<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 getParent(int id, unordered_map<int,int>& parent) {
        if(parent[id] == id) {
            return id;
        }
        int curr_parent = getParent(parent[id], parent);
        parent[id] = curr_parent;
        return curr_parent;
    }

    void combine(int a, int b, unordered_map<int,int>& parent) {
        int parentA = getParent(a, parent);
        int parentB = getParent(b, parent);
        parent[parentA] = parentB;
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        unordered_map<int,int> parent;
        vector<int> dx = {1,0,-1,0};
        vector<int> dy = {0,1,0,-1};
        for(int i = 0;i < n;i++) {
            for(int j = 0;j < n;j++) {
                if(grid[i][j] == 1) {
                    int id = i*n + j;
                    parent[id] = id;
                    for(int k = 0;k < 4;k++) {
                        int x1 = i + dx[k], y1 = j + dy[k];
                        if(x1 >= 0 && x1 < n && y1 >= 0 && y1 < n && grid[x1][y1] == 1) {
                            int id1 = x1 * n + y1;
                            if(parent.find(id1) != parent.end()) {
                                combine(id, id1, parent);
                            }
                        }
                    }
                }
            }
        }
        int ans = 0;
        unordered_map<int,int> parent_to_size;
        for(int i = 0;i < n;i++) {
            for(int j = 0;j < n;j++) {
                if(grid[i][j] == 1) {
                    int cell_parent = getParent(i * n + j, parent);
                    parent_to_size[cell_parent]++;
                    ans = max(ans, parent_to_size[cell_parent]);
                }

            }
        }  
         for(int i = 0;i < n;i++) {
            for(int j = 0;j < n;j++) {
                if(grid[i][j] == 0) {
                    int curr = 1;
                    set<int> unique_parents;
                    for(int k = 0;k < 4;k++) {
                        int x1 = i + dx[k], y1 = j + dy[k];
                        if(x1 >= 0 && x1 < n && y1 >= 0 && y1 < n && grid[x1][y1] == 1) {
                            int id1 = x1 * n + y1;
                            int parent1 = getParent(id1, parent);
                            if(unique_parents.find(parent1) == unique_parents.end()) {
                                curr += parent_to_size[parent1];
                                unique_parents.insert(parent1);
                            }
                        }
                    }
                    ans = max(ans, curr);
                }
            }
        }
        return ans;
    }
};
128446