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# Time: O(n)
# Space: O(n)
# 456. 132 Pattern
'''
Packing information into names
'''

# version 1.0
class Solution(object):
    def find132pattern(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        ak = float("-inf")
        st = []
        for i in reversed(xrange(len(nums))):
            if nums[i] < ak:
                return True 
            else:
                while st and nums[i] > st[-1]:
                    ak = st.pop()
                st.append(nums[i])
        
        return False 
        
# version 1.1
class Solution(object):
    def find132pattern(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        real_2 = float("-inf")
        potenial_2 = []
        for i in reversed(xrange(len(nums))):
            if nums[i] < real_2:
                return True 
            else:
                while potenial_2 and nums[i] > potenial_2[-1]:
                    real_2 = potenial_2.pop()
                potenial_2.append(nums[i])
        
        return False 

# version 1.2
class Solution(object):
    def find132pattern(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        cur_2 = float("-inf")
        pool_2 = []
        for i in reversed(xrange(len(nums))):
            if nums[i] < cur_2:
                return True 
            else:
                while pool_2 and nums[i] > pool_2[-1]:
                    cur_2 = pool_2.pop()
                pool_2.append(nums[i])
        
        return False 


# version 1.3
class Solution(object):
    def find132pattern(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        max_2 = float("-inf")
        pool_2 = []
        for i in reversed(xrange(len(nums))):
            if nums[i] < max_2:
                return True 
            else:
                while pool_2 and nums[i] > pool_2[-1]:
                    max_2 = pool_2.pop()
                pool_2.append(nums[i])

        return False 
    
# version 1.4