<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:
    string coordinateHash(pair<int, int> coordinates) {
        return to_string(coordinates.first) + "," + to_string(coordinates.second);
    }

    bool valid(int row, int col, vector<vector<int>>& grid, unordered_set<string>& seen) {
        return seen.find(coordinateHash({row, col})) == seen.end()
            && 0 <= row && row < grid.size()
            && 0 <= col && col < grid[0].size()
            && grid[row][col] == 1;
    }

    int dfs(int row, int col, vector<vector<int>>& grid, unordered_set<string>& seen, vector<pair<int, int>>& directions) {
        int ans = 1;

        for(pair<int, int> direction : directions) {
            int nextRow = row + direction.first, nextCol = col + direction.second;

            if(valid(nextRow, nextCol, grid, seen)) {
                seen.insert(coordinateHash({nextRow, nextCol}));
                ans += dfs(nextRow, nextCol, grid, seen, directions);
            }
        }

        return ans;
    }

    int maxAreaOfIsland(vector<vector<int>>& grid) {
        vector<pair<int, int>> directions = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
        unordered_set<string> seen;
        int ans = 0;

        for(int row = 0; row < grid.size(); row++) {
            for(int col = 0; col < grid[0].size(); col++) {
                string coordinates = coordinateHash({row, col});
                if(grid[row][col] == 1 && seen.find(coordinates) == seen.end()) {
                    seen.insert(coordinates);
                    ans = max(ans, dfs(row, col, grid, seen, directions));
                }
            }
        }

        return ans;
    }
};
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