[algorithm][DP] thinking steps

1. Define subproblems : count number of subproblems
2. Guess(part of solution)  (fib doesn't need to guess, it's specific)
3. Relate subproblems solutions(with recursion) (想出其中的關聯)
4. Recurse & memoize OR buttom up approach(for loop). (must be asyclic, DAG, thus can use toposort.)
5. Solve original problem (確定真的解決原本的問題)

Supplement article: Tail call

http://vsdmars.blogspot.com/2015/01/c-tail-call-op-articles.html