<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>

from typing import Tuple

class Solution:
    def numIslands(self, grid: List[List[str]]) -> int:
        disjoint = [[(x, y) for y in range(len(grid[0]))] for x in range(len(grid))]
        result = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                result += 1 if grid[i][j] == '1' else 0
                
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if i == 0 and j == 0:
                    continue
                if grid[i][j] == '0':
                    continue
                for island in [(i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)]:
                    if island[0] < 0 or island[1] < 0 or island[0] >= len(grid) or island[1] >= len(grid[0]) or grid[island[0]][island[1]] == '0':
                        continue

                    root1 = self.find(disjoint, island)
                    root2 = self.find(disjoint, (i, j))
                    if root1 != root2:
                        result -= 1
                        self.union(disjoint, root1, root2)

        return result

    def find(self, disjoint: list, island: Tuple[int, int]) -> Tuple[int, int]:
        if disjoint[island[0]][island[1]] != island:
            return self.find(disjoint, disjoint[island[0]][island[1]])
        else:
            return island

    def union(self, disjoint: list, island1: Tuple[int, int], island2: Tuple[int, int]):
        disjoint[island2[0]][island2[1]] = disjoint[island1[0]][island1[1]]

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