Faster than binary search for ordered list

Question

is there an algorithm that is faster than binary search, for searching in sorted values of array?

in my case, I have a sorted values (could be any type values) in an

Answer 1

If you have a huge amount of numbers to find, and by some fluke they are ALSO sorted, you could do it in O(n + m) where m is the number of numbers to find. Basically just your typical merge algorithm, with slight modification to record which value each checked number would be inserted before, if it was to be inserted into the array.

You can always trade off space... And time of other operations. Assuming all your elements are constant size p bits, you can make a massive array which stores, for each possible value you could look up, the index of the next bigger value currently stored. This array needs to be 2^p*lg(n) bits, where n is the number values stored. Each insertion or deletion is O(2^p) but typically around 2^p/n, because you have to go through updating all those indices.

But your lookup is now O(1)!

OK, OK, it's not really practical. But dividing the input into blocks in a similar fashion could possibly reduce the constant in front of your log. Possibly.