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.

Here are two MST problems similar to the one you posted

http://code-festival-2016-qualb.contest.atcoder.jp/tasks/codefestival_2016_qualB_c

http://cf16-final-open.contest.atcoder.jp/tasks/codefestival_2016_final_g

Here's a max-flow problem of the type you want:

724E — Goods transportation

Another max-flow example: 704D - Капитан Америка

Two well-known dp problems where you should decrease the number of states to get AC.

http://codeforces.com/contest/729/problem/F

http://codeforces.com/group/jx70Vs2WZm/contest/101064/problem/L