Finding the farthest point in one set from another set

Question

My goal is a more efficient implementation of the algorithm posed in this question.

Consider two sets of points (in N-space. 3-space for the example case of RGB colorsp

Answer 1

EDIT: I meant nlog(n) where n is the sum of the sizes of both sets.

In the 1-Space set I you could do something like this (pseudocode)

Use a structure like this

Struct Item {
    int value
    int setid
}

(1) Max Distance = 0
(2) Read all the sets into Item structures
(3) Create an Array of pointers to all the Items
(4) Sort the array of pointers by Item->value field of the structure
(5) Walk the array from beginning to end, checking if the Item->setid is different from the previous Item->setid if (SetIDs are different)
check if this distance is greater than Max Distance if so set MaxDistance to this distance

Return the max distance.