<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 {
private:
    unordered_map<int, int> mp;
public:
    int largestIsland(vector<vector<int>>& grid) {
        int C = grid[0].size();
        int R = grid.size();
        int color = 2;
        int maxSize = 0;

        for (int i = 0; i < R; ++i){
            for (int j = 0; j < C; ++j){
                if (grid[i][j] != 1) continue;
                DFS(grid, i, j,  color);
                maxSize = max(maxSize, mp[color]);
                color++;
            }
        }
        vector<vector<int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

        for (int i = 0; i < R; ++i){
            for (int j = 0; j < C; ++j){
                if (grid[i][j] == 0){
                    unordered_set<int> ncs;
                    for (auto d: directions){
                        int ni = i + d[0];
                        int nj = j + d[1];
                        if (ni < 0 || ni >= R || nj < 0 || nj >= C || grid[ni][nj] == 0) continue;
                        ncs.insert(grid[ni][nj]);
                    }
                    int sizeFormed = 1;
                    for (int c: ncs) sizeFormed += mp[c];
                    maxSize = max(maxSize, sizeFormed);
                }
            }
        }



        return maxSize;
    }
    void DFS(vector<vector<int>> &grid, int i, int j, int color){
        int C = grid[0].size();
        int R = grid.size();

        if (i < 0 || i >= R || j < 0 || j >= C || grid[i][j] != 1) return;

        grid[i][j] = color;
        mp[color]++;

        DFS(grid, i + 1, j, color);
        DFS(grid, i - 1, j, color);
        DFS(grid, i, j + 1, color);
        DFS(grid, i, j - 1, color);

        


    }
};
319809