The example they give is clean: [10, 20, 30, 40] into 2 groups gives [50, 50].
Clarify that this is a multi-way number partitioning problem, which is NP-hard, so discuss both exact and heuristic approaches. Start with a greedy algorithm (e.g., sort descending and assign to the currently smallest sum) and then mention dynamic programming or backtracking for exact solutions with small inputs. Analyze time and space complexity, and discuss trade-offs between optimality and efficiency.
Pro tip: Amazon values customer obsession and ownership, so frame your solution in terms of practical impact: for large n, a greedy approach is often sufficient and scales well, but for small n, an exact method ensures fairness. Also, mention that you would validate the solution with edge cases like n=1, n=number of students, and negative scores.
Ask about input size, whether scores can be negative, and if exact balance is required. Confirm that the goal is to minimize the difference between the maximum and minimum group sums.
Explain that the problem is NP-hard (multi-way number partitioning) and that exact solutions are exponential in the worst case. This shows awareness of theoretical limits.
Describe sorting scores in descending order and assigning each to the group with the smallest current sum. This is O(m log m + m log n) with a heap and works well in practice.
For small m and n, use dynamic programming (e.g., DP over subsets) or backtracking with pruning to find the optimal partition. Mention that this is only feasible for limited sizes.
Compare time/space complexity of both approaches and discuss when to use each. Walk through edge cases and validate with examples.
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