<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> xdir = {-1,1,0,0};
    vector<int> ydir = {0,0,1,-1};


    void dfs(int x,int y,vector<vector<int>> &grid,vector<vector<int>> &vis,map<pair<int,int>,int> &comp,int cnt){
        vis[x][y]=1;
        comp[{x,y}]=cnt;
        for(int z=0;z<4;z++){
            int i =x + xdir[z];
            int j = y + ydir[z];
            if(i>=0 && j>=0 && i<grid.size() && j<grid[0].size() && grid[i][j]==1 && !vis[i][j]){
                dfs(i,j,grid,vis,comp,cnt);            }
        }
        
    }

    int largestIsland(vector<vector<int>>& grid) {
        map<int,int> mp;
        map<pair<int,int>,int> comp;
        int n=grid.size();
        int m=grid[0].size();
        vector<vector<int>> vis(n,vector<int> (m,0));
        int cnt=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && !vis[i][j]){
                    cnt++;
                    dfs(i,j,grid,vis,comp,cnt);
                }
            }
        }
        vector<int> score(cnt+1,0);
        int ans = 0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1){
                    score[comp[{i,j}]]++;
                    ans = max(ans,score[comp[{i,j}]]);
                }
            }
        }
        
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0){
                    int cnt=0;
                    set<pair<int,int>> st;
                    for(int z=0;z<4;z++){
                        int x = i+xdir[z];
                        int y = j + ydir[z];
                        if(x>=0 && y>=0 && x<grid.size() && y<grid[0].size() && grid[x][y]==1){
                            // cnt+=score[comp[{x,y}]];
                            st.insert({comp[{x,y}],score[comp[{x,y}]]});
                        }
                    }
                    for(auto it:st){
                        cnt+=it.second;
                    }
                    // cout<<cnt<<endl;
                    ans = max(ans,cnt+1);
                }
            }
        }
        return ans;
    }
};
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