I found an interesting problem on https://leetcode.com/problems/increasing-triplet-subsequence/:
Given an unsorted array return whether an increasing subsequence of length 3 exists or not in the array.


Formally the function should:
Return true if there exists i, j, k  
such that arr[i] < arr[j] < arr[k] given 0 ≤ i < j < k ≤ n-1 
else return false.



Your algorithm should run in O(n) time complexity and O(1) space complexity.


Examples:
Given [1, 2, 3, 4, 5],
return true.


Given [5, 4, 3, 2, 1],
return false.


Credits:Special thanks to @DjangoUnchained for adding this problem and creating all test cases.

I tried it in Python, but could not do it. Can you solve it?
class Solution:
     def increasingTriplet(self, nums):
         """
         :type nums: List[int]
         :rtype: bool
         """
         if len(nums) < 3: return False
         
         tails = [-float('inf')] + [float('inf')]*3
         for x in nums:
             for i in range(2, -1, -1):
                 if x > tails[i]:
                     tails[i+1] = x
                     break
             if tails[-1] < float('inf'):
                 return True
         return False