<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:

    // bfs using i, j
    int findIslandAreaAtCoordinate(vector<vector<int>>& grid, int i, int j, int islandIndex) {
        queue<pair<int, int>> island;
        island.push({i, j});
        // this is also used to mark coord as visited
        grid[i][j] = islandIndex;

        int area = 0;
        vector<pair<int, int>> directions = {
            { -1, 0 },
             { 1, 0 },
            { 0, 1 },
            { 0, -1}
        };

        while (!island.empty()) {
            auto [xCoord, yCoord] = island.front();
            area++;
            island.pop();

            for (auto [xDelta, yDelta]: directions) {
                int x = xCoord + xDelta;
                int y = yCoord + yDelta;
                if (x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size()) {
                    if (grid[x][y] == 1) {
                        island.push({ x, y });
                        grid[x][y] = islandIndex;
                    }
                }
            }
        }
        return area;
    }

    int largestIsland(vector<vector<int>>& grid) {
        // Optimized Approach:
        // keep maping of islandGroupIndex -> area of island
        // set the grid of that island to an index/id
        //   this prevents it from being recalculated
        // for every 0, look check 4 corners to see if its neighboring a island
        // if so, add the areas of the unique groups + 1
        // default to max of calculated areas if theres no 0s 

        int islandIndex = 2;
        unordered_map<int, int> indexToArea;
        int maxArea = 0;


        vector<pair<int, int>> directions = {
            { -1, 0 },
             { 1, 0 },
            { 0, 1 },
            { 0, -1}
        };


        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[i].size(); j++) {
                // found new island
                if (grid[i][j] == 1) {
                    int area = findIslandAreaAtCoordinate(grid, i, j, islandIndex);
                    indexToArea[islandIndex] = area;
                    cout << islandIndex << " " << area << endl;
                    maxArea = max(maxArea, area);
                    islandIndex++;
                }
            }
        }

        for (int i = 0; i < grid.size(); i++) {
            for (int j = 0; j < grid[i].size(); j++) {
                // turn 0 -> 1
                if (grid[i][j] == 0) {
                    int area = 1;
                    unordered_set<int> seenIslands;
                    for (auto [xDelta, yDelta]: directions) {
                        int x = i + xDelta;
                        int y = j + yDelta;
                        if (x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size()) {
                            int val = grid[x][y];
                            if (val != 0 && seenIslands.count(val) == 0) {
                                area += indexToArea[val];
                                seenIslands.insert(val);
                            }
                        }
                    }
                    maxArea = max(maxArea, area);
                }
            }
        }
        return maxArea;
    }
};
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