Debug a pre-written buggy solution to a graph problem similar to Number of Islands: find the logical flaws, fix them, and walk through the corrected solution, covering edge cases, readability and scalability.
Asked in the Round 3 (debugging, final) stage. Review the provided Python implementation and correct it without changing the function interface.
grid is a rectangular list of lists containing only strings "0" and "1". Return the number of four-directionally connected groups of "1" cells. Diagonal cells are not connected. The function may mark visited land cells in grid.
def count_islands(grid):