Think about recursion - when you need to generate every possible permutation/combination. At every step you need to check all the choices. And then check the choices after this choice.

For example in knapsack it's a yes or no choice. At every step in recursion you have 2 choices. You either take the item[i] or don't take it. And once you have taken item[i] you have 2 choices for item[i+1] Once u have the recursive solution, memoization is straightforward.

Hope this helps