Worksheet

A2.4 Abstraction and models

Recursion and computational thinking · A level · OCR H446 2.1.1, AQA 7517 4.4.1.3 · about 20 min

What this lesson is about

Representational abstraction, generalisation, problem reduction, and a grid model of the mat that differs from reality.

• What abstraction is, and why it is needed
• Representational abstraction
• Abstraction and reality
• Abstraction by generalisation
• Problem abstraction and reduction

Questions 6 marks in all

1. [1 mark]What is abstraction?

   1. ARemoving details that do not matter for the purpose, to focus on those that do
   2. BBreaking a problem into smaller parts
   3. CWriting a program in a high-level language
   4. DHiding the code of a program from its users

2. [1 mark]A metro map shows stations in the right order on each line but ignores real distances and bends. What kind of abstraction is it?

   1. ARepresentational abstraction
   2. BAbstraction by generalisation
   3. CFunctional abstraction
   4. DData abstraction

3. [1 mark]"A time-of-flight sensor is a kind of distance sensor, which is a kind of sensor." Which kind of abstraction is this?

   1. AAbstraction by generalisation (categorisation)
   2. BRepresentational abstraction
   3. CProcedural abstraction
   4. DProblem reduction

4. [1 mark]A room is modelled as a grid of 20 cm cells, blocked if the centre of the cell is inside an obstacle. What is a danger of this abstraction?

   1. AA thin obstacle between cell centres is missing from the model, so a planned route could hit it
   2. BThe model is too large to store
   3. CThe robot cannot drive sideways
   4. DThe grid cannot be searched by an algorithm

5. [1 mark]Euler turned the Königsberg bridges puzzle into a question about points and lines. What is this an example of?

   1. AProblem abstraction or reduction
   2. BDecomposition
   3. CInformation hiding
   4. DAutomation

6. [1 mark]Why is abstraction needed when solving problems with computers?

   Tick every answer that is true.

   1. AReal situations have too much detail to store and process
   2. BA simpler model can be solved by an algorithm
   3. CThe same model can be reused for similar situations
   4. DIt makes the model exactly match reality

The task: a grid model of the mat

The mat is 100 cm by 100 cm, with (0, 0) in the bottom left corner. The four obstacles in the figure are these rectangles, each (x, y, width, height) in cm, where (x, y) is the rectangle's bottom left corner: (25, 64, 40, 10), (72, 5, 8, 50), (5, 22, 30, 16) and (84, 40, 12, 60) Build the 5 by 5 grid model with 20 cm cells. - Write a function blocked(cx, cy) that returns True if the point (cx, cy) is inside any rectangle (a point exactly on an edge counts as inside) and False otherwise. - A cell is blocked if its centre is blocked. Row 0 is the top row of the mat and column 0 the left, so the cell in row 0, column 0 has its centre at (10, 90). - Print the five rows, row 0 first, each as a string of five characters: # for a blocked cell and . for a free one. - Then print blocked: <n>, the number of blocked cells.

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

obstacles = [(25, 64, 40, 10), (72, 5, 8, 50), (5, 22, 30, 16), (84, 40, 12, 60)]

def blocked(cx, cy):
    return False

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

Do it on the robot
www.bugbotlab.com/learn/a2-4-abstraction-and-models/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Change your model to 10 cm cells (10 rows of 10). Does the post appear now? What has it cost?
2. Instead of testing only the centre, mark a cell blocked if any part of a rectangle overlaps it. Which model is safer for the robot, and which wastes more space?
3. Draw an abstract model of your school's corridors that a delivery robot could plan with. What have you left out, and could any of it matter?