Problem 658. Find the biggest empty box

You are given a matrix that contains only ones and zeros. Think of the ones as columns in an otherwise empty floor plan. You want to fit a big square into the empty space (denoted by zeros). What is the largest empty square sub-matrix you can find in the given matrix? You will return the row and column extent of the sub-matrix. The answer may not be unique. We will test that your sub-matrix is square, that it is empty, and that it contains the correct number of elements.

Example:

 Input a = [1 0 0; 0 0 0; 0 0 0]
 Output si = [2 3 2 3]

That is, the square indices are a(2:3,2:3). We verify that sum(sum(a(2:3,2:3))) is zero, and that it has four elements.