<p>You are given an <code>m x n</code> binary matrix <code>grid</code>. An island is a group of <code>1</code>&#39;s (representing land) connected <strong>4-directionally</strong> (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.</p>

<p>The <strong>area</strong> of an island is the number of cells with a value <code>1</code> in the island.</p>

<p>Return <em>the maximum <strong>area</strong> of an island in </em><code>grid</code>. If there is no island, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/maxarea1-grid.jpg" style="width: 500px; height: 310px;" />
<pre>
<strong>Input:</strong> 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]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The answer is not 11, because the island must be connected 4-directionally.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,0,0,0]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        // Run a bfs on each island. If it is the largest seen then return that
        int maxArea = 0;
        vector<vector<bool>> visited (grid.size(), vector<bool>(grid[0].size(), false));
        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[0].size(); j++) {
                if (grid[i][j] && !visited[i][j]) {
                    visited[i][j] = true;
                    int area = bfs(grid, visited, i, j);
                    maxArea = max(area, maxArea);
                }
            }
        }

        return maxArea;
    }
    int bfs(vector<vector<int>>& grid, vector<vector<bool>>& visited, int i, int j) {
        queue<pair<int, int>> q;
        q.push({i, j});
        int area = 0;
        while (!q.empty()) {
            pair<int, int> front = q.front();
            q.pop();
            area++;
            vector<pair<int, int>> dirs = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
            for (auto& dir : dirs) {
                int x = front.first + dir.first;
                int y = front.second + dir.second;
                if (x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size() && 
                    grid[x][y] && !visited[x][y]) {
                    q.push({x, y});
                    visited[x][y] = true;
                }
            }
        }
        return area;

    }
};
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