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Use monotonic stack.
Store for each element <code>grid[i][j]</code>, the longest increasing subarray of <code>grid[i]</code> ending at index <code>j</code>.
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The sorted constraint limits how submatrices can expand across rows and columns. By leveraging this property, we can maintain ordered ranges and avoid rechecking every element inside each candidate submatrix, significantly improving efficiency.
Yes, matrix submatrix-counting problems frequently appear in advanced coding interviews. Variants involving monotonic stacks, histogram techniques, and prefix optimizations are commonly discussed in FAANG-style interview preparation.
Commonly used data structures include monotonic stacks, arrays for column height tracking, and prefix-based helpers. These structures help maintain ordered constraints and compute valid submatrix ranges efficiently during row-wise scans.
The optimal approach converts the matrix into valid regions where elements are less than or equal to K and processes rows using histogram or monotonic stack techniques. This allows counting valid submatrices efficiently without enumerating all possibilities. The overall complexity can be reduced to O(m * n).