# LeetCode 475. Heaters

## Description

https://leetcode.com/problems/heaters/

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 `houses` and `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.

Example 1:

```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.
```

Example 2:

```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.
```

Example 3:

```Input: houses = [1,5], heaters = 
Output: 3
```

Constraints:

• `1 <= houses.length, heaters.length <= 3 * 104`
• `1 <= houses[i], heaters[i] <= 109`

## Python Solution

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()

for house in houses:

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).