Supported HL focus. First assessment 2027 target; official PDF returns 403; older acquired brief is final assessment 2026. Remaining guide, assessment and practical requirements retain their recorded holds.
Prerequisites: read the stated quantities and units, use arithmetic and the model conditions below. Each lesson develops its own method before independent transfer.
These are original or explicitly fictional teaching examples, not actual measurements or completed assessed learner investigations.
8.2
Abstract data types: an operation contract
What would explain this observation?
A waiting-line simulation needs the oldest pending item first. A stack 栈 gives the most recent item first, so the operation contract matters.
Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
Build the model
An abstract data type specifies values and operations independently of a particular implementation. A stack is last in, first out; a queue 队列 is first in, first out. A collection interface needs defined behaviour for empty and invalid operations.
stack: A last-in-first-out abstract data type; queue: A first-in-first-out abstract data type.
Choose evidence that can test it
Choose the structure for the required access pattern. Complexity depends on implementation and assumptions: removing the first item from a shifting array differs from advancing a head pointer in a queue.
Trace operation sequences by hand, then compare a program with the expected states. Test empty, singleton and repeated operations. State overflow behaviour if capacity is fixed.
Work from known quantities
State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
Known: enqueue A, B and C, then dequeue twice. A and B leave; C remains. After enqueue D there are two pending items, C then D. The same pushes on a stack would remove C then B.
Example:
A queue starts empty, receives 7 items and removes 4. Find the number remaining. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
Check the conclusion and its limits
An ADT is not a specific memory layout. A queue does not sort by priority unless its contract defines a priority queue.
Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
Warn:
Every queue automatically sorts items by priority. This claim is false: An ADT is not a specific memory layout. A queue does not sort by priority unless its contract defines a priority queue.
Key:
Abstract data types: an operation contract: Choose the structure for the required access pattern. Complexity depends on implementation and assumptions: removing the first item from a shifting array differs from advancing a head pointer in a queue.
Runnable trace and boundary
from collections import deque
queue = deque()
queue.extend(["A", "B"])
print(queue.popleft())
queue.append("C")
print(queue.popleft())
print(list(queue))
queue.clear()
print(queue.popleft() if queue else "EMPTY")
Expected output:
A
B
['C']
EMPTY
Removing from the left implements FIFO. The explicit empty guard defines the boundary result; deque.popleft without it would raise IndexError. A stack instead removes from the right.
