<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:
  std::map<int, int> id_to_area;
  int id = 2;
  int max_area = 0;
  int largestIsland(vector<vector<int>>& grid) {
    int n = grid.size();
    if(n == 0) return 0;
    int m = grid[0].size();
    if(m == 0) return 0;
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < m; j++) {
        if(grid[i][j] == 1) {
          dfs(grid, i, j);
          max_area = max(max_area, id_to_area[id]);;
          id++;
        }
      }
    }
    
    // Start BFS part;
    std::vector<std::vector<int>> dirs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < m; j++) {
        if(grid[i][j] == 0) {
          std::set<int> visited;
          int tmp = 0;
          for(const auto dir : dirs) {
            int x = i + dir[0];
            int y = j + dir[1];
            if(x < 0 || y < 0 || x >= n || y >= m) continue;
            const int id = grid[x][y];
            if(id < 2) continue;
            if(visited.find(id) != visited.end()) continue;
            visited.insert(id);
            tmp += id_to_area[id];
          }
          max_area = max(max_area, 1 + tmp);
        }
      }
    }
    return max_area;
  }
  void dfs(vector<vector<int>>& grid, int x, int y) {
    if(x < 0 || x >= grid.size() || y < 0 || y >= grid[0].size()) {
      return;
    }
    if(grid[x][y] != 1) {
      return;
    }
    id_to_area[id]++;
    grid[x][y] = id;
    dfs(grid, x - 1, y);
    dfs(grid, x + 1, y);
    dfs(grid, x, y - 1);
    dfs(grid, x, y + 1);
  }
};
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