Competitive ProgrammingHard

Maximum Size Square Sub Matrix

Detailed guide and Python implementation for the 'Maximum Size Square Sub Matrix' problem.

Problem Statement

Hard

Write a function max_square_submatrix(matrix) that finds the side length of the maximum square sub-matrix composed entirely of 1s in a given binary matrix.

Constraints
  • 1 <= len(matrix), len(matrix[0]) <= 500
  • matrix[i][j] is either 0 or 1

Examples

Example 1
Input
max_square_submatrix([[0, 1, 1, 0, 1], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 1, 1, 0], [1, 1, 1, 1, 1], [0, 0, 0, 0, 0]])
Output
3
Explanation

The maximum size square sub-matrix of 1s has size 3x3, located from row 2 to 4 and column 1 to 3.

Example 2
Input
max_square_submatrix([[1, 1], [1, 1]])
Output
2
Explanation

The entire matrix is a 2x2 square of 1s.

Need a Hint?
Consider using Dynamic Programming-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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