What is the optimal time complexity of solving Redundant Connection?

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 Redundant Connection?

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 Redundant Connection?

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 Redundant Connection?

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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Redundant Connection

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

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Problem Statement

Easy

In this problem, a tree is an undirected graph that is connected and has no cycles.

You are given a graph that started as a tree with n nodes labeled from 1 to n, with one additional edge added. The added edge has two different vertices chosen from 1 to n, and was not an edge that already existed. The graph is represented as an array edges of length n where edges[i] = [ai, bi] indicates that there is an undirected edge between nodes ai and bi.

Return an edge that can be removed so that the resulting graph is a tree of n nodes. If there are multiple answers, return the answer that occurs last in the input.

Write a function findRedundantConnection(edges: List[List[int]]) -> List[int].

Constraints

•n == len(edges)
•3 <= n <= 1000
•edges[i].length == 2
•1 <= ai < bi <= n
•ai != bi

Examples

Example 1

Input

edges = [[1,2],[1,3],[2,3]]

Output

[2,3]

Explanation

Removing edge [2,3] breaks the cycle 1-2-3-1, leaving a valid tree 1-2 and 1-3.

Example 2

Input

edges = [[1,2],[2,3],[3,4],[1,4],[1,5]]

Output

[1,4]

Explanation

The cycle is 1-2-3-4-1. The last edge in the input that is part of this cycle is [1,4].

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

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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