What is the optimal time complexity of solving Pythagorean Triplets?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Pythagorean Triplets?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Pythagorean Triplets?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Pythagorean Triplets?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Pythagorean Triplets

Learn how to solve the 'Pythagorean Triplets' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function contains_pythagorean_triplet(arr) that takes an array of positive integers arr and returns True if there are three integers a, b, and c in the array such that a^2 + b^2 = c^2, or False otherwise.

Constraints

•3 <= len(arr) <= 1000
•1 <= arr[i] <= 1000

Examples

Example 1

Input

arr = [3, 1, 4, 6, 5]

Output

True

Explanation

3^2 + 4^2 = 9 + 16 = 25 = 5^2.

Example 2

Input

arr = [10, 4, 6, 12, 5]

Output

False

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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