TopCoder SRM 640 Div.1 550 - MaximumBipartiteMatchingProblem

Problem Statement:
SRM 640 Div.1 550 - MaximumBipartiteMatchingProblem

Solution:
A very mathematical problem I guess, we will get to optimise a quadratic function. Firstly, take ans vertices from both n1 and n2, and match them like this:

ans pairs of vertices:

o o o o o  -> upper-end
| | | | |
o o o o o  -> lower-end

That means we have (n1-ans) unmatched vertices from the first set F, and (n2-ans) unmatched vertices from the second set S. We cannot match any of these unmatched vertices amongst themselves, because it will immediately increase the number of bipartite matching. So we can only match them with those ans paired vertices

Topcoder SRM 640 Div. 1 250 - ChristmasTreeDecoration

Problem Statement:
SRM 640 Div. 1 250 - ChristmasTreeDecoration

Solution:
We can employ a greedy scheme:
1. For each possible remaining edge, choose the one that connects two vertices with different colors and that does not result in a loop.
2. If it is not possible anymore to do that, the remaining edges needed to form the tree will all need to connect vertices of the same color.