<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:
    vector<pair<int,int>> DIR = {{1,0}, {-1,0}, {0,1}, {0,-1}};
    int bfs(const vector<vector<int>>& grid, int r, int c, unordered_set<string> & set) {
        int size = 0;
        queue<pair<int, int>> q;
        q.push({r,c});
        set.insert(to_string(r) + "," + to_string(c));
        while(!q.empty()) {
            const auto [r,c] = q.front();
            q.pop();
            ++size;
            for(const auto & [dr, dc] : DIR){
                int nr = r + dr;
                int nc = c + dc;
                string key = to_string(nr) + "," + to_string(nc);
                if(nr < 0 || nr >= grid.size() || nc < 0 || nc >= grid[0].size() || !grid[nr][nc] || set.count(key)){
                    continue;
                }

                set.insert(key);
                q.push({nr, nc});
            }
        }

        return size;
    }
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int res = 0;
        unordered_set<string> set;
        for (int i = 0; i<grid.size(); i++) {
            for (int j = 0; j<grid[0].size(); j++){
                if(grid[i][j] && !set.count(to_string(i) + "," + to_string(j))) {
                    res = max(res, bfs(grid, i, j, set));
                }
            }
        }

        return res;
    }
};
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