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 −
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