> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/hashmap-and-hashset-and-sliding-window/grid-illumination.md).

# Grid Illumination

On a `N x N` grid of cells, each cell `(x, y)` with `0 <= x < N` and `0 <= y < N` has a lamp.

Initially, some number of lamps are on.  `lamps[i]` tells us the location of the `i`-th lamp that is on.  Each lamp that is on illuminates every square on its x-axis, y-axis, and both diagonals (similar to a Queen in chess).

For the i-th query `queries[i] = (x, y)`, the answer to the query is 1 if the cell (x, y) is illuminated, else 0.

After each query `(x, y)` \[in the order given by `queries`], we turn off any lamps that are at cell `(x, y)` or are adjacent 8-directionally (ie., share a corner or edge with cell `(x, y)`.)

Return an array of answers.  Each value `answer[i]` should be equal to the answer of the `i`-th query `queries[i]`.

**Example 1:**

```
Input: N = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,0]]
Output: [1,0]
Explanation: 
Before performing the first query we have both lamps [0,0] and [4,4] on.
The grid representing which cells are lit looks like this, where [0,0] is the top left corner, and [4,4] is the bottom right corner:
1 1 1 1 1
1 1 0 0 1
1 0 1 0 1
1 0 0 1 1
1 1 1 1 1
Then the query at [1, 1] returns 1 because the cell is lit.  After this query, the lamp at [0, 0] turns off, and the grid now looks like this:
1 0 0 0 1
0 1 0 0 1
0 0 1 0 1
0 0 0 1 1
1 1 1 1 1
Before performing the second query we have only the lamp [4,4] on.  Now the query at [1,0] returns 0, because the cell is no longer lit.
```

**Note:**

1. `1 <= N <= 10^9`
2. `0 <= lamps.length <= 20000`
3. `0 <= queries.length <= 20000`
4. `lamps[i].length == queries[i].length == 2`

```java
class Solution {
    // Solution is O(N) Time & Space Complexity
    Map<Integer, Integer> xMap, yMap, d1, d2;
    // 4 map for 4 lines & 1 extra set for lamp positions
    // Consider lines:
    // 1) x=i (Storing value of x)
    // 2) y=j (Storing value of y)
    // 3) y=mx+c (d1 -> m=tan(45deg)=1) -> (y-x)=j-i (storing value of y-x)
    // 4) y=mx+c (d2 -> m=tan(-45deg)=-1) -> (y+x)=j+i (storing value of y+x)
    public int[] gridIllumination(int N, int[][] lamps, int[][] queries) {
        xMap = new HashMap<>();
        yMap = new HashMap<>();
        d1 = new HashMap<>();
        d2 = new HashMap<>();
        Set<String> set = new HashSet<>();
        for (int[] lamp : lamps) {
            xMap.put(lamp[0], xMap.getOrDefault(lamp[0], 0) + 1);
            yMap.put(lamp[1], yMap.getOrDefault(lamp[1], 0) + 1);
            d1.put(lamp[1] - lamp[0], d1.getOrDefault(lamp[1] - lamp[1], 0) + 1);
            d2.put(lamp[1] + lamp[0], d2.getOrDefault(lamp[1] + lamp[0], 0) + 1);
            String key = Integer.toString(lamp[0]) + " " + Integer.toString(lamp[1]);
            set.add(key);
        }
        int[][] dirs = { { 1, 0 }, { 0, 1 }, { -1, 0 }, { 0, -1 }, { 1, 1 }, { -1, -1 }, { -1, 1 }, { 1, -1 } };
        int[] ans = new int[queries.length];
        for (int i = 0; i < queries.length; i++) {
            int xCoord = queries[i][0], yCoord = queries[i][1];
            if (xMap.containsKey(xCoord) || yMap.containsKey(yCoord) || d1.containsKey(yCoord - xCoord)
                    || d2.containsKey(yCoord + xCoord)) {
                ans[i] = 1;
                String center = Integer.toString(xCoord) + " " + Integer.toString(yCoord);
                if (set.contains(center)) {
                    set.remove(center);
                    removeLighting(xCoord, yCoord);
                }
                for (int[] dir : dirs) {
                    int newX = xCoord + dir[0], newY = yCoord + dir[1];
                    if (newX >= 0 && newX < N && newY >= 0 && newY < N) {
                        String lamp = Integer.toString(newX) + " " + Integer.toString(newY);
                        if (set.contains(lamp)) {
                            set.remove(lamp);
                            removeLighting(newX, newY);
                        }
                    }
                }
            } else
                ans[i] = 0;
        }
        return ans;
    }

    public void removeLighting(int x, int y) {
        xMap.put(x, xMap.get(x) - 1);
        if (xMap.get(x) == 0)
            xMap.remove(x);
        yMap.put(y, yMap.get(y) - 1);
        if (yMap.get(y) == 0)
            yMap.remove(y);
        d1.put(y - x, d1.get(y - x) - 1);
        if (d1.get(y - x) == 0)
            d1.remove(y - x);
        d2.put(y + x, d2.get(y + x) - 1);
        if (d2.get(y + x) == 0)
            d2.remove(y + x);
    }
}
```


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