Component Placement — UVa 11765. Think about how you will model this as a flow network — perhaps the source and the sink can be indicators for top/bottom placements and you could have nodes for the components... how will you capture the cost of putting two components at opposite ends?

Winger Trial — UVa 11757. A mincut problem; creating the flow network involves some geometric observations.

Red-Blue Graph on Codeforces. This is a flow variant, where you might want to impose demands (a minimum flow) through certain edges. You might have go beyond the algorithms we've covered to solve this one.