How do you solve Increasing Triplet Subsequence on LeetCode?

Increasing Triplet Subsequence (LeetCode #334) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the difference between brute force and optimal solutions is crucial.

What is the brute force solution for Increasing Triplet Subsequence?

The brute force approach for Increasing Triplet Subsequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible triplet in the array to see if it satisfies the condition of increasing order. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Increasing Triplet Subsequence?

Increasing Triplet Subsequence uses the following concepts: Array, Greedy. The recommended patterns to study are: Greedy, Array.

What are the interview tips for Increasing Triplet Subsequence?

Always clarify the problem requirements before diving into coding. Discuss your thought process and any patterns you recognize during the interview. Practice explaining your code and logic clearly, as communication is key in interviews.

What are common mistakes when solving Increasing Triplet Subsequence?

Not considering edge cases, such as arrays with fewer than three elements. Overlooking the need for a greedy approach when it can simplify the solution.

#334

Increasing Triplet Subsequence

Medium

ArrayGreedyGreedyArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal solution uses a greedy approach to keep track of the smallest and the second smallest numbers found so far. This allows us to determine if a third number can form a triplet without needing to check every combination.

⚙️

Algorithm

6 steps

1Step 1: Initialize two variables, first and second, to infinity.
2Step 2: Loop through each number in the array.
3Step 3: If the current number is less than or equal to first, update first.
4Step 4: If the current number is greater than first but less than or equal to second, update second.
5Step 5: If the current number is greater than second, return true (we found a triplet).
6Step 6: If the loop completes without finding a triplet, return false.

solution.py11 lines

1# Full working Python code
2first = float('inf')
3second = float('inf')
4for num in nums:
5    if num <= first:
6        first = num
7    elif num <= second:
8        second = num
9    else:
10        return True
11return False

ℹ

Complexity note: This approach runs in O(n) time because we only make a single pass through the array, and it uses O(1) space since we only store a fixed number of variables.

1Understanding the difference between brute force and optimal solutions is crucial.
2Recognizing patterns in problems can lead to more efficient algorithms.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.