1. COSC 1306 COMPUTER SCIENCE AND PROGRAMMING
Jehan-François Pâris 1

2. CHAPTER II COMPUTING

3. Chapter overview How computers work Hardware Software
Algorithms and Heuristics
Algorithmic thinking 3

4. HOW COMPUTERS WORK

5. programs with their data
Overall organization
MAIN MEMORY
programs with their data
CPU
Hard disk
User inputs and outputs

6. Inside the main memory Operate in user mode Operates in kernel mode
Running programs:
we call them "processes"
KERNEL
allocates memory to processes
grants CPU to processes control disk accesses
Operate
in user mode
Operates in
kernel mode

7. The running programs Reside in main memory while they are running
Include many background processes
We do not see them
Take space and often CPU time
Having a large main memory allows us to run more programs at the same time

8. TIP If your computer becomes slow whenever you switch among programs
You need more memory
If your computer takes a lot of time to boot
You could have a slow disk
Your OS has a lot of things to load into main memory
Useful and not so useful

9. The kernel Responsible for Managing the resources
Which process should get the CPU
How our files are stored …
Enforcing security and preventing crashes

10. Security issues
Must protect running programs from attempts to modify them by other programs
Mostly programming issues
Also viruses
Must protect our data on disk
Especially if computer is shared

11. Running a program OS creates a process
Allocates memory space to the process
Disk copy of program is brought from disk into main memory
Process competes with other processes for CPU time
Process is deleted when program terminates

12. Saving the results
Normally done by saving the results in a file stored on disk
Can print them later

13. What is inside a program?
Instructions:
Telling the CPU what to do
Constants:
Stable values
Variables:
Memory locations where results can be stored

14. ALGORITHMS AND HEURISTICS14 14

15. HOW COMPUTERS WORK

16. What is an algorithm?
“Effective method expressed as a finite list of well-defined instructions for calculating a function”
Wikipedia

17. Three important points
It must be an effective method
Guaranteed to produce the result
The instructions should be well-defined
Anybody using the algorithm should obtain the same answer
It should have a finite number of steps
An algorithm must terminate after a finite number of finite steps

18. These are not algorithms
On a shampoo bottle:
Lather
Rinse
Repeat

19. These are not algorithms
On a shampoo bottle:
Lather
Rinse
Repeat
How many times?

20. These are not algorithms
On fuel tank cap:
Turn until three o'clock

21. These are not algorithms
On fuel tank cap:
Turn until three o'clock
That could be a long time!

22. Example: Converting C into F
If you travel outside of the US, temperatures are likely to be given in Celsius not Fahrenheit.
How the scales differ:
In Fahrenheit: Water freezes at 32 F and boils at 212 F
In Celsius: Water freezes at 0 C and boils at 100 C

23. Example: Converting C into F
Read Celsius temperature x
Multiply by 1.8
Add 32 to obtain Fahrenheit temperature y

24. Example: Converting C into F
Another way to do it:
Read Celsius temperature x
Fahrenheit temperature y = 1.8×x +32

25. Counter-example (I) British weatherman's rule of thumb:
Multiply C temperature by 2
Add 30
Very good for temperatures in F range
During a Texas summer, better use:
Add 25

26. Counter-example (II) These two rules are heuristics, not algorithms
Do not always give the right conversion
Still useful
Double and add 25 rule converts 30 C into 85 F
Right answer is 86 F

27. A program is not algorithm
It is the expression of an algorithm in a programming language
Picking the right algorithm is the most important task
After that, we just have to code!

28. Example Finding a name in a table Naïve solution is sequential search
Binary search is much faster

29. Sequential search (I) We look for search_name in list list
Start at beginning of list
If list is empty stop and return NOT FOUND
If search_name matches name of first list entry stop and return list entry
If we have reached the end of the list stop and return NOT FOUND

30. Sequential search (II)
Look for next list entry
If search_name matches name of next list entry stop and return list entry
Go to step 4

31. Binary search (I) We look for search_name in list list
If list is empty stop and return NOT FOUND
Find entry exactly in middle of list
If search_name matches the name of that entry stop and return list entry

32. Binary search (II)
If search_name goes before the name of entry restart search for first half of list
If search_name goes after the name of entry restart search for second half of list

33. Example of binary search
List contains Alan Alice Barbara Emily Francis Gina Peter

34. Example of binary search
We look for Charles in a sorted list of names
Alan Alice Barbara Emily Francis Gina Peter

35. Example of binary search
We compare search name with entry exactly in the middle of the list (Emily) Alan Alice Barbara Emily Francis Gina Peter

36. Example of binary search
Since Charles comes before Emily we can eliminate second half of list Alan Alice Barbara

37. Example of binary search
We compare search name with entry exactly in the middle of the list (Alice) Alan Alice Barbara

38. Example of binary search
Since Charles comes after Alice we can eliminate the first half of list Barbara

39. Example of binary search
We compare search name with entry exactly in the middle of the list (Barbara) Barbara

40. Example of binary search
Since Charles comes after Alice we can eliminate the first half of the list Barbara

41. Example of binary search
Since Charles comes before Barbara we can eliminate one half of the list

42. Example of binary search
Since list to be searched is now empty we conclude that the list does not contain Charles

43. Comparing performances
List with 1024 entries
Sequential search:
Maximum number of steps: 1024
Average number of steps: 512 (one half)
Binary search:
Number of steps: 10 (= log2 1024)

44. Heuristics (I) Many problems have no practical algorithmic solution
Algorithm will take too long
Example:
Finding the absolute best price for an item
Should check everywhere
Not cost-effective

45. Heuristics (I) Heuristics provide solutions
That are not guaranteed to work in all cases
That provide a good approximation of the correct solution
Example:
When we want to buy an item, we focus on the stores that are likely to sell the item at a good price

46. An example Finding the maximum of a curve Start at any given point
Move on the curve following the upward direction
Stop when the curve reaches a start going downward

47. It works

48. It does not always work

49. Which one is the most useful?
ALGORITHM
Always provides the right answer
Can be very slow
HEURISTICS
Normally provide a good approximation of the right answer
Relatively fast

50. Algorithmic thinking
Way to analyze problems and come with one or more algorithmic solutions that
fully describe the solution
handle all special cases
can implemented on a computer system
will run at a reasonable cost
Most important skill for a programmer
Can be learned

51. Algorithmic thinking basics
Basic concepts
Order matters
Must make choices
Repeat the same task
Over different data
To get better results

52. Order matters (I) You want to bake something Preheat oven
Set up oven timer and temperature
Put item in oven
Turn off oven
Take item from oven
Can invert steps 2 and 3
Maybe 5 and 4, not the other steps

53. Order matters (II) The formulas for the surface of a circle s = pi*r2
if you are given d, you must compute
in that order!

54. Order matters (III) The general rule is
Cannot compute anything if your data are not ready
To compute s = pi*r2
Must know the values of pi and r

55. Must make choices If average >= 90 : Give an A
Else if average >= 88 :
Give an A-
Else if …

56. Repeat the same task Over different data For all exams turned in:
For all pages in exam
For each question on page
Grade question
Compute page total
Compute exam total

58. First refinement For all exams turned in: For all pages in exam
For each question on page
Grade question
Add grade score to page total
Add page total to exam total
Will abysmally fail!

59. Why? Violated basic rule:
Cannot compute anything if your data are not ready
Did not initialize
exam total and page total

60. Second refinement For all exams turned in: Reset exam total to zero
Reset page total to zero
For all pages in exam
For each question on page
Grade question
Add grade score to page total
Add page total to exam total
Will produce grade inflation!

61. The right solution For all exams turned in: Reset exam total to zero
For all pages in exam
Reset page total to zero
For each question on page
Grade question
Add grade score to page total
Add page total to exam total

62. Repeat the same task To get a more accurate result
Before the era of pocket calculators
Taught an insane method to compute square roots
Nobody used
Much older and simpler Babylonian method

63. Babylonian method
If x is an overestimate to the square root of a non-negative real number S then
S/x will be an underestimate (and vice versa)
(x + S/x)/ 2 will provide a better approximation
Why?
Because x* S/x = S

64. Computing the square root of 2
Start with x = 2
S/x = 1 and (x +S/x)/2 = 1.5
Set new value of x to 1.5
S/x = and (x +S/x)/2 = …
Stable value x = after 5 steps

65. Computing the square root of 99
Start with x = 99
S/x = 1 and (x +S/x)/2 = 50
Set new value of x to 50
S/x = 1.8 and (x +S/x) /2=25.99 …
Stable value x = after 8 steps
Use a spreadsheet to try it at home!

66. But Quite boring to go though all this steps True but
Algorithm is very simple
Computers do not complain!