Maximum Sum Rectangle
Detailed guide and Python implementation for the 'Maximum Sum Rectangle' problem.
Problem Statement
Write a function max_sum_rectangle(matrix) that finds and returns the maximum sum of a sub-matrix in a 2D matrix of integers.
- •1 <= len(matrix), len(matrix[0]) <= 100
- •-1000 <= matrix[i][j] <= 1000
Examples
max_sum_rectangle([[1, 2, -1, -4, -20], [-8, -3, 4, 2, 1], [3, 8, 10, 1, 3], [-4, -1, 1, 7, -6]])
29
The sub-matrix from row 1, column 1 to row 3, column 3 has the maximum sum of 29.
max_sum_rectangle([[-1, -2], [-3, -4]])
-1
The maximum sum is -1, which is the cell at (0, 0).
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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