Worksheet

F5.4 Trace tables

Algorithms · GCSE · OCR J277 2.1.2, AQA 8525 3.1.1, Edexcel 1CP2 1.2.4 · about 15 min

What this lesson is about

Following an algorithm line by line, and tracing to find a logic error.

• A first trace
• Let the program trace itself
• Tracing to find a bug
• Tracing a robot

Questions 5 marks in all

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

   total = 0
   for i in range(1, 5):
       total = total + i * 2
   print(total)

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

   x = 1
   y = 10
   while x < y:
       x = x * 2
       y = y - 1
   print(x, y)

3. [1 mark]A program prints the average of five readings as 4.0 when it should be 30.0. A trace shows total goes 40, 35, 30, 25, 20. What is the bug?

   1. Atotal = 0 is inside the loop, so it resets each time
   2. BThe readings are wrong
   3. CThe loop runs too many times
   4. DDivision is broken

4. [1 mark]What is a trace table used for?

   1. ARecording variable values step by step to check what an algorithm does
   2. BStoring a program's data
   3. CDrawing a flowchart
   4. DTiming a program

5. [1 mark]What does this program print?

   n = 20
   steps = 0
   while n > 1:
       n = n // 2
       steps = steps + 1
   print(n, steps)

The task: trace and fix

Fix the average program so it prints average: 30.0. Keep a trace: inside the loop, print a line i=<i> total=<total> each time round, so the program shows its own trace table.

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

readings = [40, 35, 30, 25, 20]
for i in range(len(readings)):
    total = 0
    total = total + readings[i]
print("average:", total / len(readings))

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/f5-4-trace-tables/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Trace n = 27 then while n != 1: if n is even, n = n // 2, else n = 3 * n + 1 for the first six rows. Then run it to see how long it really takes.
2. Write a trace table for the parking sensor's loop, with the distance, the gap and the beep count.
3. Swap the two lines inside the x and y loop above. Trace it again before running. Does it still stop?