5 2
1 2 1
1 3 0
3 4 0
3 5 1


Is '1' (I think) or '2' ???

I believe it's zero.  There are two branches there with weight zero (ie/ they must be preserved), and you are asked to preserve two branches.  Thus, anything with nonzero weight is hosed.

I THINK THE ANSWER IS "1",BECAUSE WE SHOULD PRESERVE THEN BRANCHES 1 2 AND 1 3

True answer is '1'