<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:

    bool static isValid(int x, int y, int rows, int cols) {
        return x >= 0 and x < rows and y >= 0 and y < cols;
    }

    int dfs(vector<vector<int>> &grid, int x, int y, int colour) {

        int rows = grid.size();
        int cols = grid[0].size();

        if (!isValid(x, y, rows, cols) || grid[x][y] != 1) {
            return 0;
        }

        grid[x][y] = colour;

        int ans  = 1;

        int r[] = {-1, 1,0, 0};
        int c[] = {0, 0, -1, 1};

        for (int i = 0; i < 4; i++) {
            ans = ans + dfs(grid, x + r[i], y + c[i], colour);
        }

        return ans;
    }
    int largestIsland(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();

        int colour = 2;

        unordered_map<int, int> mp;
        int ans = 0;
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (grid[i][j]) {
                    int sz = dfs(grid, i, j, colour);
                    mp[colour] = sz;
                    colour += 1;
                    ans = max(ans, sz);
                    // cout<<i<<" "<<j<<" "<<sz<<endl;
                }
            }
        }

        int r[] = {-1, 1,0, 0};
        int c[] = {0, 0, -1, 1};


        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (grid[i][j] == 0) {
                    int sum = 1;
                    unordered_set<int> st;
                    for (int k = 0; k < 4; k++) {
                        int newX = r[k] + i;
                        int newY = c[k] + j;

                        if (isValid(newX, newY, rows, cols)) {
                            int col = grid[newX][newY];
                            if (st.find(col) == st.end()) {
                                sum += mp[col];
                                st.insert(col);
                            }
                        }
                    }
                    ans = max(ans, sum);
                }
            }
            // cout<<endl;
        }
        return ans;
    }
};
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