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.
class Solution:
     def increasingTriplet(self, nums):
         """
         :type nums: List[int]
         :rtype: bool
         """
         # keep track of the two minimum elements and see if we have a element that is larger than two
         if len(nums) < 3:
             return False
         
         minN = nums[0]
         minSecond = None
         
         for i in range(1, len(nums)):
             if type(minSecond) == int and nums[i] > minSecond:
                 return True
             
             if minN < nums[i]:  
                 if type(minSecond) == int and minSecond > nums[i]:
                     minSecond = nums[i]
                 elif not type(minSecond) == int:
                     minSecond = nums[i]
             
             minN = min(minN, nums[i])
             
             
         return False
class Solution:
     def increasingTriplet(self, nums):
         """
         :type nums: List[int]
         :rtype: bool
         """
         # keep track of the two minimum elements and see if we have a element that is larger than two
         if len(nums) < 3:
             return False
         
         minN = nums[0]
         minSecond = None
         
         for i in range(1, len(nums)):
             if type(minSecond) == int and nums[i] > minSecond:
                 return True
             
             if minN < nums[i]:  
                 if type(minSecond) == int and minSecond > nums[i]:
                     minSecond = nums[i]
                 elif not type(minSecond) == int:
                     minSecond = nums[i]
             
             minN = min(minN, nums[i])
             
             
         return False