<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:
    vector<int> gridIllumination(int n, vector<vector<int>>& lamps, vector<vector<int>>& queries) {
        unordered_map<int, int> rowMap;
        unordered_map<int, int> colMap;
        unordered_map<int, int> diagMap;
        unordered_map<int, int> offDiagMap;
        unordered_map<int, unordered_set<int>> lampMap;

        int i, row, col;
        for(i = 0; i < lamps.size(); i++){
            row = lamps[i][0];
            col = lamps[i][1];

            if(lampMap.find(row) == lampMap.end()){
                unordered_set<int> colSet;
                lampMap[row] = colSet;
            }
            if(lampMap[row].find(col) == lampMap[row].end()){
                lampMap[row].insert(col);
                rowMap[row]++;
                colMap[col]++;
                diagMap[row - col]++;
                offDiagMap[row + col]++;
            }
        }

        vector<int> ans;
        vector<vector<int>> moves = {{-1, -1}, {-1, 0}, {-1, 1}, {0, 1}, {0, 0}, {0, -1}, {1, 0}, {1, -1}, {1, 1}}; 
        for(i = 0; i < queries.size(); i++){
            row = queries[i][0];
            col = queries[i][1];

            if(rowMap[row] || colMap[col] || diagMap[row - col] || offDiagMap[row + col]){
                ans.push_back(1);
            }
            else{
                ans.push_back(0);
            }

            for(auto& move : moves){
                int nextRow = row + move[0];
                int nextCol = col + move[1];

                if(lampMap.find(nextRow) != lampMap.end() && lampMap[nextRow].find(nextCol) != lampMap[nextRow].end()){
                    lampMap[nextRow].erase(nextCol);
                    if(lampMap[nextRow].size() == 0){
                        lampMap.erase(nextRow);
                    }

                    rowMap[nextRow]--;
                    colMap[nextCol]--;
                    diagMap[nextRow - nextCol]--;
                    offDiagMap[nextRow + nextCol]--;
                }
            }
        }
        return ans;
    }
};
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