Started with the two-pass hashmap because it's the easiest to explain out loud.
Start by clarifying the problem and constraints, then propose an O(n) time and O(n) space solution using a hash map to map original nodes to their clones. Alternatively, present the O(1) space interleaving approach if the interviewer wants to optimize space. Walk through the steps and analyze time/space complexity.
Pro tip: Mention the trade-off between the hash map approach (simpler, O(n) space) and the interleaving approach (O(1) space but modifies the original list temporarily). This shows you understand both and can choose based on constraints.
Ask if the original list should remain unchanged, if we can modify it, and if extra space is allowed. Confirm that random pointers can point to any node or be null.
Decide between hash map (O(n) space) and interleaving (O(1) space). Explain the trade-offs and pick one based on interviewer's preference.
For hash map: traverse original list, create clones and store mapping, then set next and random pointers. For interleaving: insert clones after originals, set random pointers, then separate lists.
State time complexity O(n) and space complexity O(n) for hash map or O(1) for interleaving. Mention that interleaving modifies the original list temporarily.
Discuss empty list, single node, random pointer to self, and random pointer to null. Ensure code handles these gracefully.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the interleave-and-split approach.
First clarify the constraints: what counts as 'extra space' and whether the input graph is mutable. Then explain that by interleaving cloned nodes with original nodes (e.g., inserting each clone right after its original), you can achieve O(1) auxiliary space, and finally restore the original structure.
Pro tip: Amazon interviewers value candidates who proactively discuss trade-offs: mention that this approach mutates the input temporarily, which may be unacceptable in concurrent or read-only scenarios, and offer to restore it.
Ask whether the input can be modified, whether the graph is directed/undirected, and what exactly counts as 'extra space' (e.g., recursion stack, hash map).
Describe how to insert each cloned node immediately after its original, so that the clone's next pointer can be set without a hash map.
For each original node, set its clone's random pointer to the clone of the original's random pointer (which is original.random.next).
Restore the original list and extract the cloned list by adjusting next pointers, ensuring the original structure is unchanged.
State that time complexity is O(n) and auxiliary space is O(1), but note the temporary mutation of the input and potential issues with concurrent access.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Immediately rules out the interleave trick since that temporarily modifies the original's next pointers.
Acknowledge the constraint and explain how it forces a shift from in-place mutation to creating a new list or using additional data structures. Discuss the trade-offs in time and space complexity, and propose alternative algorithms that respect immutability.
Pro tip: Emphasize that immutability often leads to cleaner, more predictable code and can prevent subtle bugs, but be prepared to discuss the cost of extra memory and how to optimize it.
Confirm whether the entire list must remain unchanged or just the original reference, and whether auxiliary data structures are allowed.
Determine which parts of the original approach relied on mutation (e.g., swapping, overwriting) and how they must be replaced.
Suggest approaches like building a new list, using extra space for indices or counts, or applying functional programming techniques.
Compare time and space complexity of the new approach versus the original, and discuss any performance implications.
Walk through a small example to demonstrate correctness and highlight edge cases like empty lists or duplicates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.