Clone Graph

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Clone Graph** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** BFS/DFS with hash map old→new node **Edge Cases to Consider:** - (1) Single node no neighbors - (2) Disconnected components - (3) Graph with cycle

Examples

Example 1

Input: [[2,4],[1,3],[2,4],[1,3]]

Output: Deep copy of same structure

Explanation: 4-node cycle

Example 2

Input: [[]]

Output: [[]]

Explanation: Single node no neighbors

Example 3

Input: []

Output: []

Explanation: Null input

Constraints

▪2 <= vertices <= 1000
▪0 <= edges <= 5000
▪Avoid infinite cycles during depth traversal

Watch Out For Edge Cases

▪Single node no neighbors
▪Disconnected components
▪Graph with cycle

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