<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:

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

    void dfs(int i,int j,int &n,int &size,int &color,vector<vector<int>>&Grid,vector<vector<bool>>&visited){
        visited[i][j]=true;
        Grid[i][j]=color;
        size++;
        int x,y;
        for(int k=0;k<4;k++){
            x=i+dx[k];y=j+dy[k];
            if(x>=0 and y>=0 and x<n and y<n and !visited[x][y] and Grid[x][y]==1){
                dfs(x,y,n,size,color,Grid,visited);
            }
        }
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        vector<vector<int>>Grid=grid;
        vector<vector<bool>>visited(n,vector<bool>(n,false));
        unordered_map<int,int>m; //color:size
        int color=0;
        int size;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(!visited[i][j] and Grid[i][j]==1){
                    color++; size=0;
                    dfs(i,j,n,size,color,Grid,visited);
                    m[color]=size;
                }
            }
        }
        if(m.empty()){
            return 1;
        }
        //finding the largest possible island
        unordered_set<int>s;int x,y;
        int ans=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(Grid[i][j]==0){
                    size=0;
                    for(int k=0;k<4;k++){
                        x=i+dx[k];y=j+dy[k];
                        if(x>=0 and y>=0 and x<n and y<n and Grid[x][y]!=0){
                            s.insert(Grid[x][y]);
                        }
                    }
                    if(!s.empty()){
                        for(int x:s){
                            size+=m[x];
                        }
                        size+=1;
                        ans=max(ans,size);
                        while(!s.empty()){
                            s.erase(s.begin());
                        }
                    }
                }
            }
        }
        if(ans==0){
            for(auto p:m){
                ans=max(ans,p.second);
            }
        }
        return ans;
    }
};
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