Dynamic programming is not a black magic, _proving it can be dynamically programmed and their correctness_ is. You need to use mathematical induction to formall

Dynamic programming is not a black magic, _proving it can be dynamically programmed and their correctness_ is. You need to use mathematical induction to formally proof it just like with greedy algorithms which are very counterintuitive (take for example, greedy coloring) when I learned them both in uni.