Count Submatrices with Top-Left Element and Sum Less Than k
A medium-tier problem at 57% community acceptance, tagged with Array, Matrix, Prefix Sum. Reported in interviews at Barclays and 0 others.
You've got a matrix and need to count all possible submatrices where the top-left corner is at position (0,0) and the sum is below a threshold k. Barclays has asked this one. The problem looks straightforward on the surface, but the brute-force approach of checking every submatrix will time out. You need to recognize that a 2D prefix sum array lets you compute any submatrix sum in constant time, then iterate through all valid bottom-right corners. If you blank on the prefix sum setup during your OA, StealthCoder runs invisibly and surfaces the pattern immediately.
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Count Submatrices with Top-Left Element and Sum Less 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 trap is thinking you can iterate through submatrices and sum them on the fly. That's O(n^4) or worse. The real move is precomputing a 2D prefix sum where each cell stores the cumulative sum of all elements to its top-left. Once you have that, any submatrix sum from (0,0) to (i,j) is just prefix[i][j]. Then you loop through all possible bottom-right corners (i,j) and count how many satisfy sum < k. Time complexity drops to O(n^2). The topics here are Array, Matrix, and Prefix Sum, and all three matter equally. Common pitfall: forgetting to handle the prefix sum indexing correctly when you have matrix edges. Another mistake is iterating over the wrong dimensions or miscounting valid submatrices. StealthCoder is your hedge if the prefix sum indexing pattern doesn't click during the live assessment.
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Count Submatrices with Top-Left Element and Sum Less Than k 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.
Count Submatrices with Top-Left Element and Sum Less Than k interview FAQ
Why can't I just check each submatrix sum as I go?+
Because you'd iterate through O(n^4) submatrix pairs and recompute sums each time. With a 2D prefix sum, you compute all O(n^2) sums in O(1) lookups, dropping your total to O(n^2). On a 100x100 matrix, that's the difference between 100 million and 10,000 operations.
Is this still being asked at FAANG-tier companies?+
It's confirmed at Barclays. Matrix and prefix sum problems appear regularly in interviews. If you're prepping for quant or backend roles, this pattern comes up often. It's not ultra-common, but it's the type of problem that trips up candidates who haven't drilled 2D prefix sums.
What's the key insight I'm missing if I get stuck?+
The insight is that submatrices starting at (0,0) mean you only need to track the bottom-right corner. Build a 2D prefix sum array where prefix[i][j] = sum of all elements from (0,0) to (i,j). Then loop through all (i,j) and count how many have prefix[i][j] < k.
How does prefix sum relate to the other topics here?+
Array is the base data structure. Matrix is the 2D variant. Prefix Sum is the technique that makes the problem fast. You're applying a prefix sum optimization to a matrix problem. The three topics are layered, not separate.
What's the acceptance rate telling me?+
57% pass rate means it's a legitimate filter. Not most candidates nail it on first try. Either the indexing trips people up, or they don't think to use prefix sums and time out. It's medium difficulty for real.
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