Designing a useful program

Clubs at a school have a limited number of places. A student — or a group of friends who want to join together — needs to know how many clubs still have enough room.

Purpose statement: help a student find out how many clubs have at least the number of remaining places they need.

A clear purpose tells you what “correct” means. Here, a correct program gives the right count of suitable clubs; it does not need to name them or sign anyone up.

The program needs two inputs:

• capacities — a list holding the number of remaining places for each club, for example [0, 5, 2, 8].
• minimum — the number of places the student needs, for example 3.

Using a list means the program does not care whether the school has four clubs or forty. The same steps work for any length, including an empty list. Each element has a value (places left) and a position (where it sits in the list). In AP pseudocode, positions start at 1. Keep the two ideas separate: in [0, 5, 2, 8], the element at position 3 has the value 2.

The program examines every capacity in turn. For each one it asks a yes-or-no question: does this club have at least minimum places? If yes, it adds 1 to a running count.

1PROCEDURE countAvailable(capacities, minimum)2{3  count ← 04  FOR EACH places IN capacities5  {6    IF (places ≥ minimum)7    {8      count ← count + 19    }10  }11  RETURN count12}

FOR EACH is iteration: it repeats once per element. IF is selection: it decides whether to run the increment. The parameter minimum makes the procedure reusable — the same code answers “clubs with 3 places?” and “clubs with 6 places?”.

The procedure returns a single number: how many clubs meet the condition. Returning the count, rather than printing a message, lets other parts of a program use the result — for example to show “2 clubs have room for you”.

Trace countAvailable([0, 5, 2, 8], 3). count starts at 0.

The procedure returns 2. Notice that count changes only on rows where the condition is true, and that it goes up by 1 — not by the value of places.

Make a prediction before you read the explanation.

One example is not enough. Good tests are chosen on purpose, each checking a different kind of situation:

The third test matters most. If someone accidentally wrote > instead of ≥, the first two tests would still pass but this one would return 2. Tests that sit exactly on a boundary catch errors that ordinary examples miss.

In the lab you will step through the same procedure yourself, change the minimum, try teacher-authored test datasets and record your reasoning.