1. Searching & Sorting

2. Algorithms
Step by step recipe to do a task…

3. Algorithms Step by step recipe to do a task where:
Operations are computable
Operations are unambiguous
Operations are well ordered
Finite number of operations

4. Linear Search I'm thinking of a number between 1 and 100
You try to guess it
I'll give too low/too high hints

5. Linear Search I'm thinking of a number between 1 and 100
You try to guess it
I'll give too low/too high hints
Method #1 – Linear Search
1, 2, 3….

6. Linear Search Algorithm
In pseudocode:

7. Binary Search Method #2 – Binary Search
Pick middle of remaining search space
Too high? Eliminate middle and above
Too low? Eliminate middle and below

8. Algorithm

9. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4

10. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4

11. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 5
7 (value at location 5) This is too big, need to search lower

12. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 5
7 (value at location 5) This is too big, need to search lower

13. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 5
7 (value at location 5) This is too big, need to search lower 3
4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2 = 8 / 2 = 4
5 Found it!!!

14. Binary Search Searching for 5: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3 4 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 5
7 (value at location 5) This is too big, need to search lower 3
4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2 = 8 / 2 = 4
5 Found it!!!

15. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher

16. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 10 / 2 = 5
7 (value at location 5) too big, need to search lower

17. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 10 / 2 = 5
7 (value at location 5) too big, need to search lower

18. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 10 / 2 = 5
7 (value at location 5) too big, need to search lower 3
4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2 = 8 / 2 = 4
5 (value at location 3) too small, need to search higher

19. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 10 / 2 = 5
7 (value at location 5) too big, need to search lower 3
4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2 = 8 / 2 = 4
5 (value at location 3) too small, need to search higher

20. Binary Search Searching for 6: Step minLocation maxLocation
middleLocation
middleValue 1 6
(1 + 6) / 2 = = 3
4 (value at location 3) too small, need to search higher 2
4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2 = 10 / 2 = 5
7 (value at location 5) too big, need to search lower 3
4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2 = 8 / 2 = 4
5 (value at location 3) too small, need to search higher 4
5 (one more than old middleLocation)
4 (unchanged)
minLocation > maxLocation - we have nothing left to check - value is not there!

21. Basic Sorts

22. Sorting
How do we sort?

23. Selection Sort
A human algorithm:

24. Selection Sort
In a computer:

25. Insertion Sort
For a human:

26. Selection Sort
In a computer: