O(n·log n) (merge sort)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The O(n·log n) calculator estimates the performance of the merge sort algorithm, which uses a 'divide and conquer' approach to organize data. The n·log₂(n) formula represents worst-case runtime, where each array division reduces the problem by half, and the merge phase combines sorted parts. It's ideal for analyzing code efficiency or comparing sorting algorithms.
Use this tool to predict processing time for large datasets in registration systems, big data analysis, or machine learning pipelines. The O(n·log n) complexity shows execution time grows proportionally to n multiplied by the input's logarithm, offering a balance between speed and scalability for critical tasks.
Common considerations include: verifying data meets merge sort assumptions (e.g., no memory constraints), evaluating alternatives like quicksort (O(n·log n) average) for random arrays, and noting theoretical complexity might differ in real implementations due to factors like recursive call overhead.
Frequently asked questions
What is merge sort?
Merge sort is a recursive sorting algorithm that splits an array into halves, sorts each part, and merges them. It ensures stability and efficiency for large datasets.
Why is the complexity O(n·log n)?
Each division halves the problem (log₂ n steps) and the merge combines n elements, resulting in n·log n operations in worst-case scenarios.
When to use this calculator?
When comparing algorithms, optimizing sorting code, or estimating processing time for large databases.
How does it compare to quicksort?
Merge sort guarantees O(n·log n), while quicksort has worst-case O(n²). Merge sort uses more memory but is more predictable.
Are there more efficient alternatives?
For nearly sorted arrays, insertion sort can be faster. For random data, quicksort often performs better, but merge sort is more stable.