问题
You are given a list of integers nums representing coordinates of houses on a 1-dimensional line. You have 3 street lights that you can put anywhere on the coordinate line and a light at coordinate x lights up houses in [x - r, x + r], inclusive. Return the smallest r required such that we can place the 3 lights and all the houses are lit up.
Constraints
n ≤ 100,000 where n is the length of nums
Example 1
Input
nums = [3, 4, 5, 6]
Output
0.5
Explanation
If we place the lamps on 3.5, 4.5 and 5.5 then with r = 0.5 we can light up all 4 houses.
思路
根据最左二分法的模板逐步遍历
代码
- 语言支持：Python3
Python3 Code:
class Solution:
def solve(self, nums):
if len(nums) <= 3:
return 0
nums.sort()
def possible(d):
start = nums[0]
end = start + d
for i in range(3):
index = bisect.bisect_right(nums, end)
if index >= len(nums):
return True
start = nums[index]
end = start + d
return False
l, r = 0, nums[-1] - nums[0]
while l <= r:
mid = (l + r) // 2
if possible(mid):
r = mid - 1
else:
l = mid + 1
return l / 2
复杂度分析
令 n 为数组长度。
- 时间复杂度：
- 空间复杂度：
