Number of Different Subsequences GCDs
A hard-tier problem at 42% community acceptance, tagged with Array, Math, Counting. Reported in interviews at Akuna Capital and 0 others.
Number of Different Subsequences GCDs is a hard problem that asks you to count how many distinct GCD values exist across all possible non-empty subsequences of an array. You'll see it in interviews with quant and trading firms like Akuna Capital. The 42% acceptance rate reflects the fact that most candidates who attempt it don't finish. The trick isn't brute force enumeration of subsequences, which would time out instantly. Instead, you need to understand how GCD properties compress the problem space. If you hit this during a live assessment and the pattern doesn't click immediately, StealthCoder surfaces the right approach in seconds.
Companies that ask "Number of Different Subsequences GCDs"
Number of Different Subsequences GCDs is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE.
Get StealthCoderThe key insight is that GCD values don't grow arbitrarily as you extend subsequences. If you take the GCD of a set and add another element, the result either stays the same or decreases. This means the number of distinct GCDs reachable from any element is bounded by log(max element), not by the number of subsequences. The winning approach uses dynamic programming: track all reachable GCD values as you process each element, then update the set of possible GCDs by taking the GCD of each existing value with the new element. Common mistakes include attempting to enumerate all 2^n subsequences, or failing to recognize that the GCD values form a narrow bottleneck. This problem lives at the intersection of Array, Math, Counting, and Number Theory. If you haven't drilled GCD reduction patterns before, StealthCoder is your hedge when this appears in the assessment.
Pattern tags
You know the problem.
Make sure you actually pass it.
Number of Different Subsequences GCDs recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Number of Different Subsequences GCDs interview FAQ
Is this problem actually asked in interviews or just a platform-specific trick?+
It's confirmed at Akuna Capital, a major quant trading firm. Acceptance rate of 42% suggests it's hard enough to filter most candidates. It's specialized but not invented for the platform. Expect it if you're in interviews with trading or quantitative finance roles.
What's the actual trick to solving this efficiently?+
GCD has a mathematical property: when you compute GCD of a value with subsequent elements, the result can only decrease or stay the same, and it does so in logarithmic steps. This bounds the distinct GCD values reachable from any point. Use DP to track all possible GCD values as you iterate through the array.
Why does the brute force approach fail so hard?+
An array of size 25 has 2^25 minus one non-empty subsequences. Generating and computing GCD for each one is exponential time and will time out immediately on any reasonable test case. You have to recognize that most GCD values repeat.
How does Number Theory help here versus pure counting?+
Number Theory explains why GCD reduction is bounded. The divisors of any number grow logarithmically, which bounds how many distinct GCDs you can reach. Without that insight, you're stuck guessing at optimization. It's core to the solution.
Is this a common interview problem outside trading firms?+
Data is limited to Akuna Capital in the reports. It's not a typical FAANG problem. It's specialized to quant and trading interviews where number theory and mathematical insight matter more than standard coding patterns.
Want the actual problem statement? View "Number of Different Subsequences GCDs" on LeetCode →