<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 disjointset{
    public :
    map<int,int>rankmap;
    map<int,int>parentmap;
    void createset(int x){
        rankmap[x] = 1;
        parentmap[x] = x;
    }
    int findset(int x){
        if(parentmap[x] == x){
            return x;
        }
        return parentmap[x] = findset(parentmap[x]);
    }
    void unionset(int x,int y){
        int lx = findset(x);
        int ly = findset(y);
        if(lx != ly){
            if(rankmap[lx] > rankmap[ly]){
                rankmap[lx] += rankmap[ly];
                parentmap[ly] = lx;
            }else{
                rankmap[ly] += rankmap[lx];
                parentmap[lx] = ly;
            }
        }
    }
};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        disjointset ds;
        int n = grid.size();
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                int x = i*n + j;
                ds.createset(x);
            }
        }
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                if(grid[i][j] == 1){
                int dx[] = {-1,1,0,0};
                int dy[] = {0,0,1,-1};
                for(int k = 0;k < 4;k++){
                int x = i + dx[k];
                int y = j + dy[k];
    if(x >= 0 and x < n and y >= 0 and y < n and grid[x][y] == 1){
        int a = x*n + y;
        int b = i*n + j;
        if(ds.findset(a) != ds.findset(b)){
            ds.unionset(a,b);
        }
    }
                }
                }
            }
        } 
    int maxarea = 0;
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                if(grid[i][j] == 0){
                int dx[] = {-1,1,0,0};
                int dy[] = {0,0,1,-1};
                set<int>s;
                for(int k = 0;k < 4;k++){
                int x = i + dx[k];
                int y = j + dy[k];
    if(x >= 0 and x < n and y >= 0 and y < n and grid[x][y] == 1){
        int a = x*n + y;
        int la = ds.findset(a);
        s.insert(la);
    }
    }
    int area = 0;
    for(int x : s){
        area += ds.rankmap[x];
    }
    s.clear();
    maxarea = max(maxarea,area + 1);
            }
        }
    }
    return maxarea == 0 ? n*n : maxarea;
    }
};
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