# Grid illumination

• Grid Illumination:

Given an NxN grid with an array of lamp coordinates. Each
lamp provides illumination to every square on their x axis, every square on
their y axis, and every square that lies in their diagonal (think of a Queen in
chess). Given an array of query coordinates, determine whether that point is
illuminated or not. The catch is when checking a query all lamps adjacent to, or
on, that query get turned off. The ranges for the variables/arrays were about:
10^3 < N < 10^9, 10^3 < lamps < 10^9, 10^3 < queries < 10^9.

• Initially I thought this might be like the "Bomb Enemy" question that Google has. Looks like it is not.

It doesn't even look like something that could use Union-Find algorithm.

Any smart ideas for this one? I am just stuck.

• @EnigmaTrance Can you explain better what the "catch" means, especially this sentence : "The catch is when checking a query all lamps adjacent to, or on, that query get turned off. "? For example there is a query for point (4,5), how do we define adjacent to this point lamps?
Could you provide an examplе?

• @elmirap Sure.
Basically when (4,5) is checked, then the 8 surrounding spots (3, 4), (3, 5), (3, 6), (4, 4), (4, 6), (7,4), (7,5), (7,6) all get turned off.

• @EnigmaTrance. I think that the problem says that only adjacent lamps get turned off when a query is made. This means that lamps which are turned off don't provide illumination in their iillumination range (x,y,coord,diagonals) while query is in progress. At least this is the way I understand the problem.
So here is my strategy. Count number of lamps in each horizontal, vertical and diagonal and store in map. On each query I count the lamps in adjacent 8 cells and check if lamps in given vertical, horizontal or diagonal are more than these in adjacent cells. If it is, I will return true, because there is at least one lamp except these in adjacent cells which illuminates the query point.

• I did not quite understand what the expected output is? Any example someone could post?

• @elmirap said in Grid illumination:

So here is my strategy. Count number of lamps in each horizontal, vertical and diagonal and store in map. On each query I count the lamps in adjacent 8 cells and check if lamps in given vertical, horizontal or diagonal are more than these in adjacent cells. If it is, I will return true, because there is at least one lamp except these in adjacent cells which illuminates the query point.

This is smart.

This is

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