Question

I have a set of values, each value has a possible group.
The value can ve repeating but in different group.

What will be an optimal algorithm to get minimum number of groups

A sample set:
(12, group b)
(38, group a)
(12, group a)

Desired outcome:
(38, group a)
(12, group a)

(only one group is used)

— edit:
I need an algorithm to find minimum number of groups from a set like the sample above.
If i would have a bad algorithm it will select
(12, group b)
(38, group a)
This is 2 groups for the same values instead of using one, not what i want

Answer 1

If I understand the question correctly, this is the Set cover problem

The greedy algorithm as described in the link starts with group a and then terminates, as this already covers all.

Note that in general it yields only an approximation to the optimal solution.