:orphan:

Max Area of Island
==================

.. highlight:: none

Problem
-------
https://leetcode.com/problems/max-area-of-island/

You are given an ``m x n`` binary matrix ``grid``. An island is a group
of ``1``'s (representing land) connected **4-directionally** (horizontal
or vertical.) You may assume all four edges of the grid are surrounded
by water.

The **area** of an island is the number of cells with a value ``1`` in
the island.

Return *the maximum* **area** *of an island in* ``grid``. If there is no
island, return ``0``.

 

**Example 1:**

|image1|

::


   Input: grid = [[0,0,1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0,0]]
   Output: 6
   Explanation: The answer is not 11, because the island must be connected 4-directionally.

**Example 2:**

::


   Input: grid = [[0,0,0,0,0,0,0,0]]
   Output: 0

 

**Constraints:**

- ``m == grid.length``
- ``n == grid[i].length``
- ``1 <= m, n <= 50``
- ``grid[i][j]`` is either ``0`` or ``1``.

.. |image1| image:: https://assets.leetcode.com/uploads/2021/05/01/maxarea1-grid.jpg

.. highlight:: python

Pattern
-------
Array, Depth-First Search, Breadth-First Search, Union-Find, Matrix

Approaches
----------

.. tab-set::

    .. tab-item:: BFS

        **Code**

        .. literalinclude:: ../problems/medium/max-area-of-island/max_area_of_island__bfs.py
            :language: python
            :lines: 9-

        **Test**

        >>> from max_area_of_island__bfs import maxAreaOfIsland
        >>> maxAreaOfIsland([[0,0,1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0,0]])
        6
        >>> maxAreaOfIsland([[0,0,0,0,0,0,0,0]])
        0

        .. autofunction:: max_area_of_island__bfs.maxAreaOfIsland