<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 island_index = 0;
    int n;
    vector<unordered_set<int>> map_to_island;
    int dfs(vector<vector<int>>& grid, vector<vector<int>> &seen, int r, int c){
        seen[r][c] = true;
        int rdir[4] = {1, -1, 0, 0};
        int cdir[4] = {0, 0, 1, -1};
        int cur = 1;
        for(int i = 0; i < 4; i++){
            int newr = r + rdir[i];
            int newc = c + cdir[i];
            if(newr >= 0 && newr < n && newc>=0 && newc < n){
                if(!grid[newr][newc]){
                    map_to_island[n * newr + newc].insert(island_index);
                }
                else if(!seen[newr][newc]){
                    cur += dfs(grid, seen, newr, newc);
                }
            }
        }
        return cur;
    }
    int largestIsland(vector<vector<int>>& grid) {
        n = grid.size();
        int total = n*n;
        map_to_island.resize(total);
        vector<int> island_sizes;
        vector<vector<int>> seen(n, vector<int>(n, false));
        int max_island = 1;
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(!seen[i][j] && grid[i][j]){
                    int size = dfs(grid, seen, i, j);
                    island_sizes.push_back(size);
                    max_island = max(max_island, size);
                    island_index++;
                }
            }
        }
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(!grid[i][j]){
                    int total = 1;
                    for(int id: map_to_island[i*n + j]){
                        total += island_sizes[id];
                    }
                    max_island = max(max_island, total);
                }
            }
        }
        return max_island;
    }
};
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