You are given an array of network towers
towers and an integer
towers[i] = [xi, yi, qi] denotes the
ith network tower with location
(xi, yi) and quality factor
qi. All the coordinates are integral coordinates on the X-Y plane, and the distance between two coordinates is the Euclidean distance.
radius denotes the maximum distance in which the tower is reachable. The tower is reachable if the distance is less than or equal to
radius. Outside that distance, the signal becomes garbled, and the tower is not reachable.
The signal quality of the
ith tower at a coordinate
(x, y) is calculated with the formula
⌊qi / (1 + d)⌋, where
d is the distance between the tower and the coordinate. The network quality at a coordinate is the sum of the signal qualities from all the reachable towers.
Return the integral coordinate where the network quality is maximum. If there are multiple coordinates with the same network quality, return the lexicographically minimum coordinate.
- A coordinate
(x1, y1)is lexicographically smaller than
(x2, y2)if either
x1 < x2or
x1 == x2and
y1 < y2.
⌊val⌋is the greatest integer less than or equal to
val(the floor function).
Input: towers = [[1,2,5],[2,1,7],[3,1,9]], radius = 2 Output: [2,1] Explanation: At coordinate (2, 1) the total quality is 13 - Quality of 7 from (2, 1) results in ⌊7 / (1 + sqrt(0)⌋ = ⌊7⌋ = 7 - Quality of 5 from (1, 2) results in ⌊5 / (1 + sqrt(2)⌋ = ⌊2.07⌋ = 2 - Quality of 9 from (3, 1) results in ⌊9 / (1 + sqrt(1)⌋ = ⌊4.5⌋ = 4 No other coordinate has higher quality.
Input: towers = [[23,11,21]], radius = 9 Output: [23,11]
Input: towers = [[1,2,13],[2,1,7],[0,1,9]], radius = 2 Output: [1,2]
Input: towers = [[2,1,9],[0,1,9]], radius = 2 Output: [0,1] Explanation: Both (0, 1) and (2, 1) are optimal in terms of quality but (0, 1) is lexicograpically minimal.
1 <= towers.length <= 50
towers[i].length == 3
0 <= xi, yi, qi <= 50
1 <= radius <= 50
class Solution: def bestCoordinate(self, towers: List[List[int]], radius: int) -> List[int]: points =  for tower in towers: point, quality = (tower, tower), tower points.append(point) points = sorted(points, key=lambda point:point) signals =  for point in points: signal = 0 for tower in towers: tower_point, quality = (tower, tower), tower distance = self.get_distance(point, tower_point) if distance <= radius: signal += floor(quality / (1 + distance)) signals.append(signal) return points[signals.index(max(signals))] def get_distance(self, point1, point2): return sqrt((point1 - point2)**2 + (point1 - point2)**2)
- Time Complexity: ~N
- Space Complexity: ~N