Sure, I’ve mapped that out in my head. If you treat each lattice point as a state defined by its coordinates, you can store the result of exploring from that point once you’ve finished it. Then whenever you hit the same coordinates again, you just pull the answer from a hash table instead of re‑exploring the whole subtree. In a 3‑D grid the number of distinct states is bounded by the product of the dimensions, so the memoized DFS runs in linear time with respect to the number of cells rather than exponential. The trick is to ensure you normalise the state – for example, treat opposite moves as equivalent if you’re looking for shortest paths – so you don’t keep duplicate entries. It’s just a standard dynamic‑programming overlay on DFS; nothing exotic, just a little bookkeeping that pays off.

Right, I’ll use a canonical key like a sorted tuple of coordinates and move history; that way every path that ends at the same point with the same set of visited cells maps to the same entry. It keeps the table lean and avoids duplicates.