<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:
    int numIslands(vector<vector<char>> &grid) {
        int n = grid.size(),
            m = grid[0].size(),
            num_islands = 0;
        
        const auto neighbors = [&](int a, int b) -> vector<pair<int, int>> {
            vector<pair<int, int>> res;
                
            for (const auto& [dx, dy] : DIRS) {
                int c = a+dx, 
                    d = b+dy;
                    
                if (c < 0 || c >= n || d < 0 || d >= m) {
                    continue;
                }
                
                res.push_back({c, d});
            }
            
            return res;
        };
        
        stack<pair<int, int>> S;
        
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                if (grid[i][j] == '0') {
                    continue;
                }
                
                // dfs to visit all cells in island
                
                grid[i][j] = '0';
                S.push({i, j});
                ++num_islands;

                while (!S.empty()) {
                    const auto& [a, b] = S.top();
                    S.pop();

                    for (const auto& [c, d] : neighbors(a,b)) {
                        if (grid[c][d] == '0') {
                            continue;
                        }
                        
                        grid[c][d] = '0';
                        S.push({c, d});
                    }
                }
            }
        }
        
        return num_islands;
    }
private:
    const vector<pair<int, int>> DIRS = {{-1,0}, {0,-1}, {1,0}, {0,1}};
};

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