CS107: Introduction to Computer Science

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CS107 Introduction to Computer Science

• Lecture 2
• Jan 29th

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• Last time
• What is not Computer Science
• What is Computer Science
• Algorithms, properties and examples
• Today
• Expressing algorithms Pseudocode
• Examples
• Algorithm for adding two m-digit numbers
• Algorithm for computing miles-per-gallon

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What is Computer Science?

• The study of algorithms
• their formal properties
• correctness, limits
• efficiency/cost (Chapters 2, 3, 10)
• their hardware realizations
• computer design (Chapters 4-6)
• their linguistic realizations
• programming languages (Chapters 7-9)
• their applications
• network design, ocean modeling, bioinformatics,
  ...

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What is an algorithm?

• Algorithm well-defined procedure that
  allows an agent to solve a problem.
• Algorithms must
• 1. Be well-ordered and unambiguous
• 2. Be executable (understandable),
• 3. Solve the problem, and
• 4. Terminate.
• Note often the agent is a computer or a robot

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Example Algorithms

• Cooking a dish
• Making a peanut-butter jelly sandwich
• Shampooing hair
• Adding two numbers (p 7)
• Programming a VCR (p 6)
• Making a pie (p 13)

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Designing Algorithms

• We need
• A problem for which an effective algorithm can be
  written (i.e., one that is tractable),
• A language (e.g., pseudocode or C),
• A methodology for translating the problem into an
  algorithm, and
• A computing agent that can understand and
  execute such algorithms.

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Expressing algorithms

• Is natural language good?
• For daily life, yesbut for CS is lacks structure
  and would be hard to follow
• Too rich, ambiguous, depends on context
• How about a programming language?
• Good, but not when we try to solve a problem..we
  want to think at an abstract level
• It shifts the emphasis from how to solve the
  problem to tedious details of syntax and grammar.

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Pseudocode

• Pseudocode English but looks like programming
• Good compromise
• Simple, readable, no rules, dont worry about
  punctuation. Lets you think at an abstract level
  about the problem.
• Contains only instructions that have a
  well-defined structure and resemble programming
  languages

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Pseudocode elements

• Basic (primitive) operations
• Read the input from user
• Print the output to the user
• Cary out basic arithmetical computations
• Conditional operations
• Execute an operation if a condition is true
• Sequential operations
• Repeat operations
• Execute a block of operation multiple times until
  a certain condition is met

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Variables

• Variable
• A named memory location that can store a value
• Think of it as a box into which you can store a
  value, and from which you can retrieve a value
• Examples
• List variables used when the input comes as a
  list of elements

i
carry
am-1 am-2 a1
a0
a1 a2 a
m-1 am


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Expression and assignment statements

• Function change the value of a variable by
  evaluating arithmetic expressions
• can use any arithmetic expression, just like on a
  typical calculator . -. , /,
• Examples
• set the value of m to 2
• set the value of i to 6.
• set the value of carry to i2m
• set the value of ai to 0

a1 a2 a
m-1 am

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Input/Output Statements

• Function transfer values from the user to a
  variable, or vice-versa
• get values for ltvariablegt
• print value of ltvariablegt
• Examples
• Get the value of n from the user
• Get value of the list of elements a1, a2, ,am
  from the user
• Print the value of result to the user

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• Sequential statements
• The steps of an algorithm are carried out in the
  order they are written.
• Conditional statements
• Function specifying a statement that may or may
  not be done
• if ltconditiongt then
• ltstatement to be donegt
• else ltstatement to be done otherwisegt
• Example
• if the value of carry is 0 then set the value of
  a to 0
• else set the vale of a to a1

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• Loop statements
• Function specify a group of statements that may
  be done several times (repeated)
• repeat until ltconditiongt
• lt statements to be repeated gt
• How does this work?
• Condition is evaluated
• If it is true than the loop terminates and the
  next instruction to be executed will be the
  instruction immediately following the loop
• If it is false, then the algorithm executes the
  ltstatements to be repeatedgt in order, one by one

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Example

• Step 1 set count to 1
• Step 2 repeat step 3 to step 5 until count is gt
  10
• Step 3 set square to count count
• Step 4 print value of square and value of count
• Step 5 add 1 to count
• Step 6 end
• What does this algorithm do?
• Note indentation
• Not necessary, but makes reading/understanding
  algorithms easier

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An example pseudocode algorithm (Fig 1.2)

• Given m 1 and two positive numbers a and b,
  each containing m digits, compute the sum c a
  b.
• 0 Get values for m, am-1 a0 and bm-1 b0
• Set the value of carry to 0.
• Set the value of i to 0.
• Repeat steps 4-6 until i gt m-1
• Set the value of ci to ai bi carry
• if ci 10 then
• subtract 10 from ci and set the value of carry
  to 1
• else set the value of carry to 0
• 6 Add 1 to i
• Set the value of cm to carry
• Print value of c cm cm-1 cm-2 c0

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So, how does this work???
For example, the input is m 4, a 3276, and b
7345. After step 0, the variables m, a, and b
have those values
m
4
3 2 7 6
7 3 4 5
a3 a2 a1 a0
b3 b2 b1 b0
After steps 1 and 2, the variables i and carry
are initialized.
i
0
carry
0
Next, steps 4-6 are repeated until the value of i
gt 3. Each repetition computes a single digit of
c.
c4 c3 c2 c1 c0
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A model for visualizing an algorithms behavior
Computer
Algorithm
Input (keyboard)
Output (screen)
Variables
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E.g., Visualizing Fig 1.2
Computer
0 Get values for 8 Print value of
Input (keyboard)
Output (screen)
m
4
i
0
carry
0
4 3276 7345
3 2 7 6
a3 a2 a1 a0
7 3 4 5
b3 b2 b1 b0
c4 c3 c2 c1 c0
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Another example computing MPG (Fig 2.5)

• 0 Set response to Yes
• Repeat steps 2-10 until response No
• Get gallons, start, end
• Set distance to end - start
• Set mpg to distance gallons
• Print mpg
• if mpg gt 25.0 then
• print You are getting good gas mileage
• else print You are NOT getting good gas mileage
• Print Do you want to do this again, Yes or No?
• Get response
• 11 Stop

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So, how does this work???
For example, suppose we use 25 gallons, beginning
at 12000 and ending at 13000 on the odometer.
Then, after step 2, some variables have the
following values
Yes
25
12000
13000
response
gallons
start
end
After step 4, the variables distance and mpg are
computed.
mpg
40
distance
1000
Steps 5-9 displays these results on the output
screen 40 You are getting good gas mileage Do
you want to do this again, Yes or No?
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Visualizing Fig 2.5
Computer
0 Set response 11 Stop
Input (keyboard)
Output (screen)
response
Yes
gallons
25 12000 13000
end
start
distance
mpg
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Summary

• Pseudocode
• Get/print statements (input/output statements)
• Conditional statements
• Sequential statements
• Loops
• Algoritms
• Compute sum of two m-digit numbers
• Compute miles-per-gallon

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Over the weekend

• 1. Get the textbook.
• 2. Read Chapter 1, 2.1 and 2.2
• 3. Discuss and solve the problems in the Lab 1
• (in groups or individually).
• Lab 1 is due on Monday in class.
• If you have questions well discuss them in
  class on Monday.
• Bring a digital picture for the lab tomorrow. You
  will need it for your website.