Looking for a generic `bisect` function

Question

I am looking for a bisect operation in Haskell similar to Python's bisect_left() and friends. The input would be a lower bound, an upper bound, a non-decreasing function (Ord a)=>(Int->a) which must be defined for all integers between the lower and upper bound, and a search value. The return value is the highest integer i where lower <= i <= upper and f(i) < search_term. Performance should be O(log(n)).

Hoogling for this:

(Ord a)=>(Int->a)->Int->Int->a->Int

does not yield any results.

Is there a standard, generic binary search operator in a library somewhere?

Answer 1

Ross Paterson's binary-search package on Hackage does what you're looking for. Specifically, see searchFromTo, which has type signature

searchFromTo :: Integral a => (a -> Bool) -> a -> a -> Maybe a

As Tikhon points out, [a] in Haskell is a linked list rather than an array. Since linked lists only support sequential access, it is not possible to get a logarithmic-time search on an [a] data structure. Instead, you should use a genuine array data structure -- see the vector library for the preferred implementation of arrays.

Dan Doel has written a family of binary search functions for the mutable vectors in the vector package: see Data.Vector.Algorithms.Search in his vector-algorithms library. In contrast to Ross Paterson's library, which provides a pure API, the API in Data.Vector.Algorithms.Search is monadic (that is, it must be run in the ST monad or the IO monad).