<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 {
    int findAreaOfIsland(vector<vector<int>>& grid, vector<vector<bool>>& seen, int r, int c, int rowSize, int colSize)
    {
        int area = 0;
        std::stack<std::pair<int,int>> to_visit;
        to_visit.push({r, c});
        seen[r][c] = true;
        while(!to_visit.empty())
        {
            auto [curr_r, curr_c] = to_visit.top();
            to_visit.pop();
            
            ++area;

            static const std::vector<std::pair<int,int>> directions = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
            for (auto [dr, dc] : directions)
            {
                int nr = curr_r + dr;
                int nc = curr_c + dc;
                if (nr >= 0 and nr < rowSize 
                    and nc >= 0 and nc < colSize 
                    and seen[nr][nc] == false and grid[nr][nc] == 1)
                {
                    seen[nr][nc] = true;
                    to_visit.push({nr, nc});
                }
            }
        }
        return area;
    }
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) 
    {
        int max_area = 0;

        int rowSize = grid.size();
        int colSize = grid.front().size();

        std::vector<std::vector<bool>> visited(rowSize, std::vector<bool>(colSize, false));

        for (int r = 0; r < rowSize; ++r)
        {
            for (int c = 0; c < colSize; ++c)
            {
                if (!visited[r][c] and grid[r][c] == 1)
                {
                    int curr_area = findAreaOfIsland(grid, visited, r, c, rowSize, colSize);
                    max_area = std::max(max_area, curr_area);
                }
            }
        }

        return max_area;
    }
};
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