<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 convert(vector<vector<char>> grid, vector<int> adj[]) {
        int m = grid.size();
        int n = grid[0].size();

        for (int i=0; i<m; i++) {
            for (int j=0; j<n; j++) {
                if (grid[i][j] == '0') {
                    continue;
                }

                int node = i*n + j;
                int next;

                // left
                if (j-1>=0 && grid[i][j-1]=='1') {
                    next = i*n + j-1;
                    adj[node].push_back(next);
                }
                //right
                if (j+1<n && grid[i][j+1]=='1') {
                    next = i*n + j+1;
                    adj[node].push_back(next);
                }
                //top
                if (i-1>=0 && grid[i-1][j]=='1') {
                    next = (i-1)*n + j;
                    adj[node].push_back(next);
                }
                //bottom
                if(i+1<m && grid[i+1][j]=='1') {
                    next = (i+1)*n + j;
                    adj[node].push_back(next);
                }

                if (adj[node].size() == 0) {
                    adj[node].push_back(node);
                }
            }
        }
    }

    void dfs(int node, vector<int> adj[], vector<int>& visited) {
        visited[node] = 1;
        cout << node << " ";

        for (int i=0; i<adj[node].size(); i++) {
            int next = adj[node][i];
            if (!visited[next]) dfs(next, adj, visited);
        }
    }

    int numIslands(vector<vector<char>>& grid) {
        int m = grid.size();
        int n = grid[0].size();

        vector<int> adj[m*n];
        convert(grid, adj);

        for (int i=0; i<m*n; i++) {
            cout << i << ": ";
            for (int j=0; j<adj[i].size(); j++) {
                cout << adj[i][j] << " ";
            }
            cout << endl;
        }

        vector<int> visited(m*n, 0);

        int count = 0;
        for (int i=0; i<m*n; i++) {
            if (!visited[i] && adj[i].size()) {
                count++;
                dfs(i, adj, visited);
            }
        }

        return count;
    }
};
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