Minimum Cost to Cut a Stick
A hard-tier problem at 62% community acceptance, tagged with Array, Dynamic Programming, Sorting. Reported in interviews at LINE and 1 others.
Minimum Cost to Cut a Stick is a hard DP problem that shows up in assessments at LINE and PhonePe. The trick is that every cut you make increases the cost of all future cuts on that piece. You can't just greedily cut the cheapest segments first. Most candidates see the array of cut positions and assume a straightforward greedy or single-pass solution, then realize mid-interview that the cost calculation compounds in a way that forces you to test all possible orderings. That's where the DP insight lives. If this problem hits your live assessment and you blank on the state definition, StealthCoder solves it in seconds, invisible to the proctor.
Companies that ask "Minimum Cost to Cut a Stick"
Minimum Cost to Cut a Stick 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 an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage.
Get StealthCoderThe problem forces you to think about state: what defines a subproblem? It's not just 'minimize cost for these cuts' but 'minimize cost when you must cut at positions L to R, and what was the last cut made.' Most people start by sorting the cuts and trying interval DP, which is correct, but the cost recurrence trips them up. When you cut at position C within segment [L, R], you pay the length of that segment plus the cost to solve both sides. The catch: the order of cuts in each subproblem matters, because each cut adds to the total. This is why a greedy 'cut the cheapest first' fails, and why you need to consider all possible last cuts within an interval. Common mistake is forgetting to add the segment length to the recursive result. StealthCoder recognizes this pattern instantly and surfaces the correct DP table structure before you spiral.
Pattern tags
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Make sure you actually pass it.
Minimum Cost to Cut a Stick 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. Built by an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Cost to Cut a Stick interview FAQ
Is this really asked at current companies?+
Yes. LINE and PhonePe both report this problem. It's not ultra-frequent, but hard problems at these companies often include interval DP or optimization problems where greedy fails. It's worth drilling if you're interviewing at either.
What's the actual trick that makes greedy fail?+
Greedy would cut the cheapest positions first, but cutting early on a segment increases the cost of all remaining cuts on that segment. You have to evaluate the full tree of cut orderings for each interval, which only DP can do efficiently in polynomial time.
How does sorting the cuts help?+
Sorting lets you define subproblems as contiguous ranges of cut positions. An unsorted cut list makes it harder to reason about which cuts affect which pieces. Once sorted, interval DP becomes natural: solve all subproblems between cut i and cut j, trying each as the last cut.
Why is this hard and not medium?+
The state definition and recurrence are non-obvious. Most medium DP problems have a clear 'what's the state' answer. Here you have to realize cuts form a tree, and the tree's shape (order) determines cost. That conceptual leap pushes it into hard territory.
What's the time complexity I should target?+
O(n cubed) is standard for the interval DP approach with n cuts. You're filling an n by n table, and each cell tries O(n) possible last cuts. That's acceptable for hard problems and passes most online assessments with reasonable n limits.
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