algorithm - 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, y and z, as usual) and point (x_p, y_p, z_p). How do I find the closest point in A to (x_p, y_p, z_p)?

As far as I know, slowest way to do it is to use linear search. Are there any better solutions?

Addition of any an auxiliary data structure is possible.

Answer 1

You may organize your points in an Octree. Then you only need to search a small subset.

A Octree is a fairly simple data structure you can implement yourself (which would be a valuable learning experience), or you may find some helpful libraries to get you going.