<p>There is a 2D <code>grid</code> of size <code>n x n</code> where each cell of this grid has a lamp that is initially <strong>turned off</strong>.</p>

<p>You are given a 2D array of lamp positions <code>lamps</code>, where <code>lamps[i] = [row<sub>i</sub>, col<sub>i</sub>]</code> indicates that the lamp at <code>grid[row<sub>i</sub>][col<sub>i</sub>]</code> is <strong>turned on</strong>. Even if the same lamp is listed more than once, it is turned on.</p>

<p>When a lamp is turned on, it <strong>illuminates its cell</strong> and <strong>all other cells</strong> in the same <strong>row, column, or diagonal</strong>.</p>

<p>You are also given another 2D array <code>queries</code>, where <code>queries[j] = [row<sub>j</sub>, col<sub>j</sub>]</code>. For the <code>j<sup>th</sup></code> query, determine whether <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> is illuminated or not. After answering the <code>j<sup>th</sup></code> query, <strong>turn off</strong> the lamp at <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> and its <strong>8 adjacent lamps</strong> if they exist. A lamp is adjacent if its cell shares either a side or corner with <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code>.</p>

<p>Return <em>an array of integers </em><code>ans</code><em>,</em><em> where </em><code>ans[j]</code><em> should be </em><code>1</code><em> if the cell in the </em><code>j<sup>th</sup></code><em> query was illuminated, or </em><code>0</code><em> if the lamp was not.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_1.jpg" style="width: 750px; height: 209px;" />
<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,0]]
<strong>Output:</strong> [1,0]
<strong>Explanation:</strong> We have the initial grid with all lamps turned off. In the above picture we see the grid after turning on the lamp at grid[0][0] then turning on the lamp at grid[4][4].
The 0<sup>th</sup>&nbsp;query asks if the lamp at grid[1][1] is illuminated or not (the blue square). It is illuminated, so set ans[0] = 1. Then, we turn off all lamps in the red square.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step1.jpg" style="width: 500px; height: 218px;" />
The 1<sup>st</sup>&nbsp;query asks if the lamp at grid[1][0] is illuminated or not (the blue square). It is not illuminated, so set ans[1] = 0. Then, we turn off all lamps in the red rectangle.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step2.jpg" style="width: 500px; height: 219px;" />
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,1]]
<strong>Output:</strong> [1,1]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[0,4]], queries = [[0,4],[0,1],[1,4]]
<strong>Output:</strong> [1,1,0]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= lamps.length &lt;= 20000</code></li>
	<li><code>0 &lt;= queries.length &lt;= 20000</code></li>
	<li><code>lamps[i].length == 2</code></li>
	<li><code>0 &lt;= row<sub>i</sub>, col<sub>i</sub> &lt; n</code></li>
	<li><code>queries[j].length == 2</code></li>
	<li><code>0 &lt;= row<sub>j</sub>, col<sub>j</sub> &lt; n</code></li>
</ul>

class Solution {
public:
    unordered_map<int, int> rows, cols, sums, diffs;
    vector<int> hor = {1, 1, 1, 0, 0, -1, -1, -1};
    vector<int> ver = {0, -1, 1, 1, -1, 0, 1, -1};
    unordered_set<string> bulbs;

    void on(int i, int j) {
        string key = to_string(i) + "," + to_string(j);
        if (bulbs.count(key)) return; // Lamp already on at this position

        bulbs.insert(key);
        rows[i]++;
        cols[j]++;
        sums[i + j]++;
        diffs[i - j]++;
    }

    void off(int i, int j) {
        string key = to_string(i) + "," + to_string(j);
        if (!bulbs.count(key)) return; // No lamp at this position

        bulbs.erase(key);
        rows[i]--;
        cols[j]--;
        sums[i + j]--;
        diffs[i - j]--;
    }

    vector<int> gridIllumination(int n, vector<vector<int>>& lamps, vector<vector<int>>& queries) {
        // Turn on all lamps
        for (auto& lamp : lamps) on(lamp[0], lamp[1]);

        vector<int> ans;
        for (auto& q : queries) {
            int x = q[0], y = q[1];

            // Check if the current cell is illuminated
            if (rows[x] || cols[y] || sums[x + y] || diffs[x - y]) {
                ans.push_back(1);  // The cell is illuminated
            } else {
                ans.push_back(0);  // The cell is not illuminated
            }

            // Turn off the lamp at (x, y) and its adjacent cells
            for (int i = 0; i < 8; i++) {
                int nx = x + hor[i], ny = y + ver[i];
                if (nx >= 0 && nx < n && ny >= 0 && ny < n) off(nx, ny);
            }
            off(x, y);  // Also turn off the current cell itself
        }

        return ans;
    }
};

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