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Would you mind pinpointing where exactly you feel I would lose students in the above approach? Would I lose people at the mention of "DAG"? in which case... isn

Would you mind pinpointing where exactly you feel I would lose students in the above approach? Would I lose people at the mention of "DAG"? in which case... isn't it easy enough to jog their memory in a few seconds ("it's like a tree, except a node can have multiple parents" <drawing>) if they've forgotten what that is? Or is it with the N-hop example? In which case, aren't there plenty of simpler ones (like Fibonacci) you can use instead? Or do you see somewhere else where people would get overwhelmed, and if so, where? Like, I would understand where you're coming from if I'd used the pumping lemma or something like you're imagining, but that's not what's happening here? All I did was merely mention the words "subproblems", "trees", and "DAGs"... that's it. No theorems, no proofs, not even any need to remember what caching is... just descriptions with vivid examples and diagrams. All of which you can re-explain in a few minutes if they've forgotten them. I have a hard time seeing why that should scare someone away who's otherwise in a position to learn DP. Also, isn't the audience kinda important here? It's not like this was intended for 10-year-olds like New Math. It was intended for college-level CS students and above. They can and should be expected to have a greater understanding (and attention span) than elementary school students.

qsantos 3y ago
The point is that dynamic programming builds on various abstract concepts that many college students only understand to a level deep enough to pass exams. Making the connection with caching, which is a mostly-unrelated, and much more concrete concept, give them the basis to build a mental framework. Sure, they might do without, but why make it harder?
- dataflow 3y ago
  I don't agree it's making it harder though. Nothing I just built it on above required any deep understanding at all, and you could even re-explain all the shallow bits (like what a DAG is) in a few minutes if not seconds. I simply don't buy that this is too onerous. As to "why explain it this way regardless", because I believe it gives them a better understanding once they hear it?
  - qsantos 3y ago
    I am not saying to not explain the theory. I am saying that using a concrete concept makes it easier to build the mental model needed to understand the theory.

qsantos 3y ago

The point is that dynamic programming builds on various abstract concepts that many college students only understand to a level deep enough to pass exams. Making the connection with caching, which is a mostly-unrelated, and much more concrete concept, give them the basis to build a mental framework. Sure, they might do without, but why make it harder?

dataflow 3y ago
I don't agree it's making it harder though. Nothing I just built it on above required any deep understanding at all, and you could even re-explain all the shallow bits (like what a DAG is) in a few minutes if not seconds. I simply don't buy that this is too onerous. As to "why explain it this way regardless", because I believe it gives them a better understanding once they hear it?
- qsantos 3y ago
  I am not saying to not explain the theory. I am saying that using a concrete concept makes it easier to build the mental model needed to understand the theory.