Chapter 1 An Introduction to Computer Science

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Chapter 1An Introduction to Computer Science
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Misconceptions of CS

• CS is the study of computers
• Incomplete definition since theory of computers
  was done even before the first computer was
  invented.
• CS is the study of how to write computer programs
• The idea of how to solve a problem is more
  important.
• A program is only a means to an end, not end
  itself.
• CS is the study of the uses and applications of
  computers and software
• Many people use software but a computer scientist
  is responsible for specifying, designing,
  building and testing software packages as well as
  computer systems on which they are run.

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Definition of CS

• CS is the study of algorithms, including
• Their formal and mathematical properties(Ch 2
  3)
• Studying the behavior of algorithms to determine
  whether they are correct and efficient.
• Their hardware realizations (Ch 4, 5 6)
• Designing and building computer systems that are
  able to execute algorithms
• Their linguistic realizations (Ch 7 10)
• Designing programming languages and translating
  algorithms into these languages so that they can
  be executed by hardware
• Their applications (Ch 11 14)
• Identifying important problems and designing
  correct and efficient software packages to solve
  these problems.

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Algorithms

• An algorithm is a step by step set of finite
  instructions to accomplish a task.
• All algorithms are written using one or more of
  these three operations.
• Sequential Operation Carries out a single well
  defined task. After which it moves on to the
  next instruction. Expressed as simple
  declarative sentences.Eg. Add the value of x to
  1.Eg. Subtract check amount from account
  balance.
• Conditional operations Question asking
  instructions of an algorithm. Ask and select.Eg.
  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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• 3. Iterative operations looping instructions
  of an algorithm. They tell us to go back and
  repeat the execution of a previous block of
  instructions.
• Eg. Repeat Steps 1, 2 and 3 until value of y
  is equal to 1Eg. Repeat the following 5 steps
  until there are no more checks to be processed.

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Example of how an algorithm looks in plain
English.

• ALGORITHM TO CHANGE A FLAT TIRE
• Step 1 Gather your spare tire, lug wrench, jack.
  
• Step 2 If car has hubcap, remove it
• Step 3 Using lug wrench loosen lug nuts. Try
  jumping on lug wrench if difficult to loosen.
  Only loosen, do not remove.
• Step 4 Position the jack under car and raise the
  jack until it contacts the frame. Extend jack
  until car is about 6 inches off the ground.
• Step 5 Remove lug nuts from the bolts and put
  them aside.
• Step 6 Pull the wheel off the car and place on
  ground.
• Step 7 Position the spare tire directly in front
  of the wheel and align the holes in the center of
  the spare tire with the bolts on the car
• Step 8 Lift the spare tire and position it on
  the threaded bolts and push the tire onto the car
  until it cannot go any farther
• Step 9 Replace the lugnuts on the bolts and
  tighten them, but not too tight. Just enough to
  hold the tire in place while you lower the car
• Step 10 Lower the car with the jack until the
  car is again resting on all four tires
• Step 11 Tighten all the lugnuts one by one.
• Step 12 Drive safe and get your flat tire
  repaired.

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Algorithm to add two m-digit numbers

• Step 1 Set the value of carry to 0
• Step 2 Set the value of I equal to value of 0
• Step 3 Repeat Steps 4 through 6 until I is
  greater than m-1
• Step 4 Add the two digits ai and bi to the
  current value of
• carry to get ci
• Step 5 If ci gt 10 then reset ci to (ci-10)
  and reset the
• value of carry to 1
  
• otherwise set the new
  value of carry to 0.
• Step 6 Add 1 to I, effectively moving one
  column to the left.
• Step 7 Set cm to the value of carry.
• Step 8 Print out the final answer,
  cmcm-1cm-2.c0
• Step 9 Stop
• (TRACE WITH 5648)

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• Why do we do this complicated technique for a
  simple task of adding two numbers?
• In order to automate the solution and make our
  life easier.
• Imagine adding millions of numbers in a few
  seconds or minutes.
• Computing agent The machine, robot, person or
  thing carrying out the steps of the algorithm is
  called a computing agent.
• An algorithm should be both correct and
  efficient.

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• Not every problem can be solved with an algorithm
• Sometimes specifying an algorithm is possible but
  the computation would take so long that the
  solution is useless. (eg. the game of chess,
  1028 years)
• Other times there are problems we dont know how
  to solve (eg. modeling how a baby recognizes and
  learns). Impossible to write an algorithm to
  paint a picture.
• ALGORITHM ENCODE IN PROGRAMMING LANGUAGE
  AUTOMATED SOLUTION
• This means we use the machine/computer for its
  speed and power to do these monotonous mundane
  tasks.

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Formal definition of an Algorithm

• It is a well ordered collection of unambiguous
  and effectively computable operations that when
  executed produces a result that halts in a finite
  amount of time.
• Unambiguous one that can be understood and
  carried out directly by the computing agent
  without needing to be further simplified or
  explained. This is called a primitive operation
  or just a primitive.
• Primitives vary on different machines as well as
  individuals.
• Effectively computable means that it should be
  doable.
• E.g. no matter how long you try to flap your
  arms, you wont fly right?E.g. x sqrt(n)
  (What if n lt 0? Then it is undefined)
• Result Now how do we know if the result we get
  from an algorithm is correct? We observe and
  test various inputs. Note that the algorithm
  should work for all possible valid inputs.
• Finite means it cannot go on forever. Otherwise
  it will be an infinite loop.

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Importance of algorithmic problem solving

• Algorithms are encoded into some appropriate
  language and given to a computing agent to
  execute.
• This lets us use algorithms to mechanize and
  automate repetitive tasks.
• People make better use of their time creating
  better algorithms instead of doing the repetitive
  tasks.
• We use algorithms all the time, baking a cake,
  registering for courses.
• See page 6 for an algorithm on how to program
  your VCR

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Problems to think about

• On Page 23
• Exercise 3
• Exercise 4
• Exercise 7

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Review

• Misconceptions of Computer Science
• The Definition of Computer Science
• Formal definition of an Algorithm
• Describe and Identify sequential, iterative and
  conditional operations.
• Examples of Algorithms
• Tracing an Algorithm
• Importance of Algorithmic Problem Solving
• What is a computing agent? What is an effectively
  computable operation.

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• THE END OF CHAPTER 1