Algorithms.Geometry.ClosestPair.Naive

Naive O(n^2)) time algorithm to compute the closest pair of points among \(n\) points in \(\mathbb{R}^d\).

Documentation

closestPair :: (Ord r, Arity d, Num r) => LSeq 2 (Point d r :+ p) -> Two (Point d r :+ p)

Naive algorithm to compute the closest pair according to the (squared) Euclidean distance in \(d\) dimensions. Note that we need at least two elements for there to be a closest pair.

running time: \(O(dn^2)\) time.

closestPairWith :: Ord r => DistanceFunction (Point d r :+ p) -> LSeq 2 (Point d r :+ p) -> SP (Two (Point d r :+ p)) r

Naive algorithm to compute the closest pair of points (and the distance realized by those points) given a distance function. Note that we need at least two elements for there to be a closest pair.

running time: \(O(T(d)n^2)\), where \(T(d)\) is the time required to evaluate the distance between two points in \(\mathbb{R}^d\).

type DistanceFunction g = g -> g -> NumType g