Transcript Mouse in a Maze - Bowdoin College

Designing Algorithms
February 2nd
Administrativia
• Lab assignments will be due every Monday
• Lab access
– Searles 128: daily until 4pm unless class in progress
– Searles 117: 6-10pm, Sat-Sun 12-10pm
• Office hours:
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– Anytime I am in the office
– Email to set up appointment
Designing algorithms
• Last time
– Pseudocode
– Algorithm 1: adding 2 m-digit numbers
– Algorithm 2: computing miles-per-gallon
• Today
– More algorithms
– Reading: chapter 2
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
1
2
3
7
8
9
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 > m-1
4
Set the value of ci to ai + bi + carry
5
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
Stop
The final MPG program (Fig 2.5)
Write a pseudocode algorithm to compute the distance travelled 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.
0
1
9
Set response to “Yes”
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 > 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
Stop
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 a loop
around it.
This visual model is good for design, too…
Computer
Algorithm
Input
(keyboard)
Output
(screen)
Variables
How was the MPG program (Fig 2.5) designed?
Problem statement (p 35):
Write a pseudocode algorithm to compute the distance
travelled 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)
Visualizing the program design
Computer
Input
(keyboard)
25
12000
13000
Output
(screen)
response Yes gallons
start
distance
end
mpg
Designing a Sequential Search Algorithm
Problem statement (p 43-44): 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: target, list, found, index
Calculate:
if the value at index in list = target
set found to true
else increment the index by 1
Put the steps in order: input, calculate, output
Determine if a loop is needed
The final sequential search program (Fig 2.9)
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 > 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
Variations of sequential search..
• Modify the sequential search algorithm such that
– 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
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
For next time..
• Think about the problems
• Read Chapter 2
– Except 2.3.3 (Pattern matching), which we’ll do
next time