Minimum Cost Tree From Leaf Values
A medium-tier problem at 68% community acceptance, tagged with Array, Dynamic Programming, Stack. Reported in interviews at MathWorks and 1 others.
Minimum Cost Tree From Leaf Values hits differently because it looks like a standard tree-building problem but it's actually asking you to understand the relationship between leaf values and internal node costs. You're given an array of leaf values, and you need to construct a binary tree where each internal node's value equals the product of its left and right subtree maximums. The goal: minimize the total cost of all internal nodes. MathWorks and PhonePe ask this one, and it's got a 67% acceptance rate, which means most people who see it don't solve it cleanly on their first attempt.
Companies that ask "Minimum Cost Tree From Leaf Values"
Minimum Cost Tree From Leaf Values 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 trap is thinking you can greedily build the tree top-down or use simple recursion. The real insight is that this is a range-based optimization problem solvable with dynamic programming or monotonic stack. For any contiguous range of leaves, the optimal tree structure depends on which leaf becomes the 'last one standing' after all multiplications collapse down. DP states track the minimum cost to merge a range, and the key is recognizing that the maximum value in a range always appears at an internal node. The stack approach works because you can avoid recomputing subproblems by processing elements in order and maintaining a stack of decreasing maximums. If you hit this on your live OA and the greedy intuition fails (it will), StealthCoder surfaces the DP or stack solution in seconds without the proctor seeing a thing.
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Minimum Cost Tree From Leaf Values 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 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 Tree From Leaf Values interview FAQ
Is this really just about finding max values in subarrays?+
Not quite. The max value in a range does appear at an internal node, but the cost calculation requires knowing how ranges partition and merge. You can't compute minimum cost by just finding maxes. You need DP to track the optimal way to split each range, or a stack to process multiplications in the right order.
Why doesn't a greedy 'always merge the two smallest values' approach work?+
Because the cost of merging two subtrees isn't based on their individual costs, it's based on the maximum values in each subtree. Greedy on subtree cost misses the global structure. You need to consider all possible splits of a range, not just local pairs.
How does the monotonic stack approach compare to DP?+
Both work. DP is O(n^3) with clear logic: iterate all ranges, try all split points. Monotonic stack is O(n) and harder to see but avoids redundant subproblems by maintaining decreasing maximums. For an OA, DP is safer if you're running low on time.
What's the actual recurrence if I go the DP route?+
dp[i][j] = minimum cost to merge leaves from index i to j. Try all split points k: cost = dp[i][k] + dp[k+1][j] + (max(arr[i..k]) * max(arr[k+1..j])). Base case: single leaf has cost 0.
MathWorks and PhonePe both ask this, so how common is it really?+
With a 67% acceptance rate, it's not a rarity but it's not a tier-1 frequently-asked either. If you're prepping for either of those companies specifically, this deserves time. For general prep, it's a solid medium-level DP problem worth knowing.
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