3-D Dynamic Programing (similar to the standard problem)

A 3D-DP label is not a complete problem. Before coding, ask what the three dimensions represent and what is being optimized, counted, or decided. A correct explanation would then define a state such as dp[i][j][k] in terms of those exact quantities, list legal predecessor states, state base cases, and estimate memory and time. This matters because 3D DP can mean three strings, grid position plus budget, two agents plus time, or entirely different problems. Inventing a standard recurrence would risk solving the wrong task; moreover, cubic storage may require memoization, sparse states, or rolling dimensions depending on constraints.

Complexity: For dimensions A, B, and C with constant transitions per state, the 3-D DP costs O(ABC) time and O(ABC) space.