What is the fastest search method for a sorted array?

Question

Answering to another question, I wrote the program below to compare different search methods in a sorted array. Basically I compared two implementations of Interpolation search

Answer 1

If you have some control over the in-memory layout of the data, you might want to look at Judy arrays.

Or to put a simpler idea out there: a binary search always cuts the search space in half. An optimal cut point can be found with interpolation (the cut point should NOT be the place where the key is expected to be, but the point which minimizes the statistical expectation of the search space for the next step). This minimizes the number of steps but... not all steps have equal cost. Hierarchical memories allow executing a number of tests in the same time as a single test, if locality can be maintained. Since a binary search's first M steps only touch a maximum of 2**M unique elements, storing these together can yield a much better reduction of search space per-cacheline fetch (not per comparison), which is higher performance in the real world.

n-ary trees work on that basis, and then Judy arrays add a few less important optimizations.

Bottom line: even "Random Access Memory" (RAM) is faster when accessed sequentially than randomly. A search algorithm should use that fact to its advantage.