ITPEC FE Subject B April 2024 Question 8

Implementing a stack with an array where index tracks the next free slot.

The stack uses a fixed-size array content[1..4] with index starting at 1 (empty stack) and max = 4.

How `index` works:
- index always points to the next free slot (where the next push will write)
- Empty: index = 1 (nothing stored yet)
- Full: index = 5 (all 4 slots used, no room left)

Blank A — `full()`:
The stack is full when all slots are used, i.e. index has moved past max. That means index > max (when index = 5, since 5 > 4). Using index ≥ max would incorrectly block the 4th push (when index = 4, only 3 elements stored).

Blank B — `push()`:
After writing content[index] ← i, move index forward: index ← index + 1.

Blank C — `pop()`:
index points to an empty slot. The top element is at index - 1. First decrement: index ← index - 1, then return content[index].

Trace example (push 10, 20, 30, 40 then pop):

Why not others:
- (a) index > max + index - 1 + index + 1 — B and C are swapped: push would decrement (shrink) and pop would increment (grow)
- (c) index ≥ max — blocks 4th push (index=4, 4≥4=true with only 3 elements stored)
- (d) index ≥ max + index + 1 + index - 1 — same ≥ problem as (c), wastes one slot
- (e)-(h) index < max or index ≤ max — these are wrong comparisons for "full" (they check the opposite condition)

Key rule: when index tracks the next free slot, the stack is full when index > max (strictly greater), push increments index, and pop decrements before returning.

AI-generated — may contain errors