<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>

auto fast = []() {
    std::ios_base::sync_with_stdio(false);
    std::cout.tie(nullptr);
    std::cin.tie(nullptr);
    return 0;
}();
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        vector<int> area;
        queue<pair<int, int>> q;
        vector<vector<int>> vis(n, vector<int>(n));
        area.push_back(0);
        int color = 1;
        int ans = 1;
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                int cnt = 0;
                if(vis[i][j] == 0 && grid[i][j]){
                    dfs(grid, i, j, n,  vis, cnt, q, color);
                    area.push_back(cnt);
                    ans = max(ans, cnt);
                    color++;
                }
               
            }
        }
        int s = q.size();
        vector<int> r = {0,0,1,-1};
        vector<int> c = {1,-1,0,0};
        while(s--){
            set<int> sp;
            int row = q.front().first;
            int col = q.front().second;
            q.pop();
            for(int i = 0; i < 4; i++){
                int nrow = row + r[i]; int ncol = col + c[i];
                if(nrow >= 0 && nrow < n && ncol >= 0 && ncol < n && vis[nrow][ncol] != 0) {sp.insert(vis[nrow][ncol]);}
            }
            int val = 0;
            for(auto col : sp) val += area[col]; 
            ans = max(ans,val+1);
        }
        return ans;
    }
    void dfs(vector<vector<int>>& grid, int i, int j, int n, vector<vector<int>>& vis, int& cnt, queue<pair<int, int>>& q, int color){
        if(i < 0 || i >= n || j < 0 || j >= n || vis[i][j]) return;
        if(grid[i][j] == 0){ q.push({i,j});return;}
        if(grid[i][j] != 1) return;
        vis[i][j] = color;
        cnt++;
        dfs(grid,i+1,j,n,vis,cnt,q,color);
        dfs(grid,i-1,j,n,vis,cnt,q,color);
        dfs(grid,i,j+1,n,vis,cnt,q,color);
        dfs(grid,i,j-1,n,vis,cnt,q,color);
    }
};
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