The problem is I'm looking on shortest path between points problem and the intuition tells me that the shortest path between points happens when paths don't cross. It's a step one. Then for all sub-paths we're connecting nearest points (I didn't thought much about that part). The problem is that I cannot prove that the shortest path is when there is no crosses. The couple of possible ways here:
- Continue reading the book, but I don't like this way because I left something not known and that feeling undermines my thrive to gain knowledge, because I feel that I left something unsolved.
- Blindly assume that I'm right (because of no other options).
- Read the solution of the problem, so I will know the exact answer. If it will be what I guessed, hopefully there will be a proof of why it's that. But what if what I guessed is not the right answer, I will never know, why.
- Ask Here if the shortest path between points is when connections between each pairs doesn't cross between each other and why it is that. This is good, as I will get thorough explaination and I will know is it right or wrong. On the other hand, in this way, I won't think much of this problem, thus I won't get knowledge deep inside.
So how to deal with this. How do mathematitions or whomever else deal when they face a problem they don't know answer but has a strong belief that answer is exactly that?
Clarification: I want to find the answer by myself because college experience told me that only learning ready answers will only give me mechanical and short-term knowledge. Only solving problems by myself will give me really deep understanding of the problem and the solution.
UPD: Problem I was talking is a travelling salesman problem.