<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 {
    void dfs (int v, vector<vector<int>>& vec, vector<bool>& used){
        used[v] = true;
        for(auto& it: vec[v]){
            if(!used[it]){
                dfs(it, vec, used);
            }
        }
    }
public:
    int numIslands(vector<vector<char>>& grid) {
        int n = grid.size();
        int m = grid[0].size();

        vector<vector<int>> vec(n*m);
        for(int i = 0; i <n;  ++i){
            for(int j = 0; j< m; ++j){
                if(grid[i][j] == '0'){
                    continue;
                }
                int number = i * m + j;
                if( j < m-1 && grid[i][j + 1] == '1'){
                    vec[number].push_back(number + 1);

                }
                if(j > 0 && grid[i][j-1] == '1'){
                    vec[number].push_back(number - 1);
                }
                if(i > 0 && grid[i-1][j] == '1'){
                    vec[number].push_back(number - m);
                }
                if(i < n-1 && grid[i+1][j] == '1'){
                    vec[number].push_back(number + m);
                }
            }
        }
        vector<bool> used(n*m, false);
        int ans = 0;
        for(int i = 0; i <n;  ++i){
            for(int j = 0; j< m; ++j){
                int number = i*m + j;
                if(grid[i][j] == '1' && !used[number]){
                
                    dfs(number, vec, used);
                    ans++;
                }
                
            }
        }
        return ans;
    }
};
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