<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>

#include <bits/stdc++.h>
using namespace std;
class DSU {
public:
    vector<int> size, rank, parent;
    DSU(int n) {
        size.resize(n + 1, 1);
        rank.resize(n + 1, 0);
        parent.resize(n + 1);
        for (int i = 0; i <= n; i++) {
            parent[i] = i;
        }
    }
    int findUPar(int node) {
        if (parent[node] == node)
            return node;
        return parent[node] =
                   findUPar(parent[node]); // Path compression (finding parent
                                           // in O(4 alpha) rather than log n)
    }
    void UnionbyRank(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v)
            return;
        if (rank[ulp_u] > rank[ulp_v]) {
            parent[ulp_v] = ulp_u;
        } else if (rank[ulp_v] > rank[ulp_u]) {
            parent[ulp_u] = ulp_v;
        } else {
            rank[ulp_v]++;
            parent[ulp_u] = ulp_v;
        }
    }
    void UnionbySize(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v)
            return;
        if (size[ulp_u] > size[ulp_v]) {
            size[ulp_u] += size[ulp_v];
            parent[ulp_v] = ulp_u;
        } else {
            size[ulp_v] += size[ulp_u];
            parent[ulp_u] = ulp_v;
        }
    }
};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        DSU ds(n * n);
        int mov[] = {0, -1, 0, 1, 0};
        queue<pair<int, int>> q;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    for (int k = 0; k < 4; k++) {
                        int r = mov[k] + i;
                        int c = mov[k + 1] + j;
                        if (r >= 0 && c >= 0 && r < n && c < n && grid[r][c]) {
                            int node = i * n + j, adj = r * n + c;
                            if (ds.findUPar(node) != ds.findUPar(adj)) {
                                ds.UnionbySize(node, adj);
                            }
                        }
                    }
                } else {
                    q.push({i, j});
                }
            }
        }
        int ans = 0, islands;
        while (!q.empty()) {
            int r = q.front().first;
            int c = q.front().second;
            q.pop();
            unordered_set<int> nodes;
            islands = 0;
            for (int k = 0; k < 4; k++) {
                int row = mov[k] + r;
                int col = mov[k + 1] + c;
                if (row >= 0 && col >= 0 && row < n && col < n &&
                    grid[row][col] == 1) {
                    int node = row * n + col;
                    nodes.insert(ds.findUPar(node));
                }
            }
            for (auto& it : nodes) {
                islands += ds.size[it];
            }
            ans = max(ans, islands + 1);
        }
        for (int cell = 0; cell < n * n; cell++) {
            ans = max(ans, ds.size[ds.findUPar(cell)]);
        }
        return ans;
    }
};
178059