The document discusses searching and sorting algorithms. It covers linear search and binary search algorithms for searching, including their time and memory complexities. For sorting, it discusses properties of sorting algorithms and compares insertion sort, selection sort, bubble sort, count sort, bucket sort, and radix sort. It provides analysis of the time and space complexities of each sorting algorithm.

1. Week 8
Searching and sorting
Searching

2. Linear search
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?

3. Binary search
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?
Sorting

4. Properties of sorting
algorithms
Comparison-based
sorting
Insertion sort

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

6. 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?
Selection sort

7. • Termination: Trivial — nested finite for-loops
• Correctness:
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?
Bubble sort

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

9. 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?
Index-based sorting
Count sort

10. Bucket sort
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?
Radix sort

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