<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{

    public: 
    vector<int> parent;
    vector<int> count;

    DSU(int n){
        parent.resize(n);
        count.resize(n);

        for(int i=0;i<n;i++){
            parent[i] = i;
            count[i] = 1;
        }
    }

    int getCount(int x){
        int x_rep = getParent(x);
        return count[x_rep];
    }

    int getParent(int x){
        int x_par = parent[x];
        if(x==x_par){
            return x;
        }

        parent[x] = getParent(x_par);
        return parent[x];
    }

    void unionByRank(int x, int y){
        int x_rep = getParent(x);
        int y_rep = getParent(y);

        if(x_rep == y_rep){
            return;
        }

        if(count[x_rep]>count[y_rep]){
            parent[y_rep] = x_rep;
            count[x_rep] += count[y_rep];
        }
        else if(count[y_rep]>count[x_rep]){
            parent[x_rep] = y_rep;
            count[y_rep] += count[x_rep];
        }else{
            parent[y_rep] = x_rep;
            count[x_rep] += count[y_rep];
        }

    }


};


class Solution {
public:

    vector<int> dx{-1,1,0,0};
    vector<int> dy{0,0,-1,1};

    // 0,0 = 0 , 1,4 = 1*5+4 = 9
    int getHash(int x, int y, int n, int m){
        return ((x*m)+y);
    }

    bool isSafe(int x, int y, vector<vector<int>> &grid){
        int n = grid.size();
        int m = grid[0].size();

        return(x>=0 && x<n && y>=0 && y<m && grid[x][y]==1);
    }

    void dfs(int x, int y, vector<vector<int>> &grid, vector<vector<int>> &visited, int &par, DSU &dsu){
        visited[x][y] = 1;
        int n = grid.size();
        int m = grid[0].size();
        for(int i=0;i<4;i++){
            int newX = x+dx[i];
            int newY = y+dy[i];
            if(isSafe(newX, newY, grid)){
                if(visited[newX][newY]==0){
                    dsu.unionByRank(par, getHash(newX, newY, n, m));
                    //cout<<"Adding "<<par<<" and "<<newX<<" "<<newY<<endl; 
                    dfs(newX, newY, grid, visited, par, dsu);
                }
            }
        }
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        vector<vector<int>> visited(n, vector<int>(m, 0));
        DSU dsu(n*m);

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && visited[i][j]==0){
                    int par = getHash(i,j,n,m);
                    dfs(i, j, grid, visited, par, dsu);
                }
            }
        }

        int ans = 0;

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                ans = max(ans, dsu.getCount(getHash(i,j,n,m)));
                if(grid[i][j]==0){
                    //cout<<"checking for x= "<<i<<" y = "<<j<<endl;

                    int sum = 1;
                    vector<int> neigh;
                    unordered_set<int> parentFound;
                    for(int k=0;k<4;k++){
                        int newX = i+dx[k];
                        int newY = j+dy[k];
                        
                        if(isSafe(newX, newY, grid)){
                            neigh.push_back(dsu.getParent(getHash(newX, newY, n, m)));
                        }
                    }
                    //cout<<"Valid neighbours = "<<neigh.size()<<endl;
                    if(neigh.size()==0){
                        //cout<<endl;
                        continue;
                    }
                    int count = dsu.getCount(neigh[0]);
                    int par = dsu.getParent(neigh[0]);
                    parentFound.insert(par);

                    sum+=count;
                    for(int i=1;i<neigh.size();i++){
                        int tempPar = dsu.getParent(neigh[i]);
                        if(parentFound.find(tempPar)==parentFound.end()){
                            sum+=dsu.getCount(neigh[i]);
                            parentFound.insert(tempPar);
                        }
                    }
                    //cout<<"Sum = "<<sum<<endl;
                    ans = max(ans, sum);
                    //cout<<endl;
                }
            }
        }

        return ans;

    }
};
/*

1 0 0
0 1 0
1 1 0


*/
199321