← Accenture Interview Insights
I knew immediately this was a bin packing variant and that brute force over subsets would be exponential, which I said out loud.
First, clarify that this is a 2D bin packing problem, which is NP-hard, so exact solutions are exponential. Then, discuss the brute-force bitmask DP over subsets (O(3^N)) and explain its limitations, and finally propose better approaches like branch-and-bound, approximation algorithms, or heuristics for practical use.
Pro tip: Acknowledge the NP-hardness and focus on practical trade-offs: for small N, use DP with pruning; for large N, use heuristics like First-Fit Decreasing with 2D constraints, and mention that the problem can be modeled as a graph coloring or set cover problem.
Restate the problem as 2D bin packing with fixed bin capacities (A, B) and items (x_i, y_i). Ask about the expected size of N and whether an exact or approximate solution is needed.
Explain that a bitmask DP over subsets can solve the problem in O(3^N) time by precomputing valid subsets that fit in one rack, then finding the minimum partition. Note that this is only feasible for N up to ~15-20.
Mention branch-and-bound with pruning, or integer linear programming (ILP) formulations that can solve larger instances optimally. Also note that the problem is NP-hard, so no polynomial-time exact algorithm is likely.
For large N, recommend heuristics like First-Fit Decreasing (FFD) adapted to 2D, or metaheuristics like simulated annealing. Discuss approximation ratios and practical performance.
Summarize that the choice depends on N and required optimality: use DP for small N, ILP or branch-and-bound for medium N, and heuristics for large N. Emphasize that the problem is NP-hard, so trade-offs are inevitable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.