<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 markIsland(vector<vector<int>>& grid, int rows, int cols, int i, int j, int counter){
        if(i < 0 || i >= rows || j < 0 || j >= cols)
            return 0;

        if(grid[i][j] == 0 || grid[i][j] > 1)
            return 0;

        grid[i][j] = counter;
        int area = 1;

        area += markIsland(grid, rows, cols, i+1, j, counter);
        area += markIsland(grid, rows, cols, i-1, j, counter);
        area += markIsland(grid, rows, cols, i, j-1, counter);
        area += markIsland(grid, rows, cols, i, j+1, counter);
        return area;
    }

    int findArea(vector<vector<int>>& grid, int rows, int cols, int i, int j, map<int, int>& areaMap){
        if(i < 0 || i >= rows || j < 0 || j >= cols)
            return 0;

        int area = 1;
        set<int> localSet;

        if(i+1 < rows && grid[i+1][j] != 0) {
            area += areaMap[grid[i+1][j]];
            localSet.insert(grid[i+1][j]);
        }
        if(i-1 >= 0 && grid[i-1][j] != 0 && !localSet.contains(grid[i-1][j])){
            area += areaMap[grid[i-1][j]];
            localSet.insert(grid[i-1][j]);
        }
        if(j+1 < cols && grid[i][j+1] != 0 && !localSet.contains(grid[i][j+1])){
            area += areaMap[grid[i][j+1]];
            localSet.insert(grid[i][j+1]);
        }
        if(j-1 >= 0 && grid[i][j-1] != 0 && !localSet.contains(grid[i][j-1])){
            area += areaMap[grid[i][j-1]];
        }

        return area;
    }

    int largestIsland(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();
        int counter = 2;
        map<int, int> areaMap;
        areaMap[0] = 0;
        int result = 0;

        for(int i=0; i < rows; i++){
            for(int j=0; j < cols; j++){
                if(grid[i][j]==1){
                    int area = markIsland(grid, rows, cols, i, j, counter);
                    areaMap[counter] = area;
                    result = max(result, area);
                    counter++;
                }
            }
        }

        for(int i=0; i < rows; i++){
            for(int j=0; j < cols; j++){
                if(grid[i][j]==0){
                    int newArea = findArea(grid, rows, cols, i, j, areaMap);
                    result = max(result, newArea);
                }
            }
        }
        return result;
    }
};
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