Quick Sort.
Choose Heap Sort for guaranteed O(n log n) with minimal memory; choose Merge Sort when stability or external sorting is required.