The O(1) space constraint is what makes this annoying.
Clarify constraints and assumptions, then propose using the array itself as a hash table by marking visited elements via negation or index mapping. Walk through the algorithm step-by-step, analyze time and space complexity, and discuss edge cases and potential pitfalls.
Pro tip: Acknowledge that the O(1) space solution modifies the input array, and ask if that's acceptable; if not, discuss trade-offs. Also, mention that without built-in functions, you'll implement any needed operations manually.
Ask about input size, value range, whether the array can be modified, and if duplicates can appear more than twice. Confirm that O(1) space means no additional data structures like hash sets.
If values are in range 1 to n, use index marking: for each element, treat its absolute value as an index and negate the element at that index to mark visited. If already negative, it's a duplicate.
If the range is unknown or larger, consider sorting the array first (if allowed) or using a cyclic sort approach to place elements at their correct indices, then scan for mismatches.
Demonstrate the algorithm on a small array, showing how marking and detection work step by step, and how duplicates are collected.
State time complexity O(n) and space O(1). Discuss edge cases: no duplicates, all duplicates, negative numbers, zeros, and large values. Mention that the array is modified.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.