1. Search
Recall the employee database used in class examples: employeeRecordT workforce[5] =
Given "Vance, Emelline", how can we find her salary?
Name Empl. ID Dept. Salary
Fudge, Cornelius admin
Weasley, Percy admin
Bones, Amelia legal
Vance, Emelline research
Doge, Elphias sales

2. Linear Search
Obvious answer: Look through all the names until we find a match:
int find_salary (employeeRecordT workforce[ ], char *name) {
for (int i = 0; i < SIZE; i++)
if (strcmp(name, workforce[i].name) ==0 )
return workforce[i].salary;
return -1; /* Not found */ }

3. Linear Search Not clever: Better idea:
To find 1 entry, we may have to test all SIZE entries
Better idea:
Sort first (by name)
This will take some time, but if we are planning to do many searches, it will be worth it in the end.
Then search more efficiently
Think: how would you search the phonebook?

4. Binary Search MAIN IDEA:
Find middle of list
Compare target to element at middle
Is this it? If yes, we are done.
If no, which half has the target? Keep only that half and ignore the other.
Repeat until you find the target or discover that it's not in the list.
Important: This type of search can only be used on sorted data.

5. Binary Search Target: Core idea: Where is "Logan, James"? Ba Ca Ce Fa
Read middle of list to split it into 2 halves.
Where is "Logan, James"? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra

6. Binary Search Target: Core idea: Where is "Logan, James"? Ba Ca Ce Fa
Read middle of list to split it into 2 halves.
Compare target to middle element: no match
Where is "Logan, James"? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra

7. Binary Search Target: Core idea: Where is "Logan, James"? Lo < ? La
Read middle of list to split it into 2 halves.
Compare target to middle element: no match
Which half would "Low, Sampson" be in?
Where is "Logan, James"? Lo
< ? La Lo
> ? La Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra

8. Binary Search Target: Core idea: Where is "Logan, James"? Lo < ? La
Read middle of list to split it into 2 halves.
Compare target to middle element: no match
Which half would "Low, Sampson" be in? Keep only that half.
Repeat until answer found.
Where is "Logan, James"? Lo
< ? La Lo
> ? La Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra

9. Binary Search Target: Implementation: Where is "Logan, James"? Ba Ca
At each step, indices left, right define the subarray we are working on.
Where is "Logan, James"? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
left=0, right=19

10. Binary Search Target: Implementation: Where is "Logan, James"? Ba Ca
Find the midpoint: workforce[ (left+right) / 2 ]
Where is "Logan, James"? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid
left=0, right=19, mid=9

11. Binary Search Target: Implementation: Where is "Logan, James"? Ba Ca
If the data at the midpoint is equal to the target, return the index: if (strcmp(workforce[mid], name) == 0) return mid;
But it's not...
Where is "Logan, James"? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid

12. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
if the data at the midpoint is greater than the target, move right to the left of the midpoint so you can work on the first half: else if (strcmp(workforce[mid], name) > 0) right = mid – 1;
But it's not... Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid

13. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
If the data at the midpoint is less than the target, move left to the right of the midpoint so you can work on the second half. else left = mid + 1;
Indeed, "Lo" > "La Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right

14. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
Updated left-hand and right-hand indices define the new subarray: Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
left=10, right=19

15. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
Repeat: find the midpoint Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
mid
right
left=10, right=19
mid = (10+19)/2

16. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
"Lo" < "No", so move right to the left of mid. Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
left=10, right=13

17. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
Repeat: find the new midpoint: Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid
left=10, right=13
mid=(10+13)/2

18. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
"Lo" < "Mi", so move the right index to the left of mid. Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
left=10, right=10

19. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
Repeat: find the new midpoint Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
left=10
right=10
mid=10
right
mid

20. Binary Search Where is "Logan, James"? Target: Implementation: Ba Ca
We have a match, return index mid.
What if the target is not in the list?
How will the loop terminate? Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra

21. Binary Search Where is "Morgan, Elliot"? Target: Implementation: Ba Ca
The first few steps are the same as before: Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid
left=10, right=13
mid=(10+13)/2

22. Binary Search Where is "Morgan, Elliot"? Target: Implementation: Ba Ca
"Mo" > "Mi", so move the left index to the right of mid. Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
right
left
left=12, right=13

23. Binary Search Where is "Morgan, Elliot"? Target: Implementation: Ba Ca
Repeat: find the midpoint Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
mid
left=12, right=13
mid = 12

24. Binary Search Where is "Morgan, Elliot"? Target: Implementation: Ba Ca
"Na" > "Mo" so move the right index to the left of mid. Ba Ca Ce Fa Fe Fo Ga He Ho La Lo Mi Na Ne No Nu Pa Ph Qu Ra
left
right
left=12, right=11

25. Binary Search Where is "Morgan, Elliot"? Target: Implementation:
What happened? The left and right indices have swapped (i.e right is to the left and left is to the right).
Now we know that the element cannot possibly be in the list. Return -1 (invalid index) to indicate this
Alternatively, we could have checked one step earlier whether left == right and whether the element they refer to matches the target.

26. Why Bother? HUGE speed improvement!
Every iteration cuts list length by half
Cost for a list of length 2k is just k iterations.
For one search of a list of length N:
Linear search cost : N
Binary search cost : log2(N)
Example: search a 32-million-element list
Linear search : up to 32 million iterations (comparisons)
Binary search : up to 25 iterations (comparisons)

27. Sorting
Sorting = arranging data in some order according to their values
Example:
arranging a sequence of numbers from largest to smallest
arranging a sequence of names in alphabetical order
arranging a sequence of records based on a "key" (e.g. the name field or the salary field)

28. Sorting
There are several sorting algorithms, some more efficient than others. We will discuss:
selection sort
insertion sort
In all of our examples, we will assume that
the items to be sorted are stored in an array
we want to sort the items in ascending order

29. Selection Sort Idea: Select item that should be first in order
How? Traverse the array keeping track of the largest element as you go.
Swap it with the actual first item in the array.
The part of the array containing the first item is now sorted. From now on, ignore it.
The rest of the array is still unsorted.
Repeat the process on the unsorted part of the array.

30. Selection Sort
As we "move" items to the sorted part of the array, this imaginary wall between the parts moves towards the end of the array. When it reaches the edge, we are done!

31. Selection Sort
Selection Sort

32. Insertion Sort
Idea:
Divide the array in two imaginary parts: sorted, unsorted
The sorted part is initially empty
Pick the first element from the unsorted part and insert it in its correct slot in the sorted part.
Do the insertion by traversing the sorted part to find where the element should be placed. Shift the other elements over to make room for it.
Repeat the process.
This algorithm is very efficient for sorting small lists
Example: sorting homeworks by name

33. Insertion Sort
As we "move" items to the sorted part of the array, this imaginary wall between the parts moves towards the end of the array. When it reaches the edge, we are done!

34. Insertion Sort