<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 largestIsland(vector<vector<int>>& grid) {
        vector<int> table {0,0};
        int result = 0;
        for(int i = 0; i < grid.size(); ++i){
            for(int j = 0; j < grid[0].size(); ++j){
                if(grid[i][j] == 1){
                    int count = DFS(grid, i, j, table.size());
                    table.push_back(count);
                    result = max(result, count);
                }
            }
        }

        vector<pair<int,int>> dir {{-1,0}, {1,0}, {0,-1}, {0,1}};
        for(int i = 0; i < grid.size(); ++i){
            for(int j = 0; j < grid[0].size(); ++j){
                if(grid[i][j] == 0){
                    unordered_set<int> exist;
                    int count = 0;
                    for(int k = 0; k < dir.size(); ++k){
                        int newX = i + dir[k].first;
                        int newY = j + dir[k].second;
                        if(newX >= 0 && newY >= 0 && newX < grid.size() && newY < grid[0].size() && exist.count(grid[newX][newY]) == 0){
                            count += table[grid[newX][newY]];
                            exist.insert(grid[newX][newY]);
                        }
                    }
                    result = max(result, count + 1);
                }
            }
        }
        return result;
    }

private:
    int  DFS(vector<vector<int>> & grid, int x, int y, int id){
        if(x < 0 || y < 0 || x >= grid.size() || y >= grid[0].size() || grid[x][y] != 1) return 0;

        grid[x][y] = id;
        int count = 1;
        count += DFS(grid, x-1, y, id);
        count += DFS(grid, x+1, y, id);
        count += DFS(grid, x, y-1, id);
        count += DFS(grid, x, y+1, id);
        return count;
    }
};
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