You did pretty well on homework 1! It does seem that you could benefit from working out the details of your algorithms more precisely. The CLRS readings would probably be helpful to see algorithms and proofs worked out in detail (which lecture may skim over).

While it is important to intuitively grasp the mechanism behind an algorithm, that’s not enough when you want to come up with algorithms yourself! You need both the intuition (Lucky) and detail (Plucky), whether you want to actually implement algorithms in code, or just think about them theoretically. If you really want to check that you’ve worked out all the details, you could try implementing your proposed algorithm in a language of your choice. If that’s difficult, or if it doesn’t work, then you’ve probably left out some important details!