I couldn't prove the greedy algorithm which used in the A part of this problem, so I looked it up on the internet and found this. There is a proof there, but I think that it's incomplete. Specifically, it doesn't prove subproblem needs to be solved optimally for problem to be solved optimally. Thanks for help in advance.

Also, I'm really bad at greedy algorithms. Is there any text on proof techniques for greedy algorithms, must-solve problems, or other important stuff on greedy algorithms you know?