<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<vector<int>> dirs={{0,1},{1,0},{-1,0},{0,-1}};
    void traverse_cur_island(vector<vector<int>>& grid, int row, int col, int& curArea, int& island_id){
        curArea++;
        grid[row][col]=island_id;
        for(vector<int> dir:dirs){
            int nrow=row+dir[0];
            int ncol=col+dir[1];
            if(nrow < 0 || ncol < 0 || nrow >= grid.size() || ncol >= grid.size() || grid[nrow][ncol]!=1){
                continue;
            }
            traverse_cur_island(grid,nrow,ncol,curArea,island_id);
        }
    }
    
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        unordered_map<int,int> area;
        int maxArea=0;
        int curArea=0;
        int island_id=2;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1){
                    traverse_cur_island(grid,i,j,curArea,island_id);
                    maxArea=max(maxArea,curArea);
                    area[island_id]=curArea;
                    curArea=0;
                    island_id++;
                }
            }
        }
        
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    set<int> adj_islands;
                    for(vector<int> dir:dirs){
                        int nrow=i+dir[0];
                        int ncol=j+dir[1];
                        if(nrow < 0 || ncol < 0 || nrow >= n || ncol >= n || grid[nrow][ncol]==0){
                            continue;
                        }
                        adj_islands.insert(grid[nrow][ncol]);
                    }
                    int adj_island_sum=1;
                    for(int i:adj_islands){
                        adj_island_sum+=area[i];
                    }
                    maxArea=max(maxArea,adj_island_sum);
                }
            }
        }
        return maxArea;
    }
};
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