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Eytzinger Binary Search – Algorithmica

Eytzinger Binary Search – Algorithmica

2023-04-28 04:00:15

Eytzinger Binary Search – Algorithmica

I’m writing a book. It is free and obtainable on-line. You will discover an up to date model of this and lots of extra of my outdated articles there.
— Sergey Slotin

This tutorial is loosely primarily based on a 46-page paper by Paul-Virak Khuong and Pat Morin “Array layouts for comparison-based looking out” and describes one explicit means of performing environment friendly binary search by rearranging parts of a sorted array in a cache-friendly means.

We briefly evaluation related ideas in processor structure; if you wish to get deeper, we suggest studying the unique 2015 paper, in addition to these articles:

Our minimalistic implementation is barely ~15 strains of code whereas providing 4-5x speedup over std::lower_bound. The precise speedup relies upon rather a lot on obtainable reminiscence bandwidth (see notes beneath).

In case you are writing a contest proper now, caught on an issue the place binary search is a bottleneck, and abruptly remembered about this text, soar straight to “full implementation”, it’s compilable and copy-pastable.

Why is binary search sluggish?

Here’s a commonplace means of trying to find the primary factor not lower than (x) in a sorted array:

branch predictors have been developed. These are complicated ad-hoc methods that use statistical strategies—some even use easy neural networks—to make a extra correct guess.

See Also

In case of binary search, if all of our information is random, department prediction doesn’t assist in any respect, simply because it could possibly’t: all comparisons are 50-50. For this reason we have to eliminate if-s and rewrite our major loop the next means:

Part 2 explores environment friendly implementation of implicit static B-trees in bandwidth-constrained atmosphere.

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