This question might be a bit to vague, not make sense, or not developed enough yet to ask, but I thought I might give it a shot. This questions stems from a conversation a friend and I were having about the google interview process. It boiled down to my argument that they are searching for individuals who are fundamentally better problem solvers than others (His argument is that prior job experience proves this, mine is that it doesn't).This got me thinking. Say we want to solve a simple problem 2 + 2, we could go about this the simply way and just count 1 2, 3 4 to get to the answer or we could chose a much more complex way to arrive there. I argue that both ways fundamentally solve the problem the same way; that the more complex solution is reducible to the simplest. This linked up in my brain to Big O. It has been shown that all problems in NP are equivalent and can be translated (reduced?) to each other (I might be completely wrong on this); essentially if you solve one (in P time) you solve them all. It kind of shows to me that all problems within their given class are fundamentally the same. This leads me to question, is the way that problems are solved fundamentally the same? Moreover, is there a way to solve all problems (nothing about running time)?Again disclaimer, not a full complete thought. I just wanted to get it out there before I forget it and never think of it again. I found it interesting enough to share and just wanted input. Please correct if (where.) I am wrong.
Are all problems approached and solved in fundamentally the same way?
algorithms;algorithm analysis;asymptotics