<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 withinBound(int i, int j, int m, int n) {
        return 0<=i && i<m && 0<=j && j<n;
    }
    int numIslands(vector<vector<char>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> v(m, vector<int>(n,0));
        queue<pair<int,int>> q;
        int out=0;
        int r[] = {0, -1, 1, 0};
        int c[] = {-1, 0, 0, 1};
        for(int i=0;i<m;i++) {
            for(int j=0;j<n;j++) {
                if(grid[i][j] == '1' && !v[i][j]) {
                    out++;
                    v[i][j] = 1;
                    q.push({i,j});
                    while(!q.empty()){
                        pair<int,int> p = q.front();
                        q.pop();
                        for(int k=0;k<4;k++) {
                            int i1 = p.first + r[k];
                            int i2 = p.second + c[k];
                            if(withinBound(i1,i2,m,n) && grid[i1][i2] == '1' && !v[i1][i2]) {
                                v[i1][i2] = 1;
                                q.push({i1, i2});
                            }
                        }
                    }        
                }
            }
        }
        return out;
    }
};
16576