<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 
{
    // Steps:
    // 1. move in all four directions from all nodes to valid (land) nodes
    // 2. count number of connected components

public:
    // Input grid
    vector<vector<char>> grid;
    int m;
    int n;
    // Seen matrix
    vector<vector<bool>> seen;
    // Direction deltas
    vector<vector<int>> directions = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};

    // Method to find the number of islands (connected components)
    int numIslands(vector<vector<char>>& grid)
    {
        // Initialize the grid
        this->grid = grid;
        m = grid.size();
        n = grid[0].size();
        // Initialize seen matrix
        seen = vector<vector<bool>>(m, vector<bool>(n, false));

        // Determine connected components using DFS
        int components = 0;
        for(int row = 0; row < m; row++)
        {
            for(int col = 0; col < n; col++)
            {
                if(grid[row][col] == '1' && !seen[row][col])
                {
                    components++;
                    seen[row][col] = true;
                    dfs(row, col);
                }
            }
        }

        return components;
    }

private:
    // Helper method for DFS
    void dfs(int row, int col)
    {
        // Base cases:


        // Recurssion:
        for(auto direction : directions)
        {
            int nextRow = row + direction[0];
            int nextCol = col + direction[1];
            if(isValid(nextRow, nextCol) && !seen[nextRow][nextCol])
            {

                seen[nextRow][nextCol] = true;
                dfs(nextRow, nextCol);
      
            }
        }
    }

    // Helper method to check if the cell is valid
    bool isValid(int row, int col)
    {
        return (0 <= row && row < m) && (0 <= col && col < n) && (grid[row][col] == '1');
    }
};
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