Designing Algorithms

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Designing Algorithms

• Csci 107
• Lecture 3

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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
• Mon, Wed 4-5, Tue after lab
• Quick questions Anytime I am in the office
• Email to set up appointment
• My office Searles 219
• Study group Mondays 8-10 pm in Searles 224

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Designing algorithms

• Last time
• Pseudocode
• Algorithm computing the sum 12n
• List variables
• Today
• Adding two m-digit numbers
• Computing MPG
• Search and variations

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List variables

• How to represent (in pseudocode) inputs of
  arbitrary size?
• Suppose that we need to read 100 numbers from the
  user, or 1000, or..
• we could give each variable a different
  nametedious!!
• Use a list variable
• Variable list a of size n
• This means that a is a list of n elements a1,
  a2, a3,,an
• To read the list from the user use
• Get n and a1, a2, a3,,an
• To print the list use
• Print a1, a2, a3,,an
• We can treat each element in the list as a
  variable
• Set a3 to 5
• Set a4 to a3 2

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Problem

• Adding two m-digit numbers
• 7597831
• 1287525
• -------------------
• 8885356
• Write an algorithm to solve this problem.
  Assume the basic operation is adding one-digit
  numbers.

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Algorithm for adding two m-digit numbers (Fig 1.2)

• Given m 1 and two positive numbers a and b,
  each containing m digits, compute the sum c a
  b.
• Variables m, list a0 ..am-1, list b0 . bm-1
  , list c0 cm-1 cm, carry, i
• 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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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. Repeat this
  process until user wants to stop.
• 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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A Search Algorithm

• Problem statement Write a pseudocode algorithm
  to find the location of a target value in a list
  of values.
• Input a list of values and the target value
• Output the location of the target value, or else
  a message that the value does not appear in the
  list.
• Variables

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The (sequential) search algorithm (Fig 2.9)
Variables target, n, list list of n values Get
the value of target, n, and the list of n
values Set index to 1 Set found to false Repeat
until found true or index gt n If the value of
listindex target then Output the index Set
found to true else Increment the index by 1 If
not found then Output a message that target was
not found Stop
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Variations of sequential search..

• Modify the sequential search algorithm in order
• To find all occurrences of target in the list and
  print the positions where they occur
• To count the number of occurrences of target in
  the list
• To count how many elements in the list are larger
  than target

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More algorithms

• Write algorithms to find
• the largest number in a list of numbers (and the
  position where it occurs)
• the smallest number in a list of numbers (and the
  position where it occurs)
• the range of a list of numbers
• Range largest - smallest
• the average of a list of numbers
• the sum of a list of numbers

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For next time..

• Read Chapter 2
• Except 2.3.3 (Pattern matching), which well do
  next time
• Lab 1 is due tomorrow