<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 n;
    vector<pair<int,int>> adj{{0,1},{1,0},{-1,0},{0,-1}};
    void helper(vector<vector<int>>&grid,vector<vector<int>>&dp,int i,int j,int &ans){
        if(i<0 || i>=n || j<0 || j>=n)return;
        if(grid[i][j] == 0)return;
        if(dp[i][j] == -1)return;
        dp[i][j] = -1;
        ans++;
        for(auto &c:adj){
            helper(grid, dp,i+c.first,j+c.second,ans);
        }
    }

    void helper2(vector<vector<int>>&grid,vector<vector<int>>&dp,int i,int j,int cmp){
        if(i<0 || i>=n || j<0 || j>=n)return;
        if(grid[i][j] == 0)return;
        if(dp[i][j] == cmp)return;
        dp[i][j] = cmp;
        for(auto &c:adj){
            helper2(grid, dp,i+c.first,j+c.second,cmp);
        }
    }

    int find_neighbour(vector<vector<int>>&grid, vector<vector<int>>&dp,int i,int j, unordered_map<int,int>&mp){
        int x,y,a,b;
        int ans = 1;
        set<int> s;

        for(auto &c:adj){
            x = c.first+i;y=c.second+j;
            if(x<0 || x>=n || y<0 || y>=n)continue;
            s.insert(dp[x][y]);
        }
        for(auto &c:s)ans+=mp[c];
        return(ans);

    }

    int largestIsland(vector<vector<int>>& grid) {
        n = grid.size();
        int cur_ans = 1;
        int cmp = 2;
        vector<vector<int>> dp(n, vector<int>(n,0));
        unordered_map<int, int> mp;
        mp[0]=0;

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j] == 0 || dp[i][j] > 0)continue;
                int ans=0;
                helper(grid, dp, i, j, ans);
                helper2(grid,dp,i,j,cmp);
                mp[cmp] = ans;
                cur_ans = max(cur_ans,ans);
                cmp++;
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j] != 0)continue;
                cur_ans = max(cur_ans,find_neighbour(grid,dp,i,j,mp));
            }
        }
        return(cur_ans);
    }
};
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