The Number of Beautiful Subsets
A medium-tier problem at 51% community acceptance, tagged with Array, Hash Table, Math. Reported in interviews at Infosys and 0 others.
The Number of Beautiful Subsets is a medium-difficulty combinatorics problem that's harder than it sounds. Infosys has asked it. You're looking at a constraint-satisfaction counting problem where most candidates either brute-force and timeout, or miss that the constraint makes certain subsets mutually exclusive. The pattern isn't obvious until you see it, and if you blank during the live OA, StealthCoder surfaces a working solution in seconds, invisible to the proctor.
Companies that ask "The Number of Beautiful Subsets"
The Number of Beautiful Subsets 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. Built by a senior engineer who knows the OA is theater. This is the script.
Get StealthCoderThe trap is thinking you can just enumerate subsets and validate. The real move is recognizing that the 'beautiful' constraint (usually no two elements in a subset differ by exactly 1) partitions the array into independent chains. Once you see that, you can use dynamic programming or backtracking on each chain separately, then multiply the counts. Most candidates either implement naive backtracking that times out on larger inputs, or they miss the independence structure altogether. The combinatorics piece is non-obvious: you're counting valid subset selections, not generating them, and that's where DP shines. When you hit this live and the brute-force path collapses, StealthCoder delivers the constraint-graph approach instantly.
Pattern tags
You know the problem.
Make sure you actually pass it.
The Number of Beautiful Subsets 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. Built by a senior engineer who knows the OA is theater. This is the script. Works on HackerRank, CodeSignal, CoderPad, and Karat.
The Number of Beautiful Subsets interview FAQ
Is this problem actually medium or is the acceptance rate lying?+
Acceptance sits around 51 percent, which signals most people solve it but a real chunk doesn't. The problem itself is genuinely medium in constraint difficulty. The trick is seeing the independence structure in the constraint. If you spot that, the code flows. If you don't, you'll timeout on medium inputs.
What's the core algorithmic trick here?+
The key is that the constraint isolates elements into independent subproblems. You can group elements, apply DP or backtracking to each group independently, then multiply results. Backtracking alone without this insight will TLE. Recognizing the structure is the entire problem.
Is Backtracking or Dynamic Programming the right approach?+
Both work once you've partitioned the problem by the constraint. Backtracking is more intuitive for subset enumeration with pruning. DP is faster if you memoize by state. The topics list includes both for a reason. Start with backtracking and optimize if needed.
How does combinatorics fit into the solution?+
You're counting valid subsets, not generating them. After you partition by constraint, each partition becomes a counting problem: how many ways can I select elements from this group such that they're independent. That's pure combinatorics, often solved with multiplication principle.
Will sorting help or is it just noise?+
Sorting is essential. It lets you identify which elements can coexist without checking every pair. A sorted array exposes the structure instantly. Without sorting, your constraint-checking logic stays O(n^2) per validation. Sorting moves it to O(n) once grouped.
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