Algorithm Design and Standard Methods: Question 7

Worked solution

Part (a): Identifying the flowchart shape

Steps 4 and 5 (Weight = -1 ? and Weight > 20 ?) use the decision shape, drawn as a diamond in a standard flowchart. [1] This shape represents a point where the algorithm tests a condition and the flow of control splits into two separate paths. One followed if the condition is true, the other if it is false, unlike a process box, which always leads to exactly one next step. [1]

Part (b): What the algorithm calculates and when it stops

This is a counting algorithm: Count starts at 0 and only increases (Count ← Count + 1) when a parcel’s weight tests true against Weight > 20, so after the loop ends Count holds the number of parcels that weigh more than 20 kg and therefore need the surcharge. [1]

The algorithm does not stop after any fixed number of parcels. Instead, every time a new weight is entered, Step 4 first checks Weight = -1 ?. As long as the answer is “No”, the flow continues to Step 5 and eventually loops back to Step 3 to read another weight. Only when the value -1 is entered, a sentinel value that is not a real parcel weight, does Step 4 send the flow to Step 8 instead, ending the loop and outputting Count. [1]

Part (c): Tracing the algorithm

Starting with Count ← 0, each weight is read and tested in turn:

Each correctly completed row of the trace earns credit, up to [4] for the full table, including recognising that the sentinel value -1 ends the loop at Step 4 without ever reaching the Weight > 20 ? test.

The algorithm outputs Count = 2, since only the parcels weighing 22 kg and 30 kg exceed 20 kg.

Part (d): Converting the flowchart to pseudocode

The flowchart’s structure, read a value, test for the sentinel, otherwise test the surcharge condition, then loop back, maps directly onto a REPEAT ... UNTIL loop, since the input must always happen at least once before the sentinel can be checked:

DECLARE Weight : INTEGER
DECLARE Count : INTEGER

Count ← 0
REPEAT
    INPUT Weight
    IF Weight <> -1 THEN
        IF Weight > 20 THEN
            Count ← Count + 1
        ENDIF
    ENDIF
UNTIL Weight = -1
OUTPUT Count

Mark-earning features: [1] Count initialised to 0 before the loop; [1] the sentinel test IF Weight <> -1 THEN guarding the surcharge check so -1 itself is never compared against 20; [1] the loop condition UNTIL Weight = -1 correctly matching the flowchart’s Step 4 test, with OUTPUT Count placed after the loop ends.

Final answers

• (a) Decision (diamond) shape, tests a condition and branches the flow along two paths.
• (b) Counts parcels weighing more than 20 kg; stops when the sentinel value -1 is entered.
• (c) Count = 0, 1, 1, 2, then 2 is output when -1 is entered.
• (d) See the REPEAT ... UNTIL pseudocode above.