QUESTION 05

What is the final peek after the supplied eight operations?

2 marks

Answer

It is 30. The initial bottom-to-top stack is 10, 20, 50, 30, 90, 60; apply the operations in order rather than sorting values.

Trace the supplied sequence of stack operations and find the final peek.

5 marks

Answer in brief

A stack trace updates the logical top after every operation while preserving the untouched bottom portion.

Initial state

Bottom to top: 10, 20, 50, 30, 90, 60. Capacity is 10 and the initial count is 6. The top is 60.

Operation trace

pop removes 60: top becomes 90.
push(30): top becomes 30.
push(40): top becomes 40.
pop removes 40: top becomes 30.
push(60): top becomes 60.
pop removes 60: top becomes 30.
pop removes that pushed 30: top becomes 90.
pop removes 90: top becomes the original 30.

Final state

Bottom to top: 10, 20, 50, 30. Peek is 30 and does not remove it. The count is 4. None of these operations reaches empty or exceeds capacity, so there is no underflow or overflow.

How to avoid mistakes

Record the complete remaining sequence or a clear top marker after each step. Distinguish a newly pushed 30 from an earlier equal value if labels help, but the final requested value is still 30. Never remove the bottom item for pop; that would violate LIFO.

Complexity

For k operations on the bounded array representation, each operation is O(1), so the trace requires O(k) work. This specific trace has a fixed eight operations. Writing every intermediate full stack for display can add output work beyond the stack operations themselves.