| Copyright | (C) Frank Staals |
|---|---|
| License | see the LICENSE file |
| Maintainer | Frank Staals |
| Safe Haskell | None |
| Language | Haskell2010 |
Algorithms.BinarySearch
Description
Synopsis
- binarySearch :: Integral a => (a -> Bool) -> a -> a -> a
- binarySearchUntil :: (Fractional r, Ord r) => r -> (r -> Bool) -> r -> r -> r
- class BinarySearch v where
Documentation
binarySearch :: Integral a => (a -> Bool) -> a -> a -> a Source #
Given a monotonic predicate p, a lower bound l, and an upper bound u, with: p l = False p u = True l < u.
Get the index h such that everything strictly smaller than h has: p i = False, and all i >= h, we have p h = True
running time: \(O(\log(u - l))\)
binarySearchUntil :: (Fractional r, Ord r) => r -> (r -> Bool) -> r -> r -> r Source #
Given a value \(\varepsilon\), a monotone predicate \(p\), and two values \(l\) and \(u\) with:
- \(p l\) = False
- \(p u\) = True
- \(l < u\)
we find a value \(h\) such that:
- \(p h\) = True
- \(p (h - \varepsilon)\) = False
>>>binarySearchUntil (0.1) (>= 0.5) 0 (1 :: Double)0.5>>>binarySearchUntil (0.1) (>= 0.51) 0 (1 :: Double)0.5625>>>binarySearchUntil (0.01) (>= 0.51) 0 (1 :: Double)0.515625
Binary Searching in some data structure
class BinarySearch v where Source #
Methods
binarySearchIn :: (Elem v -> Bool) -> v -> Maybe (Elem v) Source #
Given a monotonic predicate p and a data structure v, find the element v[h] such that that
for every index i < h we have p v[i] = False, and for every inedx i >= h we have p v[i] = True
returns Nothing if no element satisfies p
running time: \(O(T*\log n)\), where \(T\) is the time to execute the predicate.
binarySearchIdxIn :: (Elem v -> Bool) -> v -> Maybe (Index v) Source #
Given a monotonic predicate p and a data structure v, find the index h such that that
for every index i < h we have p v[i] = False, and for every inedx i >= h we have p v[i] = True
returns Nothing if no element satisfies p
running time: \(O(T*\log n)\), where \(T\) is the time to execute the predicate.
Instances
| Vector v a => BinarySearch (v a) Source # | |
| BinarySearch (Seq a) Source # | |
| BinarySearch (Set a) Source # | |