<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 {
    int dx[4]={-1, 1, 0, 0}, dy[4]={0, 0, 1, -1};
public:
    void dfs(int x, int y, vector<vector<int>>&grid, int &num, int &count, int n, int m){
        if(x<0 || x>=n || y<0 || y>=m || grid[x][y]!=1){
            return;
        }
        grid[x][y]=num;
        count++;
        for(int i=0;i<4;i++){
            dfs(x+dx[i], y+dy[i], grid, num, count, n, m);
        }
    }
    
    int largestIsland(vector<vector<int>>& grid) {
        unordered_map<int,int>mp;
        int n=grid.size(), m=grid[0].size();
        int count, num=2;
        int ans=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1)
                {
                    //assign a number to each island and then assign number to each node of island
                    //store the count for each island number
                    count=0;
                    dfs(i, j, grid, num, count, n, m);
                    mp[num]=count;
                    num++;
                    ans=max(ans, count);
                }
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0){
                    int island1=(i>0 && grid[i-1][j]? grid[i-1][j]: -1);
                    int island2=(i<n-1 && grid[i+1][j]? grid[i+1][j]: -1);
                    int island3=(j>0 && grid[i][j-1]? grid[i][j-1]: -1);
                    int island4=(j<m-1 && grid[i][j+1]? grid[i][j+1]: -1);
                    int sum=0;
                    if(island1!=-1)
                        sum+=mp[island1];
                    if(island2!=-1 && island2!=island1){
                        sum+=mp[island2];
                    }
                    if(island3!=-1 && island3!=island1 && island3!=island2){
                        sum+=mp[island3];
                    }
                    if(island4!=-1 && island4!=island1 && island4!=island2 && island4!=island3){
                        sum+=mp[island4];
                    }
                    sum++;
                    ans=max(ans, sum);
                }
            }
        }
        return ans;
    }
};
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