Beautiful Arrangement
A medium-tier problem at 65% community acceptance, tagged with Array, Dynamic Programming, Backtracking. Reported in interviews at Salesforce and 5 others.
Beautiful Arrangement lands on your OA and you realize the naive brute force dies on larger inputs. You're given an array of numbers and need to count permutations where the element at position i divides evenly by i, or i divides evenly by the element. It's a classic constraint-satisfaction problem with a backtracking heart, asked by Salesforce, Cisco, and UBS among others. The 64% acceptance rate tells you most candidates either overthink it or hit a wall on optimization. If the pattern doesn't click during your live assessment, StealthCoder surfaces a clean bitmask DP solution in seconds, invisible to the proctor.
Companies that ask "Beautiful Arrangement"
Beautiful Arrangement 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 FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know.
Get StealthCoderThe trap is thinking you need to enumerate all n! permutations and check each one. That works for tiny n, but the problem scales. The real insight is backtracking with early pruning: build valid permutations one position at a time, and if the current number doesn't satisfy the divisibility condition at that position, don't recurse further. Bitmask DP or memoization with backtracking cuts exploration drastically. Dynamic Programming combined with Bit Manipulation lets you track which numbers you've used without constantly rebuilding sets. Most candidates skip the bitmask optimization and submit a solution that times out on n=15. That's where StealthCoder's hedge matters: if you freeze on how to encode state efficiently, you get a working approach that passes in-session.
Pattern tags
You know the problem.
Make sure you actually pass it.
Beautiful Arrangement recycles across companies for a reason. It's medium-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 FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Beautiful Arrangement interview FAQ
Is Beautiful Arrangement actually asked in live OAs?+
Yes. Salesforce, Cisco, UBS, and four other companies have reported it. At 64% acceptance, it's medium-difficulty and popular enough to show up in real assessments. It's not a tier-1 classic like Two Sum, but it's frequent enough to be on your radar.
What's the difference between backtracking and the DP solution?+
Pure backtracking explores permutations and prunes invalid branches. DP with bitmask memoizes states (position and used-number set) so you don't recompute. Backtracking is intuitive; DP is faster. Both work, but DP scales better past n=10.
How does Bit Manipulation fit into this problem?+
A bitmask encodes which numbers you've already placed. Instead of passing a set or list around, you pass an integer where bit i is 1 if number i is used. This compresses state and makes memoization keys tiny, speeding up lookups.
What's the common mistake that tanks the time complexity?+
Generating all permutations upfront and checking each one. That's O(n!) and fails on n > 10. Instead, build permutations incrementally and skip branches that violate the divisibility rule early. Pruning is the whole game here.
Does the order of topics matter for studying this?+
Start with backtracking logic: recursively place numbers and check constraints. Then layer in memoization (Dynamic Programming). Bit Manipulation is the optimization layer, not the foundation. You can solve it without bitmask, but it'll be slower.
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