<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 largestIsland(vector<vector<int>>& grid) {
       int n = grid.size();
       vector<vector<int>> vis(n,vector<int>(n,0));
       int dx[] = {-1,1,0,0};
       int dy[] = {0,0,-1,1};
       map<int,int> mp;
       int cv = 1;
       int ans = 0;
       for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
           if(grid[i][j] && !vis[i][j]){
            int sz = 1;
            queue<pair<int,int>> q;
            q.push({i,j});
            vis[i][j]=cv;
            while(!q.empty()){
                int x = q.front().first;
                int y = q.front().second;
                q.pop();
                for(int k=0;k<4;k++){
                    int nx = x + dx[k];
                    int ny = y + dy[k];
                    if(nx>=0 && ny>=0 && nx<n && ny<n && !vis[nx][ny] && grid[nx][ny]==1){
                        q.push({nx,ny});
                        vis[nx][ny] = cv;
                        sz++;
                    }
                }
            }
            mp[cv] = sz;
            ans = max(ans,sz);
            cv++;
           }
        }
       }
       for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            if(grid[i][j]==0){
                set<int> st;
                for(int k=0;k<4;k++){
                    int nx = i + dx[k];
                    int ny = j + dy[k];
                    if(nx>=0 && ny>=0 && nx<n && ny<n){
                        st.insert(vis[nx][ny]);
                    }
                }
                int cans = 1;
                for(auto i:st) cans+=mp[i];
                ans = max(ans,cans);
            }
        }
       }
       return ans;
    }
};
224128