<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:
    void dfs(vector<vector<int>> &grid, int r, int c, int &m, int &n, vector<vector<int>> &mapping, int &v) {
        grid[r][c] = 2;
        mapping[r][c] = v;
        //cout<<r<<" "<<c<<" "<<grid[r][c]<<"\n";
        //cout<<v<<"\n";
        for(int i = -1; i <= 1; i++) {
            for(int j = -1; j <= 1; j++) {
                if(i == j) {
                    continue;
                }
                if(i == -1 && j == 1) {
                    continue;
                }
                if(i == 1 && j == -1) {
                    continue;
                }
                if((r + i) >= 0 && (r + i) < m && (c + j) >= 0 && (c + j) < n && grid[r + i][c + j] == 1) {
                    dfs(grid, r + i, c + j, m, n, mapping, v);
                }
            }
        }
    }
    int largestIsland(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size(), v = 1, c, ans = 0;
        vector<vector<int>> mapping(m, vector<int>(n, 0));
        unordered_map<int, int> count;
        unordered_set<int> st;
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                if(grid[i][j] == 1) {
                    // cout<<i<<" "<<j<<" "<<grid[i][j]<<"\n";
                    dfs(grid, i, j, m, n, mapping, v);
                    v++;
                }
                if(mapping[i][j] != 0) {
                    count[mapping[i][j]]++;
                }
            }
        }
        // for(auto i : count) {
        //     cout<<i.first<<" "<<i.second<<"\n";
        // }
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                if(grid[i][j] == 0) {
                    c = 0;
                    st.clear();
                    if(i - 1 >= 0) {
                        st.insert(mapping[i - 1][j]);
                        c += count[mapping[i - 1][j]];
                    }
                    if(j - 1 >= 0 && st.find(mapping[i][j - 1]) == st.end()) {
                        st.insert(mapping[i][j - 1]);
                        c += count[mapping[i][j - 1]];
                    }
                    if(i + 1 < m && st.find(mapping[i + 1][j]) == st.end()) {
                        st.insert(mapping[i + 1][j]);
                        c += count[mapping[i + 1][j]];
                    }
                    if(j + 1 < n && st.find(mapping[i][j + 1]) == st.end()) {
                        st.insert(mapping[i][j + 1]);
                        c += count[mapping[i][j + 1]];
                    }
                    ans = max(c + 1, ans);
                }
                ans = max(ans, count[mapping[i][j]]);
            }
        }
        return ans;
    }
};
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