<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:
    unordered_map<int, int> parent;
    unordered_map<int, int> rank;
    int n;
    
    void dfs(int i, int j, int &count, int &p, vector<vector<int>> &grid) {
        if (!inrange(i, j) || grid[i][j] == 0) return;
        
        grid[i][j] = 0;
        count++;
        int node = hash(i, j);
        parent[node] = p;
        
        dfs(i + 1, j, count, p, grid);
        dfs(i - 1, j, count, p, grid);
        dfs(i, j + 1, count, p, grid);
        dfs(i, j - 1, count, p, grid);
    } 
    int largestIsland(vector<vector<int>>& grid) {
        n = grid.size();
        vector<vector<int>> copyGrid = grid;
        vector<int> dir = {0, 1, 0, -1, 0};
        int maxArea = 0;
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (copyGrid[i][j] == 1) {
                    int p = hash(i, j);
                    int count = 0;
                    dfs(i, j, count, p, copyGrid);
                    rank[p] = count;
                    maxArea = max(maxArea, count);
                }
            }
        }
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0) {
                    unordered_set<int> found;
                    int count = 1;
                    
                    for (int k = 0; k < 4; k++) {
                        int nX = i + dir[k];
                        int nY = j + dir[k + 1];
                        int side = hash(nX, nY);
                        if (inrange(nX, nY) && found.find(parent[side]) == found.end() && grid[nX][nY] == 1) {
                                count += rank[parent[side]];
                            found.insert(parent[side]);
                        }
                    }//cout<< endl << count << endl<<endl;
                    maxArea = max(maxArea, count);
                }
            }
        }
        
        return maxArea;
    }
private:
    bool inrange(int i, int j) {
        return min(i, j) >= 0 && i < n && j < n;
    }
    int hash(int i, int j) {
        return i * n + j % n;
    }
};
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