The problem is - We have a series of boxes (A, B, C, D, ...). Each box contains bricks of different colours. For eg.
Box A - red, blue Box B - blue, red, green ... and so on...
and there are multiple versions of each of the boxes -
Box A1 - red, blue Box A2 - green, red, yellow ... Box B1 - blue, red, green Box B2 - blue, red ... and so on ...
The idea is to choose one of the versions of each of the boxes, such the total number of unique bricks is minimum. For eg. in this example -
Box A1 + Box B1 = blue, red, green (3 unique bricks)
Box A2 + Box B1 = blue, red, green, yellow (4 unique bricks)
Box A1 + Box B1 is the better choice.
We need to build a collection of such boxes, choosing at least one version of each box such that the total unique number of bricks is minimum.
Is there a known algorithm to solve this problem?