<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 n;
    map<int, int> landMap;
    int islandSize(vector<vector<int>>& grid, int i, int j, vector<vector<int>>& dp, int landIdx) {
        
        if(i >= 0 && i < n && j >= 0 && j < n && grid[i][j]) {
            //cout << i << " --------- " << j << endl;
            
            if(dp[i][j] != -1) return landMap[landIdx];
            //cout << " Recursion" << endl;
            dp[i][j] = landIdx;

            int size = 1 + islandSize(grid, i+1, j, dp, landIdx) + islandSize(grid, i, j+1, dp, landIdx) +
                islandSize(grid, i-1, j, dp, landIdx) + islandSize(grid, i, j-1, dp, landIdx);

            return size;
        }

        return 0;
    }

    int largestIsland(vector<vector<int>>& grid) {
        n = grid.size();
        vector<vector<int>> dp(n, vector<int>(n, -1));
        int landIdx = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    
                    //cout << "i: " << i << " j: " << j << " idx" << landIdx << " size: ";
                    landMap[landIdx] = islandSize(grid, i, j, dp, landIdx);
                    //cout << landMap[landIdx] << endl;
                    landIdx++;
                    
                }
            }
        }
        int dir[4][2] = {{1,0}, {0,1}, {-1,0}, {0,-1}};
        int ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0) {
                    //cout << " i: " << i << " j: " << j << endl;
                    set<int> neibourLandIdxSet;
                    for(auto& d: dir) {
                        int x = i + d[0];
                        int y = j + d[1];

                        if(x>=0 && x<n && y>=0 && y<n && grid[x][y] && dp[x][y] != -1) {
                            neibourLandIdxSet.insert(dp[x][y]);
                        
                            //cout << " x: " << x << " y: " << y;
                        }
                    }
                    int potentialSize = 1;
                    for(auto nei: neibourLandIdxSet) {
                        potentialSize += landMap[ nei ];
                    }
                    //cout << " size: " << potentialSize << endl;
                    
                    ans = max(ans, potentialSize);
                }
            }
        }
        return ans == 0 ? n*n : ans;
    }
};
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