What is the optimal time complexity of solving Find all Symmetric pairs in an array?

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 Find all Symmetric pairs in an array?

The space complexity is O(1) 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 Find all Symmetric pairs in an array?

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 Find all Symmetric pairs in an array?

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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Find all Symmetric pairs in an array

Learn how to solve the 'Find all Symmetric pairs in an array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function symmetric_pairs(arr) that takes a list of pairs (list of 2-element lists) and returns all symmetric pairs. A pair [a, b] is symmetric with another pair [b, a] if both exist in the array. Return the result as a sorted list of pairs where the first element of the pair is smaller. Each symmetric pair should appear only once.

Constraints

•1 <= len(arr) <= 10^4
•Each element is a list of 2 integers
•-10^6 <= arr[i][j] <= 10^6

Examples

Example 1

Input

arr = [[1, 2], [2, 1], [3, 4], [4, 3], [5, 6]]

Output

[[1, 2], [3, 4]]

Explanation

[1,2] and [2,1] are symmetric. [3,4] and [4,3] are symmetric. [5,6] has no symmetric pair.

Example 2

Input

arr = [[1, 2], [3, 4]]

Output

[]

Explanation

No pair has its reverse in the array.

Example 3

Input

arr = [[10, 20], [20, 10]]

Output

[[10, 20]]

Explanation

[10,20] and [20,10] form a symmetric pair.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

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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