Count Maximum Profitable Groups
Reported by candidates from Amazon's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Amazon's January 2024 OA included a problem asking you to count maximum profitable groups. This is a classic optimization puzzle that trips up candidates who miss the grouping structure. You're not just maximizing profit; you're counting how many different ways you can form groups that hit that maximum. The trick is recognizing when you need dynamic programming or greedy logic to find the best partition, then careful enumeration to count all valid solutions. StealthCoder can spot the pattern in seconds if you blank during the live assessment.
Pattern and pitfall
The problem likely hinges on partitioning a set of items (or people) into groups where each group has a profit value, and you need to find all partitions that achieve maximum total profit. The common mistake is solving for the maximum profit value, then failing to count distinct group configurations. You'll probably need to either use DP to track (state, count) pairs, or recognize a greedy property that lets you construct groups deterministically. The enumeration step is where candidates lose points: not handling duplicates, not respecting constraints on group size or membership. StealthCoder will have the decomposition ready if you hit a wall during the OA, letting you skip the false starts and lock in the right approach.
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You can drill Count Maximum Profitable Groups cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Made for the candidate who got the OA invite this morning and has 72 hours, not six months.
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Count Maximum Profitable Groups FAQ
Is this a pure DP problem or greedy?+
Both. You likely need greedy or DP to find max profit, then DP or backtracking with memoization to count distinct ways to achieve it. The profit calculation might be greedy (e.g., always pair high-value items), but the counting step is typically DP with state compression or careful combinatorial logic.
What's the trick Amazon usually includes here?+
Constraints on group size, value thresholds, or item exclusivity rules that break naive greedy solutions. Also watch for duplicate items: if two people are identical, do they form one group configuration or two? Amazon always tests your clarity on counting versus choosing.
How do I count distinct groups without double-counting?+
Use DP with a state that represents which items are already assigned. Canonical ordering helps: always process items in sorted order, only form groups where the smallest item hasn't been used. Alternatively, use bitmask DP if the input is small enough (N under 20).
Can I brute-force this in 45 minutes?+
Only if N is very small (under 12-15). For larger N, you need to identify the DP state and transition. If you can't see the polynomial structure in 10 minutes, pivot to a memoized recursive solution and optimize later. Amazon gives partial credit for correct, slow code.
What if I blank on the counting logic?+
Write out the profit maximization first and lock in a working solution. Then add a counter and run examples by hand to understand the group enumeration. StealthCoder will have the full pattern if you need a hedge during the live OA.