Find top N elements in an Array

Question

What would be the best solution to find top N (say 10) elements in an unordered list (of say 100).

The solution which came in my head was to 1. sort it using quick s

Answer 1

If you're dealing with simple elements like fixed-length integers, then provided you can spare a memory buffer of the same size as the input data, sorting can be done in O(n) time using bucket or radix sorts, and this will be the fastest.

Although there are linear-time selection algorithms, the hidden constant is very high -- around 24. That means an O(nlog n) algorithm will be typically faster for fewer than several million elements.

Otherwise, in the general case when you can only compare 2 elements and determine which is greater, the problem is best solved by a heap data structure.

Suppose you want the top k of n items. All solutions based on fully sorting the data require O(nlog n) time, while using a heap requires only O(nlog k) time -- just build a heap on the first k elements, then keep adding an element and removing the maximum. This will leave you with a heap containing the smallest k elements.