<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 {
    //time complexity : O(n2)
    // mark all unique island with some unique number and map its mark no. to 
    //total no of block on that marked island
public:
    map<int,int> mp;
    void solve(vector<vector<int>>& grid, int i, int j, int mark){
        queue<pair<int,int>> q;
        q.push({i,j});
        int row[] = {0,1,0,-1};
        int col[] = {1,0,-1,0};

        int count = 1;
        while(q.size()){
            int r = q.front().first;
            int c = q.front().second;
            q.pop();

            for(int k = 0; k < 4; k++){
                int x = r + row[k];
                int y = c + col[k];

                if(x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size() && grid[x][y] == 1){
                    grid[x][y] = mark;
                    count++;
                    q.push({x,y});
                }
            }
        }

        mp[mark] = count;

    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();

        mp[0] = 0;
        int mark = 2;

        for(int i = 0; i < n; i ++){
            for(int j = 0; j < grid[0].size(); j++){
                if(grid[i][j] == 1){
                    grid[i][j] = mark;
                    solve(grid,i,j,mark);
                    mark++;
                }
            }
        }

        // for(int i = 0; i < n; i ++){
        //     for(auto val : grid[i]) cout<<val<<" ";
        //     cout<<endl;
        // }

        // cout<<endl;
        // for(auto it : mp) cout<<it.first<<"->"<<it.second<<endl;

        int ans = 1;

        int row[] = {0,1,0,-1};
        int col[] = {1,0,-1,0};
        for(int i = 0; i < n; i ++){
            for(int j = 0; j < grid[0].size(); j++){
                if(grid[i][j] != 0) ans = max(ans,mp[grid[i][j]]);
                else{
                    set<int> st;
                    for(int k = 0; k < 4; k++){
                        int x = i + row[k];
                        int y = j + col[k];

                        if(x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size()){
                            st.insert(grid[x][y]);
                            // if(i == 3 && j == 1) cout<<grid[][j]<<" ";
                        }
                    }
                    int res = 1;
                    for(auto val : st) {
                        res += mp[val];
                    }
                    // cout<<endl;
                    ans = max(ans,res);
                    // if(i == 3 && j == 1) cout<<i<<" "<<j<<"->"<<res<<endl;
                }
            }
        }

        return ans;
    }
};
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