<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:
    def numIslands(self, grid: List[List[str]]) -> int:
        n_rows = len(grid)
        n_cols = len(grid[0])
        parents = [-1 if grid[i // n_cols][i % n_cols] == "0" else i for i in range(n_rows * n_cols)]
        ranks = [-1 if grid[i // n_cols][i % n_cols] == "0" else 0 for i in range(n_rows * n_cols)]

        def union(x, y):
            parentX = find(x)
            parentY = find(y)
            if parentX == parentY:
                return

            if ranks[x] > ranks[y]:
                parents[parentY] = parentX
                return

            if ranks[x] < ranks[y]:
                parents[parentX] = parentY
                return

            parents[parentX] = parentY
            ranks[parentX] += 1
        
        def find(x):
            if x == parents[x]:
                return x
            parents[x] = find(parents[x])
            return parents[x]

        for row in range(n_rows):
            for col in range(n_cols):
                if grid[row][col] == "0":
                    continue
                x = row * n_cols + col
                if row > 0 and grid[row-1][col] == "1":
                    union(x, x-n_cols)
                if col > 0 and grid[row][col-1] == "1":
                    union(x, x-1)

        islands = set(find(i) for i in range(n_rows * n_cols) if parents[i] != -1)
        return len(islands)
21076