CS107%20Introduction%20to%20Computer%20Science

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CS107Introduction to Computer Science

• Lecture 2

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Administrativia

• Lab access
• Searles 128 daily until 4pm unless class in
  progress
• Searles 117 6-10pm, Sat-Sun 12-10pm
• Office hours
• M, W 4-5 pm
• Quick questions Anytime I am in the office
• Email to set up appointment
• My office Searles 219
• Study group
• Mondays 8-9pm in Searles 224

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• Last time
• What is (not) Computer Science
• Algorithms, properties and examples
• Expressing algorithms Pseudocode
• Who was Alan Turing and what is he famous for?
• Today
• More pseudocode elements
• Algorithm examples

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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 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
• Repeat operations
• Execute a block of operation multiple times until
  a certain condition is met

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Basic operations

• Read the input from user
• Get x
• Get a, b, c
• Print the output to the user
• Print x
• Print Your mileage is x
• Cary out basic arithmetical computations
• Set x to 10
• Set y to xx/3

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• Conditional statements
• Specify 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
• 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

• Variables count
• 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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Pseudocode examples

• Equivalent
• Set the value of a to 1
• Set a to 1
• a1
• Equivalent
• Add 1 to count
• Set count to count 1
• Increment the value of count by 1
• count count 1
• Writing in pseudocode gives you the freedom to
  choose any of these!

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• Incorrect
• Set 1 to a
• Add a b (what do you do with the result?)
• Set ab 3
• Note not the same
• set a to b
• set b to a
• Example what is the output of the following
  algorithms?
• set a to 2 set a to 2
• set b to 4 set b to 4
• set a to b set b to a
• print a, b print a, b

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A model for visualizing an algorithms behavior
Computer
Algorithm
Input (keyboard)
Output (screen)
Variables
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Algorithm for computing MPG (Fig 2.5)

• Write a pseudocode algorithm to compute
  the distance traveled and the average miles per
  gallon on a trip when given as input the number
  of gallons used and the starting and ending
  mileage readings on the odometer.
• Variables response, gallons, start, end,
  distance, mpg
• 0 Set response to Yes
• 1 Repeat steps 2-8 until response No
• 2 Get gallons, start, end
• 3 Set distance to end - start
• 4 Set mpg to distance gallons
• 5 Print mpg
• 6 if mpg gt 25.0 then
• print You are getting good gas mileage
• else print You are NOT getting good gas
  mileage
• 7 Print Do you want to do this again, Yes or
  No?
• 8 Get response
• 9 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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Designing Algorithms A Methodology

1. Read the problem, identifying the input and the
   output.
2. What variables are needed?
3. What computations are required to achieve the
   output?
4. Usually, the first steps in your algorithm bring
   input values to the variables.
5. Usually, the last steps display the output
6. So, the middle steps will do the computation.
7. If the process is to be repeated, add loops.

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How was the MPG program (Fig 2.5) designed?

• Problem statement
• Write a pseudocode algorithm to compute the
  distance traveled and the average miles per
  gallon on a trip when given as input the number
  of gallons used and the starting and ending
  mileage readings on the odometer.
• Input number of gallons, starting mileage,
  ending mileage
• Output distance traveled, average miles per
  gallon
• Variables gallons, start, end, distance, mpg
• Calculate distance end - start
• mpg distance / gallons
• Put the steps in order input, calculate, output
  (steps 2-8)
• Determine if a loop is needed (steps 0, 1, 9, 10)
  

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Problem

• Adding two n-digit numbers
• 7597831
• 1287525
• -------------------
• 8885356
• How would you write an algorithm to solve
  this problem? Assume the basic operation is
  adding one-digit numbers.

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Computing the sum 12.n

• Problem Write an algorithm which reads a
  positive integer from the user and computes the
  sum of all positive integers smaller than or
  equal to te number entered by the user.
• Example if the user enters 10, the algorithm
  should compute 12310

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Gauss formula

• Find a formula for 1 2 . n
• Gauss noticed that
• 1 n n1
• 2 (n-1) n1
• .
• gt 1 2 (n-1) n n(n1)/2