Maximize Sum of Array Multiplication
Reported by candidates from Amazon's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Amazon's February OA is testing array multiplication optimization, and this one trips up candidates who overthink the indexing. You've got an array and need to maximize the sum of products using some operation or constraint. The instinct to brute-force all pairs or greedily pick max values usually backfires. StealthCoder will catch the pattern if you blank on the trick during the live assessment. Most candidates spend 15 minutes going in circles before realizing there's a constraint they missed or a pairing rule they overlooked.
Pattern and pitfall
The core pattern here is figuring out which elements multiply with which to get the maximum total. This isn't a simple 'pair largest with largest' greedy play. Usually there's either a constraint on valid pairings (indices, rotations, or alternating), or you need to figure out an optimal permutation or reordering. The pitfall is assuming you can pick any two elements. Read the constraint carefully: can elements be reused, do they have to be adjacent, are there index bounds. Once you lock the rule, it often becomes a dynamic programming problem or a sorted two-pointer sweep. StealthCoder will flag the exact constraint and the optimal approach if you're stuck live.
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Maximize Sum of Array Multiplication FAQ
Is this a DP problem or can I greedy it?+
Greedy fails here. You need DP or a permutation insight because the order or pairing rule matters. Sort, then think about optimal matching. If there's a rotation or modular index rule, DP states track position and sum. Don't assume you can just pick the highest numbers.
What's the most common wrong answer?+
Pairing max with max without respecting the constraint. Candidates also forget that negative numbers can flip the best strategy. Multiply two negatives to get a positive, or one negative with a large positive might be worse than a small positive pair. Test with mixed signs.
How do I know if elements can be reused or if it's a one-time pairing?+
Check the problem text carefully. If it says 'select pairs' or 'choose indices,' each element is usually used once. If it says 'operations' or 'multiply and add,' you might reuse. This detail changes the entire solution. Ask via the clarification feature if the OA allows it.
Should I sort the array?+
Often yes, but not always before solving. Sorting breaks index-based constraints. Solution strategy: if the constraint is purely on values (not positions), sort and use two-pointers. If it's index-bound or circular, work on the original array and use DP or observation.
What if there are negative numbers in the array?+
Negatives are a trick. Two negatives multiply to a positive, so pairing them can beat positive pairs. Include negative numbers in your greedy scan or DP state. Test your solution on an array like [-5, -3, 2, 4] to verify it handles sign flips correctly.