<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 Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        def find_par(v):
            v = par[v]
            if par[v] == v:
                return v
            par[v] = find_par(v)
            return par[v]
        
        par = dict()
        siz = dict()
        ans = 0
        for i, row in enumerate(grid):
            for j, c in enumerate(row):
                u = (i, j)
                if c == 1:
                    par[u] = u
                    siz[u] = 1
                    if i > 0 and grid[i-1][j] == 1:
                        v = find_par((i-1, j))
                        par[v] = u
                        siz[u] += siz[v]
                    if j > 0 and grid[i][j-1] == 1:
                        v = find_par((i, j-1))
                        if v != u:
                            par[v] = u
                            siz[u] += siz[v]
                    ans = max(ans, siz[u])
        
        print(par)
        print(siz)
        for i, row in enumerate(grid):
            for j, c in enumerate(row):
                if c == 0:
                    ii = [0, 1, -1, 0]
                    jj = [-1, 0, 0, 1]
                    ans_cur = 1
                    s = set()
                    for k in range(4):
                        v = (ii[k] + i, jj[k] + j)
                        if v[0] >= 0 and v[1] >= 0 and v[0] < len(grid) and v[1] < len(row) and grid[v[0]][v[1]] == 1:
                            v = find_par(v)
                            if v not in s:
                                s.add(v)
                                ans_cur += siz[v]
                    ans = max(ans, ans_cur)
        return ans



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