Setting row and column to zeros

You are given a 2-dimensional integer array Arr[M][N]. A few of the
elements in this array are zero. Write an algorithm such that if
A[i][j] is zero, all the elements in row i and all the elements in
column j should be set to 0. In other words, if any element is zero,
its entire row and column should be zero.

Answer:

Solution in O(mn) time.

Step 1: Init array[m] = {-1}

Step 2:
for ( i = 0; i< m; ++i )
  for ( j = 0; j < n; ++j)
  {
    if ( matrix[i][j] == 0 )
       array[i] = j;
       break;
  }

Complexity : O(mn)

step 3:
for ( k = 0; k < m; ++k)
{
  if(array[k] != -1)
  {
    for( i = 0; i < m; ++i)
      matrix[k][i] = 0;
    for( i = 0; i < n ; ++i)
      matrix[i][array[k]] = 0;
  }
}

complexity: O(m(m+n))

Total complexity = O(mn) + O(m^2) + O(n)