# [leetcode] 334. Increasing Triplet Subsequence _ Algorithm Problem Solve for python

## 1. Problem

334. Increasing Triplet Subsequence

Given an integer array nums, return true if there exists a triple of indices (i, j, k) such that i < j < k and nums[i] < nums[j] < nums[k]. If no such indices exists, return false.

Example 1:

Input: nums = [1,2,3,4,5]
Output: true
Explanation: Any triplet where i < j < k is valid.


Example 2:

Input: nums = [5,4,3,2,1]
Output: false
Explanation: No triplet exists.


Example 3:

Input: nums = [2,1,5,0,4,6]
Output: true
Explanation: The triplet (3, 4, 5) is valid because nums[3] == 0 < nums[4] == 4 < nums[5] == 6.


Constraints:

• 1 <= nums.length <= 5 * 10^5
• -2^31 <= nums[i] <= 2^31 - 1

## 2. Solution

I solved this problem like this.

### 2.1. Time problem code

This code is simple logic. We just check using for statement. But, it makes Time Limit Exceeded problem.

class Solution:
def increasingTriplet(self, nums: List[int]) -> bool:
for i in range(len(nums)):
for j in range(i+1, len(nums)):
if nums[i] >= nums[j]:
continue
for k in range(j+1, len(nums)):
if nums[j] < nums[k]:
return True

return False


### 2.2. Solution

Other solution is like this. This solution is simple and easy to understand.

class Solution:
def increasingTriplet(self, nums: List[int]) -> bool:
first = second = float('inf')
for n in nums:
if n <= first:
first = n
elif n <= second:
second = n
else:
return True
return False