An Introduction to Computer Science

1
An Introduction to Computer Science
2
Outline

• Misconceptions of Computer Science
• The Definition of Computer Science
• Algorithms
• Conclusion

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Introduction
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Misconceptions about CS (I)

• Computer Science is the study of computers
• Some earliest and most fundamental theoretical
  work in CS took place during 1920 1940 (before
  the development of computers)
• Theoretical CS study the logical and
  mathematical properties of problems and their
  solutions (formal model)
• CS is no more about computers than astronomy is
  about telescopes, biology is about microscopes,
  or chemistry is about beakers and test tubes.
  Science is not about tools. It is about how we
  use them, and what we find out when we do

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Misconceptions about CS (II)

• Computer Science is the study of how to write
  computer programs
• Programming is a tool by which researchers can
  study new ideas and build and test new solutions
• When a computer scientist has designed and
  analyzed a new approach to solving a problem or
  has created a new way to represent information,
  then he will implement that idea as a computer
  program in order to test it on an actual computer
  system
• Permit researchers to see how well these new
  ideas work and whether they perform better than
  previous methods
• How much memory and time is required?

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Misconceptions about CS (II) (Cont.)

• Computer Science is the study of how to write
  computer programs
• In CS, it is not only the construction of a
  high-quality program that is important, but also
  the methods it embodies, the services it
  provides, and the results it produces.
• A program is only a means to an end, not an end
  in itself
• ????????
• ???????????,???????

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Misconceptions about CS (III)

• Computer Science is the study of the uses and
  applications of computers and software
• Word, Excel?
• A lot of people use software, but
• Computer scientist is responsible for specifying,
  designing, building and testing software packages
  as well as the computer systems on which they run.

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Definition of Computer Science
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Computer Science

• Computer Science is the study of algorithms,
  including
• Their formal and mathematical properties
• Study the behavior of algorithms to determine
  whether they are correct and efficient
• Their hardware realizations
• Design and build computer systems that are able
  to execute algorithms
• Their linguistic realizations
• Design programming languages and translating
  algorithms into these languages so that they can
  be executed by the hardware
• Their applications
• Identify important problems and design correct
  and efficient software packages to solve these
  poroblems

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Whats An Algorithm?
Algorithm is everywhere, not only in CS

• Dictionary definition a procedure for solving a
  mathematical problem in a finite number of steps
  that frequently involves repetition of an
  operation broadly a step-by-step method for
  accomplishing some task
• Informal definition an ordered sequence of
  instructions (operations) that is guaranteed to
  solve a specific problem
• Step 1 Do something
• Step 2 Do something
• Step 3 Do something
• Step N Stop, you are finished

Operations
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Operations In An Algorithm (I)

• A sequential operation carries out a single
  well-defined task. When that task is finished,
  the algorithm moves on to the next operation.
• Add 1 cup of butter to the mixture in the bowl
• Set the value of x to 1
• A conditional operation is the question-asking
  instructions of an algorithm. It asks a question
  and then select the next operation to be executed
  according to the question answer
• If the mixture is too dry, then add 0.5 cup of
  water to the bowl
• If x is not equal to 0, then set y equal to 1/x
  otherwise, print an error message that says we
  cannot divide by 0

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Operations In An Algorithm (II)

• An Iterative operation is a looping instruction
  of an algorithm. It tells us not to go on to the
  next instruction, but, instead, to go back and
  repeat the execution of a pervious block of
  instructions
• Repeat the previous two operations until the
  mixture has thickened
• Repeat steps 1, 2, and 3 until the value of y is
  equal to 1

When you want to command a computer to execution
your algorithm, you have to convert your
algorithm into a programming language.
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Algorithm for Programming Your VCR
Which instructions are sequential, conditional,
and iterative?
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Algorithm for Adding Two m-Digit Numbers
Which instructions are sequential, conditional,
and iterative?
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Algorithm for Adding Two m-Digit Numbers (Demo)

• Add (47 25)
• m2
• a14 a07
• b12 b05
• Step 1 carry0
• Step 2 i0
• Step 3 repeat 4-6, until i gt 1
• First iteration (i has the value 0)
• 4 Add (a0b0carry) ? c012
• 5 c0 gt 10 ? c02, carry1
• 6 Reset i to (01)1. Because i is not greater
  than 1, go back to step 4

• Second iteration (i has the value 1)
• 4 Add (a1b1carry) ? c17
• 5 c1 lt 10 ? reset carry to 0
• 6 Reset i to (11)2. Because i is greater than
  1, do not repeat but go to step 7
• Step 7 set c20 (cmcarry)
• Step 8 Print out the answerc2 c1 c0 072
• Step 9 Stop

??????,?????????
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Algorithm for Adding Two m-Digit Numbers (Demo)
i 0carry 0
i 1carry 1
Step 7
c2carry0
1 0
1 0
Step 8
a 4 7 b 2 5
a 4 7 b 2 5
c2 c1 c0 072
2
c
2
c
7
c0a0b0carry75012 c0 gt 10 ?
c012-102 carry 1
c1a1b1carry4217 c1 lt 10 ? c1 does not
change carry 0
First Iteration (i0)
Second Iteration (i1)
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Why Are Formal Algorithms So Important in CS?

• If we can specify an algorithm to solve a
  problem, then we can automate its solution
  (convert it into a program)
• Computer Science ? the science of algorithmic
  problem solving
• Discover correct and efficient algorithms for a
  wide range of interesting problems, studying
  their properties, designing programming languages
  into which those algorithms can be encoded, and
  designing and building computer systems that can
  automatically executed these algorithms in an
  efficient manner

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Algorithms
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Formal Definition of An Algorithm

• An Algorithm is a well-ordered collection of
  unambiguous and effectively computable operations
  that, when executed, produces a result and halts
  in a finite amount of time
• Is the following an algorithm?
• Step 1 Wet hair
• Step 2 Lather
• Step 3 Rinse
• Step 4 Repeat

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a well-ordered collection

• Clear and un-ambiguous ordering to these
  operations
• Whats the next operation when we finish any one
  operation?
• At step 4, what operations should be repeated?
• Ambiguous ordering
• Go back and do it again
• Go back to step 3 and begin execution from that
  point
• Start over
• Start over from step 1
• If you understand this material, you may skip
  ahead
• If you understand this material, skip ahead to
  line 21

??????,????????????!
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of unambiguous and effectively computable
operations

• An unambiguous operation is one that can be
  understood and carried out directly by the
  computing agent without needing to be further
  simplified or explained
• Primitive (operation)
• Effectively computable or doable operation
• There exists a computational process that allows
  the computing agent to complete that operation
  successfully

?????????????????! Sigh ????,??????
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of unambiguous and effectively computable
operations (Cont.)

• Step 1 Make the crust
• Step 2 Make the cherry filling
• Step 3 Pour the filling into the crust
• Step 4 Bake at 350F for 45 minutes

• Step 1 Make the crust
• 1.1 Take one and one-third cups flour
• 1.2 Sift the flour
• 1.3 Mix the sifted flour with one-half cup butter
  and one-fourth cup water
• Roll into two 9-inch pie crusts
• Step 2 make the cherry filling
• 2.1 open a 16-ounce can of cherry pie filling and
  pour into the bowl
• 2.2 add a dash of cinnamon and nutmeg, and stir

Algorithm for making a cherry pie
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of unambiguous and effectively computable
operations (Cont.)

• Which of the following are primitive operations
  for a computer?
• Add x and y to get the sum z
• See whether x is greater than, equal to, or less
  than y
• Sort a list of names into alphabetical order
• Factor an arbitrary integer into all of its prime
  factors
• Make a cherry pie

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of unambiguous and effectively computable
operations (Cont.)

• Find and Print out the 100th prime number
• Step 1 generate a list L of all the prime
  numbers
• Step 2 Sort the list L into ascending order
• Step 3 Print out the 100th element in the list
• Step 4 Stop

• Write out the exact decimal value of ?
• ? cannot be represented exactly
• Set Average to Sum/Number
• What if number 0
• Set the value of result to
• What if N lt 0
• Add 1 to the current value of x
• What if x currently has no value

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that produces a result

• In order to know whether a solution is correct,
  an algorithm must produce a result that is
  observable to a user
• What are the results of the VCR algorithm,
  addition algorithms, cherry-pie making algorithm?
• Sometimes it is not possible for an algorithm to
  produce the correct answer because for a given
  set of input, a correct answer does not exist
• Error messages (result) should be produced instead

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and halts in a finite amount of time

• The result must be produced after the execution
  of a finite number of operations, and we must
  guarantee that algorithm eventually reaches a
  statement that says Stop, you are done
• The original shampooing algorithm does not stop

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Algorithm for Shampooing Your Hair

• Wet your hair
• Set the value of WashCount to 0
• Repeat Steps 4 through 6 until the value of
  WashCount equals 2
• Lather your hair
• Rinse your hair
• Add 1 to the value of WashCount
• Stop, you have finished shampooing your hair

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Alternative Algorithm for Shampooing Your Hair

• Wet your hair
• Lather your hair
• Rinse your hair
• Lather your hair
• Rinse your hair
• Stop, you have finished shampooing your hair

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Can every problem be solved algorithmically?

• There are problems for which no generalized
  algorithmic solution can possibly exist
  (unsolvable)
• There are also problems where it is possible to
  specify an algorithm, but it would take a
  computing agent so long to execute that the
  solution is essentially useless
• Brute force algorithm for get a computer to play
  winning chess ? examine every legal move and
  response
• There are problems that we dont know how to
  solve algorithmically

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Conclusion

• Computer Science is the study of algorithms,
  including
• Their formal and mathematical properties
• Study the behavior of algorithms to determine
  whether they are correct and efficient
• Their hardware realizations
• Binary numbers, boolean logics, gates, and
  computer organization (memory, cache, I/O, ALU,
  Control)
• Their linguistic realizations
• Programming Languages, Data Structures,
  Object-oriented
• Compiler
• Their applications
• Spreadsheet, computer networks, artificial
  intelligence