I have been looking for problems in which the solution looks at a famous algorithm, and applies it to the problem at hand. However, because of some special property of the problem, the algorithms complexity is reduced. An example is USACO 2016 February Platinum Fenced In (http://usaco.org/index.php?page=viewproblem2&cpid=625). The problem involves applying Kruskals algorithm in a clever way.

I was wondering if someone has more examples of these kinds of problems, specifically ones that use MST or max flow algorithms.