# An island in matrix is a group of linked areas, all having the same value.
# This code counts number of islands in a given matrix, with including diagonal
# connections.
class Matrix:  # Public class to implement a graph
    """This public class represents the 2-Dimensional matrix to count
    the number of islands.An island is the connected group of 1s,including the top,
    down, right, left as well as the diagonal connections.
    >>> matrix1 = Matrix(3, 3, [[1, 1, 0], [0, 1, 0], [1, 0, 1]])
    >>> matrix1.count_islands()
    1
    >>> matrix2 = Matrix(2, 2, [[1, 1], [1, 1]])
    >>> matrix2.count_islands()
    1
    """

    def __init__(self, row: int, col: int, graph: list[list[bool]]) -> None:
        """Initializes the matrix with the given number of rows, columns and matrix.
        Args:
            row (int): number of rows in the matrix
            col (int): number of columns in the matrix
            graph (list[list[bool]]): 2-D list of 0s and 1s representing the matrix
        """
        self.ROW = row
        self.COL = col
        self.graph = graph

    def is_safe(self, i: int, j: int, visited: list[list[bool]]) -> bool:
        """This checks if the current cell can be included in the current island.
        Args:
            i (int): row index
            j (int): column index
            visited (list[list[bool]]): 2D list tracking the visited cells
        Returns:
            bool: True if the cell is in bounds, not yet visited and part of
            an island (its value is ``1``); False otherwise.
        >>> visited = [[False, False], [False, False]]
        >>> graph = [[1, 0], [0, 1]]
        >>> m = Matrix(2, 2, graph)
        >>> m.is_safe(0, 0, visited)
        True
        >>> m.is_safe(0, 1, visited)
        False

        A cell that is out of bounds is never safe:

        >>> m.is_safe(-1, 0, visited)
        False
        >>> m.is_safe(0, 2, visited)
        False

        Only cells whose value is exactly ``1`` are part of an island, so any
        other value (e.g. ``2``) is treated as water, matching the seeding rule
        used by ``count_islands``:

        >>> m2 = Matrix(1, 1, [[2]])
        >>> m2.is_safe(0, 0, [[False]])
        False
        """
        return (
            0 <= i < self.ROW
            and 0 <= j < self.COL
            and not visited[i][j]
            and self.graph[i][j] == 1
        )

    def diffs(self, i: int, j: int, visited: list[list[bool]]) -> None:
        """This is the recursive function to mark all the cells visited which
        are connected to (i, j) indices.
        Args:
            i (int): row index
            j (int): column index
            visited (list[list[bool]]): 2D list tracking the visited cells
        >>> visited = [[False, False], [False, False]]
        >>> graph = [[1, 1], [0, 1]]
        >>> m = Matrix(2, 2, graph)
        >>> m.diffs(0, 0, visited)
        >>> visited
        [[True, True], [False, True]]
        """
        # Checking all 8 elements surrounding nth element
        row_nbr = [-1, -1, -1, 0, 0, 1, 1, 1]  # Coordinate order
        col_nbr = [-1, 0, 1, -1, 1, -1, 0, 1]
        visited[i][j] = True  # Make those cells visited
        for k in range(8):
            if self.is_safe(i + row_nbr[k], j + col_nbr[k], visited):
                self.diffs(i + row_nbr[k], j + col_nbr[k], visited)

    def count_islands(self) -> int:  # And finally, count all islands.
        """
        This counts all the islands in the given matrix.
        Returns:
            int: the number of islands in the given matrix.
        Example -
        >>> mat = Matrix(1, 1, [[1]])
        >>> mat.count_islands()
        1
        >>> mat2 = Matrix(2, 2, [[0, 0], [0, 0]])
        >>> mat2.count_islands()
        0

        Two 1s that only touch on a diagonal still form a single island:

        >>> Matrix(2, 2, [[1, 0], [0, 1]]).count_islands()
        1

        Two islands separated by a column of water:

        >>> Matrix(3, 3, [[1, 0, 1], [1, 0, 1], [0, 0, 1]]).count_islands()
        2

        ``count_islands`` seeds a new island only on cells equal to ``1``.
        Before ``is_safe`` was aligned to the same rule it expanded into any
        truthy cell, so a matrix containing values other than ``0``/``1``
        reported the wrong count.  Here two ``1``s are bridged by a ``2``:
        because a ``2`` is not part of an island they must be counted as two
        separate islands.  The old truthy check absorbed the ``2`` and
        merged them into one, returning ``1`` instead of ``2``:

        >>> Matrix(1, 3, [[1, 2, 1]]).count_islands()
        2

        A lone ``2`` is likewise not an island:

        >>> Matrix(1, 1, [[2]]).count_islands()
        0
        """
        visited = [[False for j in range(self.COL)] for i in range(self.ROW)]
        count = 0
        for i in range(self.ROW):
            for j in range(self.COL):
                if visited[i][j] is False and self.graph[i][j] == 1:
                    self.diffs(i, j, visited)
                    count += 1
        return count