Program to find minimum radius to light up all houses on a street in Python

Suppose we have a list of numbers called nums that are representing position of houses on a 1-dimensional line. Now consider we have 3 street lights that we can put anywhere on the line and a light at position x lights up all houses in range [x - r, x + r], inclusive. We have to find the smallest r required to light up all houses.

So, if the input is like nums = [4,5,6,7], then the output will be 0.5, as we can place the lamps on 4.5, 5.5 and 6.5 so r = 0.5. So these three lights can light up all 4 houses.

To solve this, we will follow these steps −

• Define a function valid() . This will take r

• last_location := nums[0] + r

• count := 1

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

  • val := nums[i]

  • if val - last_location > r, then

    • count := count + 1

    • last_location := val + r

• return true when count <= 3, otherwise false

• From the main method do the following −

• sort the list nums

• left := 0

• right := last element of nums

• res := inf

• itr := 0

• while left <= right and itr < 20, do

  • mid := left +(right - left) / 2

  • if valid(mid) is true, then

    • res := minimum of res and mid

    • right := mid

  • otherwise,

    • left := mid

    • itr := itr + 1

• return res

Example 

Let us see the following implementation to get better understanding −

 Live Demo

class Solution:
   def solve(self, nums):
      def valid(r):
         last_location = nums[0] + r
         count = 1
         for i in range(len(nums)):
            val = nums[i]
            if val - last_location > r:
               count += 1
               last_location = val + r
         return count <= 3
      nums.sort()
      left = 0
      right = nums[-1]
      res = float("inf")
      itr = 0
      while left <= right and itr < 20:
         mid = left + (right - left) / 2
         if valid(mid):
            res = min(res, mid)
            right = mid
         else:
            left = mid
         itr += 1
      return res
ob = Solution()
nums = [4,5,6,7]
print(ob.solve(nums))

Input

[4,5,6,7]

Output

0.5

Arnab Chakraborty

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Updated on: 22-Dec-2020

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