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Data Structures & Algorithms in Dart

Second Edition · Flutter · Dart 3.0 · VS Code 1.78

Section VI: Challenge Solutions

Section 6: 21 chapters
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16. Chapter 16 Solutions
Written by Jonathan Sande

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Solution to Challenge 1

If you start with the following list:

[4, 2, 5, 1, 3]

Here are the steps a bubble sort would take:

[2, 4, 5, 1, 3] // 4-2 swapped
[2, 4, 5, 1, 3] // 4-5 not swapped
[2, 4, 1, 5, 3] // 5-1 swapped
[2, 4, 1, 3, 5] // 5-3 swapped

[2, 4, 1, 3, 5] // 2-4 not swapped
[2, 1, 4, 3, 5] // 4-1 swapped
[2, 1, 3, 4, 5] // 4-3 swapped

[1, 2, 3, 4, 5] // 2-1 swapped
[1, 2, 3, 4, 5] // 2-3 not swapped

[1, 2, 3, 4, 5] // 1-2 not swapped

Bubble sort needed the full O(n²) traversal to finish the sort. It made ten comparisons and six swaps.

Solution to Challenge 2

Given the following list:

[4, 2, 5, 1, 3]
[4, 2, 5, 1, 3] // start, lowest: 4

[4, 2, 5, 1, 3] // compare 2-4, lowest: 2
[4, 2, 5, 1, 3] // compare 5-2, lowest: 2
[4, 2, 5, 1, 3] // compare 1-2, lowest: 1
[4, 2, 5, 1, 3] // compare 3-1, lowest: 1

// swap 4-1, reset lowest: 2

[1, 2, 5, 4, 3] // compare 5-2, lowest: 2
[1, 2, 5, 4, 3] // compare 4-2, lowest: 2
[1, 2, 5, 4, 3] // compare 3-2, lowest: 2

// no swap needed, reset lowest: 5

[1, 2, 5, 4, 3] // compare 4-5, lowest: 4
[1, 2, 5, 4, 3] // compare 3-4, lowest: 3

// swap 5-3, reset lowest: 4

[1, 2, 3, 4, 5] // compare 5-4, lowest: 4

// no swap needed

Solution to Challenge 3

Using the following list:

[4, 2, 5, 1, 3]
[2, 4, 5, 1, 3] // 4-2 swapped

[2, 4, 5, 1, 3] // 4-5 not swapped

[2, 4, 1, 5, 3] // 5-1 swapped
[2, 1, 4, 5, 3] // 4-1 swapped
[1, 2, 4, 5, 3] // 2-1 swapped

[1, 2, 4, 3, 5] // 5-3 swapped
[1, 2, 3, 4, 5] // 4-3 swapped
[1, 2, 3, 4, 5] // 2-3 not swapped

Solution to Challenge 4

Each of the sort algorithms below is working on the following sorted collection:

[1, 2, 3, 4, 5]

Bubble Sort

Here are the steps bubble sort would take:

[1, 2, 3, 4, 5] // 1-2 not swapped
[1, 2, 3, 4, 5] // 2-3 not swapped
[1, 2, 3, 4, 5] // 3-4 not swapped
[1, 2, 3, 4, 5] // 4-5 not swapped

Selection Sort

These are the steps selection sort would take:

[1, 2, 3, 4, 5] // compare 2-1, lowest: 1
[1, 2, 3, 4, 5] // compare 3-1, lowest: 1
[1, 2, 3, 4, 5] // compare 4-1, lowest: 1
[1, 2, 3, 4, 5] // compare 5-1, lowest: 1

// no swap needed, reset lowest: 2

[1, 2, 3, 4, 5] // compare 3-2, lowest: 2
[1, 2, 3, 4, 5] // compare 4-2, lowest: 2
[1, 2, 3, 4, 5] // compare 5-2, lowest: 2

// no swap needed, reset lowest: 3

[1, 2, 3, 4, 5] // compare 4-3, lowest: 3
[1, 2, 3, 4, 5] // compare 5-3, lowest: 3

// no swap needed, reset lowest: 4

[1, 2, 3, 4, 5] // compare 5-4, lowest: 4

// no swap needed

Insertion Sort

And these are the steps insertion sort would take:

[1, 2, 3, 4, 5] // 1-2 not swapped
[1, 2, 3, 4, 5] // 2-3 not swapped
[1, 2, 3, 4, 5] // 3-4 not swapped
[1, 2, 3, 4, 5] // 4-5 not swapped
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