Is Find Sorted Submatrices With Maximum Element at Most K easy or hard?

The problem is classified as Hard because it combines multiple concepts: matrix preprocessing, sorted constraints, and monotonic stack rectangle counting. Recognizing the transformation to a histogram-style problem is the main difficulty.

Find Sorted Submatrices With Maximum Element at Most K Python/Java solution

Implement the algorithm by first computing a width matrix that stores the longest sorted segment ending at each column with values ≤ k. Then iterate row by row while maintaining a monotonic stack to count rectangles. The same logic translates directly across Python, Java, C++, and Go implementations.

What is the best approach for Find Sorted Submatrices With Maximum Element at Most K?

The optimal approach uses row preprocessing combined with a monotonic stack. First compute the maximum valid sorted width ending at every cell where values are ≤ k. Then treat each column as a histogram and use a monotonic stack to count submatrices while maintaining the minimum width constraint. This runs in O(m * n) time with O(n) extra space.

Is Find Sorted Submatrices With Maximum Element at Most K asked at Google/Amazon/Meta?

Matrix counting problems combined with monotonic stack patterns appear frequently in interviews at companies like Google, Amazon, and Meta. Variants of histogram rectangle counting and submatrix enumeration are common in hard-level coding interviews.

What data structure is used in Find Sorted Submatrices With Maximum Element at Most K?

The key data structure is a monotonic stack. It maintains rows with increasing width values while processing each column. This allows efficient aggregation of submatrix counts while preserving the minimum width constraint required for a valid sorted submatrix.

What is the time complexity of Find Sorted Submatrices With Maximum Element at Most K?

The optimal algorithm runs in O(m * n) time, where m is the number of rows and n is the number of columns. Each cell is processed once during preprocessing and once during the monotonic stack pass. The auxiliary space complexity is O(n) for the stack and running counts.

Description Hints 2

3359. Find Sorted Submatrices With Maximum Element at Most K

Q: How to solve Find Sorted Submatrices With Maximum Element at Most K in O(n)?

For an m × n matrix the optimal complexity becomes O(m * n). Compute the width of the longest sorted segment ending at each cell while ensuring the value ≤ k. Then iterate column-wise and use a monotonic stack to maintain increasing widths, allowing efficient counting of all valid submatrices ending at each row.

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You are given a 2D matrix grid of size m x n. You are also given a non-negative integer k.

Return the number of submatrices of grid that satisfy the following conditions:

The maximum element in the submatrix less than or equal to k.
Each row in the submatrix is sorted in non-increasing order.

A submatrix (x1, y1, x2, y2) is a matrix that forms by choosing all cells grid[x][y] where x1 <= x <= x2 and y1 <= y <= y2.

Example 1:

Input: grid = [[4,3,2,1],[8,7,6,1]], k = 3

Output: 8

Explanation:

The 8 submatrices are:

[[1]]
[[1]]
[[2,1]]
[[3,2,1]]
[[1],[1]]
[[2]]
[[3]]
[[3,2]]

Example 2:

Input: grid = [[1,1,1],[1,1,1],[1,1,1]], k = 1

Output: 36

Explanation:

There are 36 submatrices of grid. All submatrices have their maximum element equal to 1.

Example 3:

Input: grid = [[1]], k = 1

Output: 1

Constraints:

1 <= m == grid.length <= 10³
1 <= n == grid[i].length <= 10³
1 <= grid[i][j] <= 10⁹
1 <= k <= 10⁹

Topics

Hints open one at a time

Hint 1

Use monotonic stack.

Hint 2

Store for each element grid[i][j], the longest increasing subarray of grid[i] ending at index j.

3359. Find Sorted Submatrices With Maximum Element at Most K

Topics

Hints open one at a time

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