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F13.2 Trace tables

Exam preparation · GCSE · about 15 min

BugBotLab

What this lesson is about

Being the computer: a row for every change, and the checks that catch a slip.

Questions 5 marks in all

  1. [1 mark]In a trace table, when do you write a new row?

    1. AEvery time a variable changes
    2. BOnce at the end
    3. COnly when something is printed
    4. DOnce for each variable
    Answer: A. With no table given, a new row for every change is the safest method, and nothing is rubbed out. If the question's table has a row for each time round the loop, follow that instead.

  2. [1 mark]What does this program print?

    total = 0
n = 4
while n > 0:
    total = total + n
    n = n - 1
print(total)
    Answer:
    10

    4 + 3 + 2 + 1 = 10.

  3. [1 mark]total = 0, n = 5. WHILE n > 1: total = total + n, n = n - 2. What is total at the end?

    Answer: 8. 5 + 3 = 8, then n is 1 and the loop stops.

  4. [1 mark]A loop ends when its condition is false. What should the trace show for that check?

    1. AA row with the check written as false
    2. BNothing: the loop has ended
    3. CThe first row again
    4. DOnly the output
    Answer: A. The final check is usually worth a mark.

  5. [1 mark]What does 7 // 2 give?

    Answer: 3. Integer division throws the remainder away.

The task: print the trace

Trace the algorithm in the comment by running it, printing one line per row in the form n=<n> total=<total> check=<true or false>, in the order the computer reaches them. Print the check as true while the loop keeps going and false on the row that ends it. Finish with output: <total>.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

# total = 0
# n = 5
# WHILE n > 1
#     total = total + n
#     n = n - 2
# ENDWHILE
# OUTPUT total
total = 0
n = 5

The hint students can ask for: Print the row at the top of each pass, before changing anything, with the result of the check. The row that ends the loop is printed too, with the check false, and then the output.

A solution

from bugbot import *
connect()
total = 0
n = 5
while n > 1:
    print(f"n={n} total={total} check=true")
    total = total + n
    n = n - 2
print(f"n={n} total={total} check=false")
print("output:", total)

Any program that meets the task's checks is marked correct in the simulator; this is one way, not the only way.