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Hash lookup vs binary search

Hash algorithms are O(1) while binary search is O(log n). So as n approaches infinity, hash performance improves relative to binary search. Your mileage will vary depending on n, your hash implementation, and your binary search implementation.

O(1) doesn't mean instantaneous. It means that the performance doesn't change as the size of n grows. You can design a hashing algorithm that's so slow no one would ever use it and it would still be O(1). I'm fairly sure .NET/C# doesn't suffer from cost-prohibitive hashing, however ;)
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