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Consider a stack data structure into which we can PUSH and POP records. Assume that each record pushed in the stack has a positive integer key and that all keys are distinct.
We wish to augment the stack data structure with an O(1) time MIN operation that returns a pointer to the record with smallest key present in the stack
1) without deleting the corresponding record, and
2) without increasing the complexities of the standard stack operations.
Which one or more of the following approach(es) can achieve it?
- Keep with every record in the stack, a pointer to the record with the smallest key below it.
- Keep a pointer to the record with the smallest key in the stack.
- Keep an auxiliary array in which the key values of the records in the stack are maintained in sorted order.
- Keep a Min-Heap in which the key values of the records in the stack are maintained.
Correct answer: Keep with every record in the stack, a pointer to the record with the smallest key below it.
Solution
This approach allows each record to directly reference the smallest key below it, enabling O(1) access to the minimum key without altering the time complexity of standard stack operations like PUSH and POP.
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