COSC 1306 COMPUTER SCIENCE AND PROGRAMMING

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COSC 1306COMPUTER SCIENCE AND PROGRAMMING

• Jehan-François Pâris
• jfparis_at_uh.edu

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CHAPTER IIIAlGORITHMS
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Chapter overview

• How computers work
• Hardware
• Software
• Algorithms and Heuristics
• Algorithmic thinking

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HOW COMPUTERS WORK
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Overall organization
MAIN MEMORY programs with their data
CPU
User inputs and outputs
Hard disk
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Inside the main memory
Operate inusermode
Operatesin kernelmode
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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

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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

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The kernel

• Responsible for
• Managing the resources
• Which process should get the CPU
• How our files are stored
• Enforcing security and preventing crashes

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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

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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

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Saving the results

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

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What is inside a program?

• Instructions
• Telling the CPU what to do
• Constants
• Stable values
• Variables
• Memory locations where results can be stored

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CHAPTER III ALGORITHMS

• Work in progress
• Will still add new materials

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What is an algorithm?

• Effective method expressed as afinite list of
  well-defined instructionsfor calculating a
  function
• Wikipedia

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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

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These are not algorithms

• On a shampoo bottle
• Lather
• Rinse
• Repeat

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These are not algorithms

• On a shampoo bottle
• Lather
• Rinse
• Repeat
• How many times?

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These are not algorithms

• On fuel tank cap
• Turn until three o'clock

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These are not algorithms

• On fuel tank cap
• Turn until three o'clock
• That could be a long time!

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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 FahrenheitWater freezes at 32 F and boils at
  212 F
• In CelsiusWater freezes at 0 C and boils at 100
  C

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Example Converting C into F

• Read Celsius temperature x
• Multiply by 1.8
• Add 32 to obtain Fahrenheit temperature y

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Example Converting C into F

• Another way to do it
• Read Celsius temperature x
• Fahrenheit temperature y 1.8x 32

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Counter-example (I)

• British weatherman's rule of thumb
• Multiply C temperature by 2
• Add 30
• Very good for temperatures in 41-59 F range
• During a Texas summer, better use
• Multiply C temperature by 2
• Add 25

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Counter-example (II)

• These two rules are heuristics, not algorithms
• Do not always give the right conversion
• Still useful
• Double and add 25 rule converts30 C into 85 F
• Right answer is 86 F

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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!

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Example

• Finding a name in a table
• Naïve solution is sequential search
• Binary search is much faster

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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 liststop and
  return NOT FOUND

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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

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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

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Binary search (II)

1. If search_name goes before the name of
   entry restart search for first half of list
2. If search_name goes after the name of
   entry restart search for second half of list

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Example of binary search

• List containsAlanAliceBarbaraEmilyFrancisGi
  naPeter

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Example of binary search

• We look for Charles in a sorted list of names
• AlanAliceBarbaraEmilyFrancisGinaPeter

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Example of binary search

• We compare search name with entry exactly in the
  middle of the list (Emily)AlanAliceBarbaraEmi
  lyFrancisGinaPeter

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Example of binary search

• Since Charles comes before Emilywe can eliminate
  second half of listAlanAliceBarbara

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Example of binary search

• We compare search name with entry exactly in the
  middle of the list (Alice)AlanAliceBarbara

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Example of binary search

• Since Charles comes after Alicewe can eliminate
  the first half of listBarbara

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Example of binary search

• We compare search name with entry exactly in the
  middle of the list (Barbara)Barbara

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Example of binary search

• Since Charles comes after Alicewe can eliminate
  the first half of the listBarbara

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Example of binary search

• Since Charles comes before Barbara we can
  eliminate one half of the list

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Example of binary search

• Since list to be searched is now emptywe
  conclude that the list does not contain Charles

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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)

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Heuristics (I)

• Many problems have nopractical algorithmic
  solution
• Algorithm will take too long
• Example
• Finding the absolute best price for an item
• Should check everywhere
• Not cost-effective

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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

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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

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It works
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It does not always work
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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

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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

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Typicalalgorithmicpatterns
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Sequences

• Almost trivial
• Specifies steps that must be taken in sequence
• Default for most programming languages
• Read Celsius temperature x
• Fahrenheit temperature y 1.8x 32

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Alternatives

• Can be
• Simple
• Double
• Multiple

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Simple alternative

• Describes an action that will be taken if some
  condition is true
• Other choice is doing nothing
• If item is taxable tax item_value
  tax_rate

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Double alternative

• Describes two actions that can be taken depending
  on a Boolean condition
• One of them will always be executed
• if a lt b max aelse max b

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Typical newbie mistakes

• if a lt b max aif b gt a replace by
  else max b
• if a lt b max aelif b gt a replace
  by else max b

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Multiple choices

• Describes several actions that can be taken
  depending on multiple conditions
• Can end with an elif or an else
• if average gt 90 grade 'A'elif average
  gt 87 grade 'A-'elif average gt 84
  grade 'B'elif

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A typical newbie mistake

• Checking for was already checked
• if average gt 90 grade 'A'elif average
  gt 87 and average lt 90 grade 'A-'elif
  average gt 84 and average lt 87 grade
  'B'elif

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Loops

• Can be
• based on a condition
• based on a range

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Condition-based loops

• condition Truewhile condition
  condition False last loop iteration
• while True break immediate
  exit
• Can combine both!

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Iterative algorithms

• An important special case of loop algorithms
• Idea is to compute a numerical result by
  successively computing better and better
  approximations
• Will stop when the value is accurate enough
• So many decimals

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Computing the square root (I)

• Want a simple algorithm to compute vs of a
  positive number.
• If x vs then x2 s and x s/x
• Consider an approximation a of vs
• If a lt vs then s/a gtvs
• If a gt vs then s/a ltvs
• In either case, vs is between a and s/a

STEM Students only
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Computing the square root (II)
If a gt s
x is inside
0
s/a
a

• The average of a and s/a (a s/a)/2is a better
  estimate of vs

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Babylonian method to compute square roots

• s float(input("Enter a number "))
• old 1 anything but 0 or s
• new (s1)/2
• while abs(old - new) gt 1E-5
• old new
• new (old s/old)/2
• print("Square root of .5f is .5f." (s,
  new))

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How does it work? (I)
For your information

• Recall
• (a b)2 a2 2ab b2
• We can write it
• a b v(a2 2ab b2)
• In our case
• s a2 2ab b2
• old a
• error b

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How does it work? (II)
For your information

• We try to evaluate the error
• a2 2ab b2 s
• b(2a b) s a2
• b (s a2)/(2ab) (s a2)/2a (s/a a)/2
• if b is small enough
• The new approximation will be
• a b a (s/a a)/2 ( 2a s/a a)/2
  (a s/a)/2

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Advantages/Disadvantages

• Simpler to program than non-iterative methods
• Each step typically performs a relatively simple
  computation
• Number of steps required to achieve the required
  accuracy level can be a critical issue
• Try to pick an algorithm that converges fast

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Range-based loops

• for i in range (k, m)
• executes loop for i k, k1, , m 1
• for i in range (0, m)
• executes loop m times
• for i 0, , m 1
• for i in range (1, m 1)
• executes loop m times
• for i 1, , m

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Example

• for i in range(0,99)
• print("I will not talk in class.")

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Loops over strings (and lists)

• Loop goes through all the elements of
• a string
• for x in anystring
• Example
• mystring input("Enter a string ")
• for ch in mystring
• print(ch)