Count Valid Paths in a Tree
A hard-tier problem at 34% community acceptance, tagged with Math, Dynamic Programming, Tree. Reported in interviews at Sprinklr and 0 others.
Count Valid Paths in a Tree is the kind of hard problem that separates interview prep from actual interview performance. With a 34% acceptance rate, it's tougher than most tree DFS problems because it layers in number theory and DP constraints that don't show themselves until you're halfway through. Sprinklr has asked it. The trap is overthinking the tree traversal and missing the mathematical constraint that gates which paths actually count. If this hits your assessment and you blank on the pattern, StealthCoder surfaces a working solution invisible to the proctor.
Companies that ask "Count Valid Paths in a Tree"
Count Valid Paths in a Tree 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 problem forces you to reason about paths in a tree under a specific mathematical validity condition, not just enumerate all paths. Most candidates start with standard tree recursion, then realize the validity check isn't a simple property like path length or node value. You need to combine DFS traversal with a constraint that usually involves number theory, primes, or divisibility. That's where the DP piece locks in: memoizing subproblem results across branches to avoid redundant checks. The gotcha is that the tree structure and the math constraint don't decouple neatly. StealthCoder handles the integration point, the exact DP formulation, and the prune-worthy edge cases. Prep heavy on GCD patterns and tree DP recurrence relations.
Pattern tags
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Make sure you actually pass it.
Count Valid Paths in a Tree 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 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.
Count Valid Paths in a Tree interview FAQ
Is this just a tree traversal problem, or is there a trick?+
It's a tree traversal with a number-theory gate on top. Standard DFS gets you the paths, but you also need to validate each path against a mathematical property. That validation rule is why it sits at hard difficulty. The combination is what trips people up live.
Why is the acceptance rate so low for a tree problem?+
34% indicates most candidates either miss the math constraint entirely, misunderstand what makes a path valid, or implement the DP incorrectly. Tree traversal is rote; adding a validity rule that spans number theory is less rote. That gap costs time and accuracy in a live assessment.
Should I drill this as a pure DP problem or a pure tree problem?+
Drill it as a hybrid. You need solid tree DFS fundamentals, but the real learning is in how the validity constraint shapes the recurrence relation. Practice GCD and divisibility patterns on trees, not in isolation. That layering is what Sprinklr is testing.
What's the most common mistake on this problem?+
Implementing a correct DFS and missing that some paths should be filtered out based on the math property. Or computing the property once and reusing it incorrectly across branches. The DP state has to account for the constraint correctly or your answer is off by a large margin.
Does this require heavy math knowledge?+
Not heavy, but you need to be comfortable with GCD, coprimality, or prime factors depending on the exact validity rule. The problem is harder because you're combining tree DP with a number-theory check, not because the math itself is advanced. Refresh GCD and modular arithmetic before the OA.
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