Max Sum of Rectangle No Larger Than K
A hard-tier problem at 45% community acceptance, tagged with Array, Binary Search, Matrix. Reported in interviews at DE Shaw and 0 others.
Max Sum of Rectangle No Larger Than K is a hard matrix problem that trips up most candidates because the obvious brute force approach times out immediately. You're given a matrix and a target sum K, and you need to find the largest rectangle sum that doesn't exceed K. DE Shaw reportedly asks this one. The twist: you can't just iterate through every rectangle and check it. You need to compress the 2D problem into 1D, then apply binary search on prefix sums. If you hit this during an assessment and freeze on the approach, StealthCoder surfaces the solution invisible to the proctor.
Companies that ask "Max Sum of Rectangle No Larger Than K"
Max Sum of Rectangle No Larger Than K 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 key insight is reducing a 2D rectangle problem to multiple 1D subarrays. You fix top and bottom row pairs, then compress columns into a single array of sums, converting it to a classic 'max subarray sum not exceeding K' problem. That subproblem lives in prefix sums and binary search: for each prefix, you hunt the smallest earlier prefix that keeps your current sum under K. Most candidates either forget this compression step entirely or try to brute-force all O(n^4) rectangles. The algorithm runs in O(n^2 * m * log m) time, which is tight but passable. Common pitfall: off-by-one errors in row/column ranges, or using a regular TreeMap instead of an ordered set to properly binary search prefix sums. During the live OA, if the pattern doesn't click, StealthCoder runs the solution in real time so you're not bleeding minutes on a single problem.
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Max Sum of Rectangle No Larger Than K 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.
Max Sum of Rectangle No Larger Than K interview FAQ
Why does brute force fail here?+
Checking all possible rectangles is O(n^4) or O(n^3 m) depending on dimensions. Modern online assessments time out anything slower than O(n^2 m log m) on a typical 50x50 matrix. You must compress dimensions first.
How does prefix sum help with the K constraint?+
Once you flatten rows into a 1D array, you can use a running prefix sum and ask: for each position, what's the closest earlier prefix that keeps my current sum under K. This binary search trick cuts time from quadratic to logarithmic per row pair.
What's an ordered set and why does it matter here?+
An ordered set (TreeSet in Java, or a balanced BST) lets you binary search stored prefix sums in O(log m) time. Without it, you'd scan linearly and lose the log factor. The problem explicitly lists Ordered Set as a topic for this reason.
Is this still asked after prep site writeups?+
De Shaw reportedly still asks it. It's a hard problem with a specific technique. Most candidates who haven't studied prefix-sum compression and binary search will time out or get stuck on the approach, not the code.
What's the biggest gotcha in implementation?+
Off-by-one errors in row and column loops, and forgetting to handle the case where the sum equals K (you still want to return it). Also, the binary search must find the greatest prefix smaller than current_sum minus K, not the other way around.
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