Maximum Side Length of a Square with Sum Less than or Equal to Threshold
A medium-tier problem at 54% community acceptance, tagged with Array, Binary Search, Matrix. Reported in interviews at IMC and 0 others.
You're given a 2D matrix and a threshold. Find the largest square submatrix where the sum of all elements stays at or below that threshold. This problem hits the intersection of matrix manipulation and optimization, and it's exactly the kind of thing that looks straightforward until you realize brute force will TLE. IMC has asked it. The trick isn't the square logic, it's how you compute sums fast enough to binary search the answer. If you freeze on this during your OA, StealthCoder surfaces a working solution in seconds, invisible to the proctor.
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Maximum Side Length of a Square with Sum Less than or Equal to Threshold 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 Amazon engineer who used it to pass JPMorgan's OA and system design loop.
Get StealthCoderThe naive approach checks every possible square and sums its elements, but that's cubic or worse. The real solution combines a 2D prefix sum (to answer any rectangle sum in constant time) with binary search on the square size. Build the prefix sum once, then binary search the side length from 1 to min(rows, cols). For each candidate size, iterate through all possible top-left corners and check if any square of that size has sum <= threshold. The prefix sum lets you verify each square in O(1), so the total runtime becomes O(rows * cols * log(min(rows, cols))). Most candidates miss the prefix sum optimization and try to recompute sums naively, tanking performance. StealthCoder handles the prefix sum setup and the binary search loop, so even if you blank on the pattern, you land a clean solution.
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Maximum Side Length of a Square with Sum Less than or Equal to Threshold 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 Amazon engineer who used it to pass JPMorgan's OA and system design loop. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Maximum Side Length of a Square with Sum Less than or Equal to Threshold interview FAQ
Is this problem actually being asked now?+
Yes. IMC has reported it. The acceptance rate sits around 53%, so it's neither trivial nor exotic. It's a medium-difficulty problem that separates candidates who know prefix sums from those who don't.
Can I solve this without binary search?+
Technically yes, but you'd iterate all possible side lengths and all positions. Binary search cuts redundant work because once a side length fails the threshold, all larger sizes will too. Without it, you risk TLE on large matrices.
What's the trick most people miss?+
Not using a 2D prefix sum. Without it, summing each square takes O(side^2) time per check. With prefix sums, it's O(1) per check. That difference is the entire problem.
How does this connect to the other topics listed?+
Array and Matrix are the data structures. Binary Search is the optimization strategy. Prefix Sum is the key algorithmic insight that makes binary search feasible instead of a TLE trap.
What's the space-time tradeoff?+
You build a 2D prefix sum array (O(rows * cols) space) to answer rectangle sums in O(1) time. This trades space for speed. Without it, you'd save space but explode the runtime, which is a losing trade on large inputs.
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