<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 dfs(int i,int j,vector<vector<int>>& grid){
        int count=1;
        if(j+1<grid.size() and grid[i][j+1]==1){
            grid[i][j+1]=grid[i][j];
            count+=dfs(i,j+1,grid);
        }
        if(i+1<grid.size() and grid[i+1][j]==1){
            grid[i+1][j]=grid[i][j];
            count+=dfs(i+1,j,grid);
        }
        if(j-1>=0 and grid[i][j-1]==1){
            grid[i][j-1]=grid[i][j];
            count+=dfs(i,j-1,grid);
        }
        if(i-1>=0 and grid[i-1][j]==1){
            grid[i-1][j]=grid[i][j];
            count+=dfs(i-1,j,grid);
        }
        return count;
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        vector<vector<int>> id(n,vector<int> (n,-1));
        int c=2;
        map<int,int> mp;
        int ans=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1) {
                    grid[i][j]=c;                    
                    mp[c]=dfs(i,j,grid);
                    if(mp[c]>ans) ans=mp[c];
                    c++;
                }
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int a,b,c,d;
                a=b=c=d=-1;
                int curr=1;
                if(grid[i][j]==0) {
                    if(i-1>=0){
                        a=grid[i-1][j];
                    }
                    if(j-1>=0){
                        b=grid[i][j-1];
                    }
                    if(i+1<n){
                        c=grid[i+1][j];
                    }
                    if(j+1<n){
                        d=grid[i][j+1];
                    }
                    if(a>1) curr+=mp[a];
                    if(b>1 and b!=a) curr+=mp[b];
                    if(c>1 and c!=a and c!=b) curr+=mp[c];
                    if(d>1 and d!=a and d!=b and d!=c) curr+=mp[d];
                }
                if(curr>ans) ans=curr;
            }
        }
        return ans;
    }
};
68203