<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 getKey(vector<int> V) {
        return V[0]*1000 + V[1];
    }
    
    vector<int> getCell(int x) {
        return { x/1000, x%1000 };
    }
    
    unordered_map<int, int> parents;
    int find(int x) {
        return parents[x] == x ? x: parents[x] = find(parents[x]);
    }
    
    void makeParent(int a, int b) {
        int pA = find(a);
        int pB = find(b);
        if (pA != pB) {
            parents[pA] = pB;
        }
    }
    
    int numIslands(vector<vector<char>>& A) {
        int n = A.size(), m = A[0].size();
        
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) {
                if (A[i][j] == '1') {
                    parents[getKey({i, j})] = getKey({i, j});
                }
            }
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (A[i][j] == '1') {
                    if (i+1 < n && A[i+1][j] == '1') 
                        makeParent(getKey({i, j}), getKey({i+1, j}));
                    if (j+1 < m && A[i][j+1] == '1') 
                        makeParent(getKey({i, j}), getKey({i, j+1}));
                }
            }
        }
        
        
        int ans = 0;
        for (auto [k, v]: parents) {
            if (k == v) ans++;
        }
        
        return ans;
    }
};
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