Coding

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

Asked at

Samsung

1Give yourself 5 minutes

2Answer out loud, not in your head

3Then compare with the answer below

Stuck? Show a way to structure it+

01Request the actual state variables, objective, transitions, and constraints.
02Name what each of three dimensions must encode before defining DP.
03Establish base cases and dependency direction.
04Check whether the cubic state space fits the constraints.

Reference answer

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.

Then expect these follow-ups

What are the inputs and objective for this 3D-DP problem?
Tests: clarification
How can one dimension often be compressed?
Tests: DP optimization

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