Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon coding interview with a dynamic programming / backtracking problem that looks deceptively like a simple greedy but really isn't. One question, fairly meaty, and the memoization angle is where things get interesting.

Questions Asked (1)

Given a list of item prices, a set of bundle deals (each specifying quantities of items and a bundle price), and a target quantity for each item, find the minimum total cost to exactly fulfill the shopping list. Bundles can be reused but you can't buy more of any item than needed. Items not in any bundle are purchased at unit price.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The greedy instinct here is to just grab the best bundle repeatedly, and that will absolutely fail on certain inputs.

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AI HintsAI Generated

Suggested Approach

Model the problem as a state-space search over remaining quantities, using dynamic programming or Dijkstra's algorithm to find the minimum cost to reach the zero state. At each state, consider all possible bundles that can be applied without exceeding the target quantities, plus the option to buy individual items at unit price. Use memoization to avoid recomputing overlapping subproblems.

Pro tip: Emphasize that the state space is bounded by the product of (target quantity + 1) for each item, and discuss pruning strategies like ignoring bundles that are dominated by others (e.g., higher cost for same or fewer items). Also mention that if the number of items is small, this approach is feasible, but for larger inputs, you might need to consider integer linear programming or approximation algorithms.

1. Clarify the problem and constraints

Ask about the size of the input (number of items, target quantities, number of bundles) and whether quantities are small enough for DP. Confirm that bundles can be reused and that overbuying is not allowed.

2. Define the state and transitions

Represent the state as a vector of remaining quantities for each item. Transitions are: apply a bundle (if it doesn't exceed remaining quantities) or buy one unit of an item at its unit price.

3. Choose an algorithm

Use dynamic programming (top-down with memoization or bottom-up) to compute the minimum cost from any state to the zero state. Alternatively, use Dijkstra's algorithm on the state graph if costs are non-negative.

4. Optimize and prune

Preprocess bundles to remove dominated ones (e.g., a bundle that costs more than another bundle with the same or fewer items). Also, consider buying items individually only if no bundle is beneficial.

5. Analyze complexity and trade-offs

Discuss time and space complexity: O(product of (target_i + 1) * (number of bundles + number of items)). Mention that for large inputs, this may be infeasible and alternatives like integer linear programming or greedy heuristics might be needed.

Key Points to Mention

State representation as a vector of remaining quantities
Dynamic programming with memoization to avoid redundant computations
Dijkstra's algorithm as an alternative for shortest path on state graph
Pruning dominated bundles to reduce state space
Complexity analysis: exponential in number of items but polynomial if quantities are small
Trade-offs between exact DP and approximation/ILP for large inputs

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.