<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 UF:
    def __init__(self, N):
        self.p = [i for i in range(N)]
        self.r = [1] * N

    def find(self, idx):
        if self.p[idx] != idx:
            self.p[idx] = self.find(self.p[idx])
        return self.p[idx]

    def union(self, a, b):
        ra = self.find(a)
        rb = self.find(b)
        if ra != rb:
            if self.r[ra] < self.r[rb]:
                self.p[ra] = rb
            else:
                self.p[rb] = ra
            self.r[rb] += self.r[ra]

    def count(self):
        ps = set()
        for i in range(len(self.p)):
            ps.add(self.find(i))
        print(self.p, self.r)
        return len(ps)

class Solution:
    def numIslands(self, grid: List[List[str]]) -> int:
        if not grid or not grid[0]:
            return 0
        R, C = len(grid), len(grid[0])
        uf = UF(R * C)
        for i in range(R):
            for j in range(C):
                if grid[i][j] == "1":
                    for ii, jj in ((i + 1, j), (i, j + 1)):
                        if 0 <= ii < R and 0 <= jj < C and grid[ii][jj] == "1":
                            uf.union(i * C + j, ii * C + jj)

        islands = set()
        for i in range(R):
            for j in range(C):
                if grid[i][j] == "1":
                    islands.add(uf.find(i * C + j))
        return len(islands)

        
23461