<p>Given an <code>m x n</code> 2D binary grid <code>grid</code> which represents a map of <code>&#39;1&#39;</code>s (land) and <code>&#39;0&#39;</code>s (water), return <em>the number of islands</em>.</p>

<p>An <strong>island</strong> is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [
  [&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;]
]
<strong>Output:</strong> 1
</pre>

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

<pre>
<strong>Input:</strong> grid = [
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;1&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],
  [&quot;0&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;]
]
<strong>Output:</strong> 3
</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;= 300</code></li>
	<li><code>grid[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution {
public:
    void islandDFS(pair<int,int> index, vector<vector<char>>& grid, set<pair<int, int>>& seen){
    stack<pair<int,int>> s;
    pair<int,int> curr;

    s.push(index);

    while (!s.empty()){
        curr = s.top();
        s.pop();
        
        if (seen.count(curr)) continue;
        seen.insert(curr);

        // Check all four possible directions
        vector<pair<int, int>> directions = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
        for (auto dir : directions) {
            int newRow = curr.first + dir.first;
            int newCol = curr.second + dir.second;
            if (newRow >= 0 && newRow < grid.size() && newCol >= 0 && newCol < grid[0].size() && grid[newRow][newCol] == '1' && !seen.count({newRow, newCol})) {
                s.push({newRow, newCol});
            }
        }
    }
}


int numIslands(vector<vector<char>>& grid) {
    set<pair<int,int>> seen;
    int island_count = 0;

    for (int i = 0; i < grid.size(); ++i){
        for (int j = 0; j < grid[0].size(); ++j){
            if (grid[i][j] == '1' && !seen.count({i, j})){
                islandDFS({i, j}, grid, seen);
                island_count++;
            }
        }
    }

    return island_count;
}
};
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