Is it possible for an algorithm with quadratic time complexity to run faster than an algorithm with O(n log n) complexity?

Yes, such a situation is possible. The algorithm's time complexity is an asymptotic estimate that describes the behavior of the algorithm with large data volumes. However, in practice, much depends on constant factors, overheads, and implementation specifics.

For example, an algorithm with quadratic complexity O(n²) can run faster than an O(n log n) algorithm on small input sizes because:

• An O(n log n) algorithm may have a more complex structure and larger constants.
• A quadratic algorithm may be simpler and have fewer overheads.

Example:

• Insertion sort (O(n²)) can be faster than quicksort (O(n log n)) on very small arrays.

Therefore, when choosing an algorithm, it is important to consider not only the asymptotic complexity but also the data size, constants, and implementation features.