Sum of Subarray Ranges
A medium-tier problem at 60% community acceptance, tagged with Array, Stack, Monotonic Stack. Reported in interviews at J.P. Morgan and 1 others.
Sum of Subarray Ranges shows up in assessments at J.P. Morgan and TikTok, and it's a classic monotonic stack trap. You see an array and need to compute the sum of (max - min) across all subarrays. The naive approach is O(n^3) or O(n^2) with a nested loop, and you'll time out. The trick is to decouple the problem: sum all subarray maxes, subtract sum of all subarray mins. A monotonic stack lets you compute each in O(n). If this problem hits your live OA and the brute force isn't fast enough, StealthCoder solves it in seconds, invisible to the proctor.
Companies that ask "Sum of Subarray Ranges"
Sum of Subarray Ranges 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 an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe conceptual leap is realizing you don't calculate max - min per subarray. Instead, for each element, count how many subarrays it's the maximum in, multiply by its value, and sum those contributions. Repeat for minimums, then subtract. A decreasing monotonic stack tracks indices of potential maxes; an increasing stack tracks mins. The stack pops when it violates the monotonic property, and the number of pops tells you the element's span. Common pitfall: off-by-one errors in left and right boundary calculation, especially when handling equal elements. Another trap is confusing which direction to build the stack. StealthCoder is the hedge if you blank on the stack mechanics during your live assessment.
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Sum of Subarray Ranges 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 an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Sum of Subarray Ranges interview FAQ
Is Sum of Subarray Ranges still asked in 2024?+
Yes. J.P. Morgan and TikTok both report it. Acceptance rate is around 60%, so candidates pass it, but it's not trivial. It's a steady ask at finance and tech interviews, especially where optimization matters.
What's the actual trick?+
Decouple max and min. For each element, use a monotonic stack to count subarrays where it's the extremum. Multiply count by value, sum them all. Do it twice: once for max contribution, once for min. Subtract min from max. O(n) time, O(n) space.
Why does monotonic stack work here?+
A monotonic stack efficiently finds the nearest smaller (or larger) element to the left and right of each index. That boundary tells you the span of subarrays where this element is the max or min. Without the stack, you'd recalculate spans per element, costing O(n^2).
What kills candidates on this problem?+
Off-by-one errors in left/right boundary calculations. Handling equal elements inconsistently (using < vs <= changes results). Forgetting to handle the stack after the loop ends. Most candidates start brute force, realize it's too slow, then freeze.
How does this relate to the Stack and Array topics?+
Stack is the data structure; Array is the input domain. Monotonic Stack is a specific pattern that answers range queries (min/max) in linear time. It's the bridge between naive nested loops and optimal solutions, fundamental to many interval and range problems.
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