The basic traversal part is fine, it's the random pointer that trips you up.
Use a hash map to map each original node to its corresponding copy, then set the next and random pointers of the copies using the map. Alternatively, interleave the copied nodes with the originals to achieve O(1) extra space, then separate the two lists.
Pro tip: Discuss the trade-offs between the hash map approach (simpler, O(n) space) and the interleaving approach (O(1) space but trickier). Mention that the interleaving method modifies the original list temporarily, which may not be acceptable in all contexts.
Confirm that the deep copy must have entirely new nodes and that the original list should remain unchanged. Ask about constraints like space complexity and whether modifying the original list is allowed.
Decide between the hash map method (O(n) space) and the interleaving method (O(1) space). Explain the trade-offs and pick one based on constraints.
For hash map: traverse the list, create copies, store mapping, then set next and random pointers. For interleaving: insert copies after originals, set random pointers, then separate the lists.
Test with empty list, single node, random pointers to null, self-pointers, and random pointers to other nodes. Ensure original list is unchanged and all pointers in copy point to new nodes.
State time and space complexity: both approaches are O(n) time; hash map uses O(n) space, interleaving uses O(1) extra space (excluding output).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.