Winter is coming! During the contest, your first job is to design a standard heater with a fixed warm radius to warm all the houses.
Every house can be warmed, as long as the house is within the heater’s warm radius range.
Given the positions of
heaters on a horizontal line, return the minimum radius standard of heaters so that those heaters could cover all houses.
Notice that all the
heaters follow your radius standard, and the warm radius will the same.
Input: houses = [1,2,3], heaters =  Output: 1 Explanation: The only heater was placed in the position 2, and if we use the radius 1 standard, then all the houses can be warmed.
Input: houses = [1,2,3,4], heaters = [1,4] Output: 1 Explanation: The two heater was placed in the position 1 and 4. We need to use radius 1 standard, then all the houses can be warmed.
Input: houses = [1,5], heaters =  Output: 3
1 <= houses.length, heaters.length <= 3 * 104
1 <= houses[i], heaters[i] <= 109
Use binary search to find the max distance between all closest pairs of house and heater.
class Solution: def findRadius(self, houses: List[int], heaters: List[int]) -> int: heaters.sort() min_heat_radius = 0 for house in houses: radius = self.get_min_heat_radius(house, heaters) min_heat_radius = max(min_heat_radius, radius) return min_heat_radius def get_min_heat_radius(self, house, heaters): left = 0 right = len(heaters) - 1 while left + 1 < right: mid = left + (right - left) // 2 if heaters[mid] <= house: left = mid else: right = mid return min(abs(heaters[left] - house), abs(heaters[right] - house))
- Time Complexity: O(MlogM + NlogM), M is the number of heaters, N is the number of houses.
- Space Complexity: O(1).