<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 {
public:
    int fp(int node, vector<int>& parent) {
        if (node == parent[node])
            return node;
        return parent[node] = fp(parent[node], parent);
    }
    void dsu(vector<int>& size, vector<int>& parent, int a, int b) {
        int ua = fp(a, parent);
        int ub = fp(b, parent);
        if (ua == ub)
            return;
        int sa = size[ua];
        int sb = size[ub];
        // connect sm to big
        if (sa > sb) {
            parent[ub] = ua;
            size[ua] += sb;
        } else {
            parent[ua] = ub;
            size[ub] += sa;
        }
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m=n;
        vector<int> parent(n * n);
        for(int i=0;i<n*n;i++) parent[i]=i;
        vector<int> size(n * n, 1);
        vector<pair<int, int>> one;
        vector<pair<int, int>> zero;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1)
                    one.push_back({i, j});
                else
                    zero.push_back({i, j});
            }
        }
        vector<int> vis(n * n, 0);
        int sz = one.size();
        if(zero.size()==0) return n*n;
        for (int i = 0; i < sz; i++) {
            int x = one[i].first;
            int y = one[i].second;
            int val = x * n + y;
            if (!vis[val]) {
                vis[val] = 1;
                vector<int> row{-1, 0, 1, 0};
                vector<int> col{0, 1, 0, -1};
                for (int k = 0; k < 4; k++) {
                    int nx = x, ny = y;
                    nx += row[k];
                    ny += col[k];
                    int nv = nx * m + ny;
                 if(val==1)    cout<<val<<" "<<nv<<endl;
                    if (nx >= 0 && ny >= 0 && nx < n && ny < m && nv >= 0 &&
                        nv < m * n && fp(val,parent) != fp(nv,parent) &&
                        vis[nv] == 1) {
                          
                        dsu( size, parent,val, nv);
                    }
                } 
            }
        }
        int mx=0;
        for(int i=0;i<n*n;i++){
            size[i]=size[fp(i,parent)];
        }
        // for(auto i:parent){
        //     cout<<i<<" ";
        // }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    int ans=0;
                vector<int> row{-1, 0, 1, 0};
                vector<int> col{0, 1, 0, -1};
                set<int>s;
                for (int k = 0; k < 4; k++) {
                    int nx = i, ny = j;
                    nx += row[k];
                    ny += col[k];
                    
                    int nv = nx * m + ny;
                    if (nx >= 0 && ny >= 0 && nx < n && ny < m && nv >= 0 &&
                        nv < m * n && grid[nx][ny]==1 ) {
                     s.insert(parent[nv]);
                    }
                }
                for(auto i:s){
                    cout<<i<<endl;
                    ans+=size[i];
                }
                mx=max(ans+1,mx); 
                }
            }
        }
        return mx;
    }
};
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