For example, if I have a function 'foo(a, b, c)' and I am using subproblems whose solutions use smaller values of a, b, and c, then the most natural solution is to tabulate the solutions in a 3-d array with the (fixed) values of a, b, and c indexing into the 3-d array to get at the (solved) subproblem.
It's of course also fine to use a hash table to construct the triplet (a, b, c) and use it as the key to store (and look up) the solution to the subproblem that corresponds to the particular value of (a, b, c), and most reasonable interviewers would be happy to accept this as a valid approach.
As for recursive solutions automatically using the method stack, the overwhelming majority of programming languages provide the ability to do this, and the generally accepted understanding is that if you use this facility, you are using automatic recursion, letting the compiler/machine/runtime maintain the stack for you. The generally accepted terminology when you explicitly allocate your own stack is 'iterative'.
Also, the generally accepted terminology is 'Dynamic Programming' == 'Bottom-up tabulation', and 'Memoization' == 'Top-down recursion with caching to avoid solving the same subproblem'.
Google interview. Explicitly told me not to use recursion.
are you serious? someone really asked you to "use array". Beyond stupid if they really did.
> you can easily blow the stack for real production grade implementations using recursion
recursive solution doesn't automatically mean using a the method stack. you can implement recursive solutions using explicit stack .
> dynamic programming proper
please. There is no "proper" dynamic programming. Please watch this MIT intro https://www.youtube.com/watch?v=OQ5jsbhAv_M .