This document discusses searching and sorting algorithms. It covers linear search and binary search, and their time and space complexities. It also discusses insertion sort, selection sort, bubble sort, and comparison-based sorting algorithms. Finally, it mentions count sort, bucket sort, radix sort, and index-based sorting algorithms. The document poses analysis questions for each algorithm.

1. Week 8
Searching and sorting

2. Searching

5. Linear search

6. Linear search
• What is the best-case running time?
• What is the worst-case running time?
• What is the memory usage?
• Which assumptions have we made about the keys and
how the data is represented?

7. Binary search

8. Binary search
• What is the best-case running time?
• What is the worst-case running time?
• What is the memory usage?
• Which assumptions have we made about the keys and
how the data is represented?

9. Sorting

10. Properties of sorting
algorithms

11. Comparison-based
sorting

12. Insertion sort

15. • Termination: Trivial — nested finite for-loops
• Correctness:

16. Insertion sort
• Which assumptions have we made?
• Is it stable?
• What is the worst-case number of comparisons?
• What is the best-case number of comparisons?
• What is the worst-case number of swaps?
• What is the best-case number of swaps?

17. Selection sort

19. • Termination: Trivial — nested finite for-loops
• Correctness:

20. Selection sort
• Which assumptions have we made?
• Is it stable?
• What is the worst-case number of comparisons?
• What is the best-case number of comparisons?
• What is the worst-case number of swaps?
• What is the best-case number of swaps?

21. Bubble sort

23. • Termination: Not trivial! (But wait for it…)
• Correctness:
j is # outer iterations

24. • Termination:
• Correctness:
j is # outer iterations
While j is only used for the analysis,
and not a real "for-loop" variable we
can use it in the termination function:
t(j) = n - j

25. Bubble sort
• Which assumptions have we made?
• Is it stable?
• What is the worst-case number of comparisons?
• What is the best-case number of comparisons?
• What is the worst-case number of swaps?
• What is the best-case number of swaps?

26. Index-based sorting

27. Count sort

28. Bucket sort

29. Bucket sort
• Which assumptions have we made?
• Is it stable?
• What is the best- and worst-case running time?
• What is the best- and worst-case memory usage?

30. Radix sort

31. Exercises!
Time to put searching
and sorting into practice