Algorithms Abstraction

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1 Algorithms Abstraction Instructions and answers for teachers These instructions should accompany the OCR resource Algorithms - Abstraction activity which supports OCR GCSE (9 1) Computer Science The Activity: This resource comprises of 7 tasks. These simple activities help the students understand the concept of abstraction and how algorithms are used to solve problems. This activity offers an opportunity for English skills development. This activity offers an opportunity for maths skills development. Associated materials: Algorithms Abstraction Lesson Element learner activity sheet. This resource is an exemplar of the types of materials that will be provided to assist in the teaching of the new qualifications being developed for first teaching in It can be used to teach existing qualifications but may be updated in the future to reflect changes in the new qualifications. Please check the OCR website for updates and additional resources being released. We would welcome your feedback so please get in touch.

3 Learners will develop an algorithm to draw a square in Scratch 2.0, first line by line (see file Scratch1.png), then as a procedure (see file Scratch1.png), then as a generic polygon. As you can see, at this stage, calling this procedure doesn't tell us how the shape is drawn; we just use it by supplying the parameters to draw the polygon as we need it. Task 2 Decomposition is the process of breaking a complex problem down in to smaller more manageable portions. Decomposition makes great use of abstraction by identifying common patterns in these portions and reusing the code written for one part on other parts. In this task, learners will look at Chinese letters which are made up of simpler parts and research the process through which the meaning gets composed. Task 3 Algorithmic Thinking A well-known problem involves getting some creatures across the river in the same boat (such as described here: Discuss what happens if the farmer uses the wrong algorithm to carry them across? Can you make this problem more complex by introducing another creature that is dangerous to any of those present in the puzzle already. Task 4 Standard searching algorithms Issues: The learners need to be aware that both searching methods are used and have their place. Regardless of the algorithm used, the learners need to be aware (it's a common mistake) that the algorithm must allow for a condition where the search is over but the item is not found. The choice of the searching algorithms depends on the data that needs to be searched. The data that is unsorted will have to be searched in a linear, no-stone-unturned-until-found, door-to-door [picture of travelling salesperson/policeman or another suitable analogy for someone visiting every single house on a street]. This is because we don't know enough about the data to use any shortcuts. We can say that unsorted data is a poorer quality than sorted as the linear search is inefficient and processor intensive. However, storing data in unsorted state works better for weaker processors that might be overwhelmed by the process of simultaneously recording new data and sorting it.

4 Binary search is much more efficient as we need to look at the fewer items before we find the one we need. How is that achieved?

5

6 When booking into this hotel, you make it to your floor and this sign is the first thing you see. If you are looking for room 318, you will not have to search the entire floor, just the left side. To simplify the search for your room, the hotel conveniently numbered their rooms in sequence and placed the entrance to the floor in the middle, so that you can halve your search effort and time. You know by now that "binary" could be translated "one of the two options" - which is what the hotel gives you here - left or right. Imagine that if you do go left and about half way through that side of the floor, the corridor turns and branches out into further 2 halves with numbers " " and " ". Which way will you turn? Binary search A hotel has 120 rooms located on 3 floors and 4 lifts/staircases. Design a floor plan (or signs for a given floor plan) for each of lifts/staircases. Assuming a person starts at lift 2. How many signs will they see before they find their room? Given pseudocode for a binary search, write it as (a) structured English; (b) code in your preferred high level language Linear search Given pseudocode for a linear search, write it as (a) structured English; (b) code in your preferred high level language

7 Task 6 Sorting and searching could end up being quite dry unless there is a visual element to them. There are many visualisations of the searching and sorting algorithms available on the internet, such as the one at You will find that learners understand the algorithms better if they also can plot the results using a language with graphics abilities, eg Scratch/BYOB/Snap/AppInventor/Python/Basic, etc. The tasks would involve generating a random list of numbers and then applying an algorithm to it. Provided is an example of visualising a list in Scratch 2.0, using abstraction via a procedure. This procedure uses the stamp feature (which imprints the copy of the sprite s costume onto the Stage. The sprite s costume should be a smallish square (although, most symmetric shapes should work, as well). Learners should be given an opportunity to implement just the plotting of a list via the provided example and then they can design. For the extension activity, here is an example of using Python Turtle to do a visualisation of the Insertion Sort.

8 import turtle; from random import sample, choice; import time COLOURS = ["firebrick", "dark goldenrod", "sienna", "chartreuse4", "DeepSkyBlue3", "medium violet red", "red4", "saddle brown", "dark olive green", "spring green", "cadet blue", "deep pink"] screen = turtle.screen() t = turtle.turtle(); t.speed(0); t.width(10) def draw_col(x, y): t.penup() t.goto(x, 0) t.pendown() t.setheading(90) t.forward(y) def draw_sort(s): for i in s: draw_col(s.index(i)*15, i) def insertion_sort(s=sample(range(100), 10)): starttime = time.time() print("insertion sort") print(s) for i in range(1, len(s)): val = s[i] j = i - 1 while (j >= 0) and (s[j] > val): s[j+1] = s[j] j = j - 1

9 s[j+1] = val t.pencolor(colours.pop()) draw_sort(s) endtime = time.time() - starttime print ("Time taken: " + str(endtime) + " seconds") return s def quick_sort(s=sample(range(100), 10)): starttime = time.time() print(s) less = [] equal = [] greater = [] if len(s) > 1: pivot = s[0] for x in s: if x < pivot: less.append(x) if x == pivot: equal.append(x) if x > pivot: greater.append(x) print(less+equal+greater) return quick_sort(less)+equal+quick_sort(greater) else: endtime = time.time() - starttime print (endtime) return s

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