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Homework 3 Sorting algorithms
Unit 6 Algorithms
Name: ........................................................................... Class:.................. Mark:................
1.
(a) What would be the state of the following list after each of the first four passes in a
Bubble sort, sorting into ascending sequence?
65, 34, 28, 68, 52, 21
[4]
1: 34, 28, 64, 52, 21, 68
2: 28, 34, 52, 21, 65, 68
3: 28, 34, 21, 52, 65, 68
4: 28, 21, 34, 52, 65, 68
(b) How many passes will be made through the list used in part (a) using the
Bubble sort algorithm in order to sort it?
[1]
5
2.
The diagram below shows an algorithm in graphical form.
(a) What is the algorithm depicted?
[1]
Merge sort
1
Homework 3 Sorting algorithms
Unit 6 Algorithms
(b) Describe the process of sorting the following list using the above algorithm:
74, 36, 81, 25, 19, 14, 61, 40
[6]
The list (74, 36, 81, 25, 19, 14, 61, 40) gets split into smaller parts until each has only one
number. These small parts then pair up and merge, arranging themselves in ascending
order: (36,74) (25,81) (14,19) (40,61). These pairs combine again, sorting in ascending
order. (25, 36, 74, 81) (14, 19, 40, 61). Finally, the two groups merge together, giving the
complete sorted list: (14, 19, 25, 36, 40, 61, 74, 81) .
3.
An insertion sort algorithm is used to sort the following numbers:
63, 45, 73, 23, 81, 18
(a) Explain briefly how an insertion sort works.
[3]
Insertion sort works by taking each number and finding its spot in the growing sorted list. It
keeps doing this for every number until the whole list is sorted.
2
Homework 3 Sorting algorithms
Unit 6 Algorithms
(b) Show the stages of the sort. The first stage is shown below:
Stage 1:
45, 63, 73, 23, 81, 18
Stage 2:
45, 63, 73, 23, 81, 18
Stage 3:
23, 45, 63, 73, 81, 18
Stage 4:
23, 45, 63, 73, 81, 18
Stage 5:
18, 23, 45, 63, 73, 81
[4]
(c) Give one reason why an Insertion sort may be chosen over a bubble sort for
sorting a large number of items.
[1]
Insertion sort uses fewer comparsions than Bubble sort for sorting big lists, so is more
efficient.
[Total 20 Marks]
3