<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:
    void dfs(int i,int j, int colour,int &ans,unordered_map<int,int>& hash, vector<vector<int>>& vis,vector<vector<int>>& grid){
        int n = grid.size();
        int m = grid[0].size();
        // if(i<0 || j<0 || i>=n || j>=m || vis[i][j]!=0 || grid[i][j]==0) return;
        vector<vector<int>> dis = {{1,0},{-1,0},{0,1},{0,-1}};
        // ans++;
        for(int k=0; k<4; k++){
            int nx = i+dis[k][0];
            int ny = j+dis[k][1];
            if(nx<0 || ny<0 || nx>=n || ny>=m || vis[nx][ny]!=0 || grid[nx][ny]==0) continue;
            vis[nx][ny]=colour;
            ans++;
            dfs(nx,ny,colour,ans,hash,vis,grid);
        }
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        int f=INT_MIN;
        int colour=1;
        unordered_map<int,int> hash;
        vector<vector<int>> vis(n,vector<int>(m,0));
        vector<vector<int>> dis = {{1,0},{-1,0},{0,1},{0,-1}};
        for(int i=0; i<n;i++){
            for(int j=0; j<m; j++){
                if(vis[i][j]==0 && grid[i][j]==1){
                    int ans = 1;
                    vis[i][j]=colour;
                    dfs(i,j,colour,ans,hash,vis,grid);
                    hash[colour]=ans;
                    colour++;
                    f=max(f,ans);
                    cout<<ans<<endl;
                }
            }
        }
        int res = 0;
        for(int i=0; i<n;i++){
            for(int j=0; j<m; j++){
                if(grid[i][j]==0){
                    set<int>neighbouringIslands;
                    for(int k=0; k<4; k++){
                        int nx = i+dis[k][0];
                        int ny = j+dis[k][1];
                        if(nx<0 || ny<0 || nx>=n || ny>=m) continue;
                        if (grid[nx][ny] == 1){
                            neighbouringIslands.insert(vis[nx][ny]);
                        }
                    }
                    int area = 1;
                    for (auto it: neighbouringIslands){
                        area += hash[it];
                    }
                    res = max(res, area);
                }
            }
        }
        return max(f,res);
    }
};
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