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Grid Illumination in Python
Suppose we have a N x N grid of cells, in each cell (x, y) there is a lamp. Initially, some of the lamps are on. The lamps[i] is the location of the i-th lamp that is on. Each lamp that is on glows every square on its x-axis, y-axis, and both diagonals. Now for the i-th query i.e. queries[i] = (x, y), the answer to the query is 1 if the cell (x, y) is glowed, otherwise 0. After each query (x, y), we turn off any lamps that are at cell (x, y) or are adjacent 8-directionally. Return an array of answers. Each value answer[i] should be equal to the answer of the i-th query queries[i].
So, if the input is like N = 5, lamps are [[0,0],[4,4]], query = [[1,1],[1,0]], then the output will be [1,0]
To solve this, we will follow these steps −
lamps := set of pairs from the given array lamps
Create maps x, y, diag1, diag2
for each pair (i, j) in lamps
x[i] := x[i] + 1, y[j] := y[j] + 1
diag1[i + j] := diag1[i + j] + 1, diag2[i - j] = diag2[i - j] + 1
ans := []
for each value i in C
a := i[0], b := i[1]
insert (1 if x[a] + y[b] + diag1[a + b] + diag2[a - b] > 0 otherwise 0) into ans
for row in range a - 1 to a + 1
for col in range b - 1 to b + 1
if row, col pair is in lamps, then −
x[row] := x[row] - 1
y[col] := y[col] - 1
diag1[row + col] = diag1[row + col] - 1
diag2[row - col] = diag2[row - col] - 1
remove(row, col) from lamps
return ans
Let us see the following implementation to get better understanding −
Example
from collections import defaultdict
class Solution(object):
def gridIllumination(self, N, b, C):
lamps = {(i[0], i[1]) for i in b}
x, y, diag1, diag2 = defaultdict(int), defaultdict(int),
defaultdict(int), defaultdict(int)
for i, j in lamps:
x[i] += 1
y[j] += 1
diag1[i + j] += 1
diag2[i - j] += 1
ans = []
for i in C:
a = i[0]
b = i[1]
ans.append(1 if x[a] + y[b] + diag1[a + b] + diag2[a - b] > 0 else 0)
for row in range( a - 1, a + 2):
for col in range(b - 1, b + 2):
if (row, col) in lamps:
x[row] -= 1
y[col] -= 1
diag1[row + col] -= 1
diag2[row - col] -= 1
lamps.remove((row, col))
return ans
ob = Solution()
N = 5
lamps = [[0,0],[4,4]]
query = [[1,1],[1,0]]
print(ob.gridIllumination(N, lamps, query))Input
5, [[0,0],[4,4]], [[1,1],[1,0]]
Output
[1, 0]
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