<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 bfs(const vector<vector<int>>& grid, int r, int c, set<pair<int, int>>& visited) {
        int area = 0;
        set<pair<int, int>> discovered;
        queue<pair<int, int>> q;
        discovered.insert({r, c});
        q.push({r, c});
        int m = grid.size();
        int n = grid[0].size();
        while(!q.empty()) {
            auto cell = q.front();
            r = cell.first;
            c = cell.second;
            q.pop();
            visited.insert({r, c});
            //cout << "r : " << r << "c : " << c << endl;
            area++;
            if (r + 1 < m && discovered.find({r + 1, c}) == discovered.end() && grid[r + 1][c] == 1) {
                discovered.insert({r + 1, c});
                q.push({r + 1, c});
            }
            if (r - 1 >= 0 && discovered.find({r - 1, c}) == discovered.end() && grid[r - 1][c] == 1) {
                discovered.insert({r - 1, c});
                q.push({r - 1, c});
            }
            if (c + 1 < n && discovered.find({r, c + 1}) == discovered.end() && grid[r][c + 1] == 1) {
                discovered.insert({r, c + 1});
                q.push({r, c + 1});
            }
            if (c - 1 >= 0 && discovered.find({r, c - 1}) == discovered.end() && grid[r][c - 1] == 1) {
                discovered.insert({r, c - 1});
                q.push({r, c - 1});
            }
            
        }
        return area;
    }

    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int res = 0;
        set<pair<int, int>> visited;
        for (int r = 0; r < grid.size(); r++) {
            for (int c = 0; c < grid[0].size(); c++) {
                // bfs
                if (grid[r][c] == 1 && visited.find({r, c}) == visited.end()) {
                    res = max(res, bfs(grid, r, c, visited));
                }
            }
        }
        return res;
    }
};
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