What is the optimal time complexity of solving Clone Graph?

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 Clone Graph?

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 Clone Graph?

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 Clone Graph?

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.

Back to Practice Dashboard

Top 150 InterviewMedium

Clone Graph

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

Mode Selected

Problem Statement

Medium

Given a reference of a node in a connected undirected graph, return a deep copy (clone) of the graph.

Each node in the graph contains a value (int) and a list of its neighbors (List[Node]).

The graph is represented as an adjacency list. Implement a function cloneGraph(adjList: List[List[int]]) -> List[List[int]] where adjList[i] represents the neighbors of node i+1 (1-indexed). Return the adjacency list of the cloned graph.

Constraints

•The number of nodes in the graph is in the range [0, 100]
•1 <= Node.val <= 100
•Node.val is unique for each node
•There are no repeated edges and no self-loops in the graph

Examples

Example 1

Input

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

Output

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

Explanation

Node 1's neighbors are 2 and 4. Node 2's neighbors are 1 and 3. Node 3's neighbors are 2 and 4. Node 4's neighbors are 1 and 3.

Example 2

Input

adjList = [[]]

Output

[[]]

Explanation

The graph contains only one node with value 1 and no neighbors.

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

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor