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

Example 1:

Input: [1,2,3,4,5]
Output: true
Example 2:

Input: [5,4,3,2,1]
Output: false
"""

# 2020-10-10

class Solution(object):
    def increasingTriplet(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        if len(nums) < 3:
            return false

        k = 3
        dp = [0 for _ in nums]
        
        for i in range(len(nums)):
            dp[i] = 1
            for j in range(i):
                if nums[i] > nums[j]:
                    dp[i] = max(dp[j]+1, dp[i])
                    if dp[i] >= k: return True
            
        return False
        

nums = [2,1,5,0,3]
test = Solution()
ret = test.increasingTriplet(nums)
print(ret)