<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 4.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class DSU:
    def __init__(self, n):
        self.parent = [i for i in range(n)]
        self.sizes = [1 for _ in range(n)]

    def find(self, u):
        if self.parent[u] != u:
            self.parent[u] = self.find(self.parent[u])
        return self.parent[u]

    def union(self, u, v):
        print(u, v)
        pu, pv = self.find(u), self.find(v)
        if pu != pv:
            if self.sizes[pu] <= self.sizes[pv]:
                self.parent[pu] = pv
                self.sizes[pv] += self.sizes[pu]
            else:
                self.parent[pv] = pu
                self.sizes[pu] += self.sizes[pv]


class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        N, M = len(grid), len(grid[0])
        dsu = DSU(N*M)

        for i in range(N):
            for j in range(M):
                if grid[i][j] == 1:
                    idx_u = i*N + j
                    if i-1 >= 0 and grid[i-1][j] == 1:
                        idx_v = (i-1)*N + j
                        dsu.union(idx_u, idx_v)
                    if j-1 >= 0 and grid[i][j-1] == 1:
                        idx_v = i*N + j-1
                        dsu.union(idx_u, idx_v)

        ans = max([dsu.sizes[i] if dsu.parent[i] == i else 0 for i in range(N*M)])

        print(dsu.sizes)
        for i in range(N):
            for j in range(M):
                if grid[i][j] == 0:
                    idx_u = i*N + j
                    parent = set()
                    if i-1 >= 0 and grid[i-1][j] == 1:
                        idx_v = (i-1)*N + j
                        parent.add(dsu.find(idx_v))
                    if j-1 >= 0 and grid[i][j-1] == 1:
                        idx_v = i*N + j-1
                        parent.add(dsu.find(idx_v))
                    if i+1 < N and grid[i+1][j] == 1:
                        idx_v = (i+1)*N + j
                        parent.add(dsu.find(idx_v))
                    if j+1 < M and grid[i][j+1] == 1:
                        idx_v = i*N + j+1
                        parent.add(dsu.find(idx_v))
                    
                    sm = sum([dsu.sizes[u] for u in parent])+1
                    ans = max(ans, sm)

        return ans



37506