What is the fastest way to find the closest point to a given point?

Question

What is the fastest way to find closest point to the given point in data array?

For example, suppose I have an array A of 3D points (with coordinates x,

Answer 1

I would use a KD-tree to do this in O(log(n)) time, assuming the points are randomly distributed or you have a way to keep the tree balanced.

http://en.wikipedia.org/wiki/Kd-tree

KD trees are excellent for this kind of spatial query, and even allow you to retrieve the nearest k neighbors to a query point.