If there are open-source implmentations available, and there usually are - test that each of them is capable of correct behaviour - sometimes some algorithms are not able to evaluate all possible inputs - so it's a good idea to check that they have the desired behaviour.
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Big O Notation[
^] - it's used to say something about the performance characteristics of an algorithm.
For some algorithms there is a significant difference between best case and worst case - can you live with the worst case?
Trial runs using realistic input data may in the end be your best choice.
Regards
Espen Harlinn