Heaters in Python

Suppose we have to design a standard heater with a fixed warm radius to warm all the houses. Now, we have given positions of houses and heaters on a horizontal line, we have to find the minimum radius of heaters so that all houses could be covered by those heaters. So, we will provide houses and heaters separately, and our expected output will be the minimum radius standard of heaters.

So, if the input is like [1,2,3,4],[1,4], then the output will be 1 as the two heaters was placed in position 1 and 4. We have to use radius 1, then all the houses can be warmed.

To solve this, we will follow these steps −

• sort the list houses

• sort the list heaters

• res := an array of size same as houses array, and fill this using inf

• for i in range 0 to size of houses, do

  • h := houses[i]

  • ind := left most index to insert h into heaters so that list remains sorted

  • if ind is same as size of heaters, then

    • res[i] := minimum of res[i], |h - heaters[-1]|

  • otherwise when ind is same as 0, then

    • res[i] := minimum of res[i], |h - heaters[0]|

  • otherwise,

    • res[i] := minimum of res[i], |h - heaters[ind]| , |h - heaters[ind-1]|

• return maximum of res

Example 

Let us see the following implementation to get a better understanding −

 Live Demo

from bisect import bisect_left
class Solution:
   def findRadius(self, houses, heaters):
      houses.sort()
      heaters.sort()
      res = [float('inf')]*len(houses)
      for i in range(len(houses)):
         h = houses[i]
         ind = bisect_left(heaters, h)
         if ind==len(heaters):
            res[i] = min(res[i], abs(h - heaters[-1]))
         elif ind == 0:
            res[i] = min(res[i], abs(h - heaters[0]))
         else:
            res[i] = min(res[i], abs(h - heaters[ind]), abs(h - heaters[ind-1]))
      return max(res)

ob = Solution()
print(ob.findRadius([1,2,3,4],[1,4]))

Input

[1,2,3,4],[1,4]

Output

1