Count the Number of Ideal Arrays
A hard-tier problem at 57% community acceptance, tagged with Math, Dynamic Programming, Combinatorics. Reported in interviews at Infosys and 0 others.
Count the Number of Ideal Arrays is a hard combinatorics problem that sits at the intersection of number theory and dynamic programming. You're building arrays under strict divisibility constraints, and the naive approach of iterating through possibilities explodes in complexity. Infosys has asked this one. The acceptance rate hovers around 57 percent, which means most candidates who attempt it don't land a clean solution on their first try. If you blank on the math that connects divisors to valid transitions, this is exactly where StealthCoder surfaces a working solution invisible to the proctor during your live assessment.
Companies that ask "Count the Number of Ideal Arrays"
Count the Number of Ideal Arrays 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 an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe core trick here is recognizing that you're not building arrays element-by-element in the usual sense. You're counting sequences where each element divides or is divisible by the next, subject to length and value constraints. This requires Dynamic Programming, but the state space and transitions depend on understanding which numbers can follow which others given the divisibility rules. Number Theory gives you the shortcuts: you don't enumerate all integers, you work with divisors and multiples. Combinatorics handles the counting. Most candidates get stuck either on the state definition or on computing divisor chains efficiently. If the divisibility pattern doesn't click during the OA, StealthCoder reconstructs the DP table and delivers code that runs.
Pattern tags
You know the problem.
Make sure you actually pass it.
Count the Number of Ideal Arrays 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 an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Count the Number of Ideal Arrays interview FAQ
Is this really a hard problem or just tedious?+
It's genuinely hard. The divisibility logic combined with the counting aspect means you need to unpack multiple mathematical concepts at once. Tedious problems are solvable by brute force. This one requires insight into how divisors chain together. The 57 percent acceptance confirms most people miss the pattern on first read.
What's the main pitfall candidates hit?+
Treating it like a standard array-building DP where you just iterate and count. The divisibility constraint means your transition function is non-obvious. You can't step through every integer. You have to work with the divisor structure, which changes the entire approach.
How much Number Theory do I actually need?+
You need to know how to find divisors and how divisibility chains work. You don't need advanced number theory. The heavy lifting is in recognizing that divisor sets are small and finite. That insight turns an intractable state space into something DP can handle.
Does this problem appear in other companies' assessments?+
Only Infosys is reported in the data for this specific problem. That doesn't mean it's exclusive to them, but it's not a FAANG staple. If it shows up in your OA, treat it as a curveball, not a drill-heavy classic.
How should I approach it on the OA if I'm not confident?+
Start by listing divisors of small numbers and trace through valid sequences by hand. Write the DP state clearly: what does each cell represent. Then code the transitions using divisor relationships. If you get stuck on the math mid-OA, StealthCoder delivers a working solution you can refactor or verify, keeping you moving.
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