Lab # 5 lists , range function more for loops, pointer/reference variables, aliasing

(This is a very important lab. Please make sure you learn and understand all of this material)

Starting Lab 5

• Open a browser and log into Brightspace
• On the left hand side under Labs tab, find lab5 material contained in lab5-students.zip file
• Download that file to the Desktop and unzip

Before starting, always make sure you are running Python 3

This slide is applicable to all labs, exercises, assignments etc

ALWAYS MAKE SURE FIRST that you are running Python 3.4 (3.5

or 3.6 is fine too)

That is, when you click on IDLE (or start Python any other way) look at the first line that the Python shell displays. It should say Python 3.4 or 3.5 or 3.6 (and then some extra digits)

If you do not know how to do this, read the material provided with Lab 1. It explains it step by step

Do all the exercises labeled as

Task in your head i.e. on a paper

Later on if you wish, you can type them into a computer (or copy/paste from the solutions once I poste them)

Study the following four fundamental algorithms:

Returns sum of all positive integers smaller than n

def summation(n): ‘(number)->number

odd_sum = 0 for num in range(n):

odd_sum = odd_sum + num

return odd_sum Sum of numbers in a given list a.

A solution with loop over elements

def sum_list_v1(a): (list)->num

list_sum = 0 for item in a:

list_sum = list_sum + item return list_sum

Returns a product of all positive integers smaller than n

def product(n): ‘(number)->number

prod = 1 for num in range(n):

prod = prod * num

return prod

Sum of numbers in a given list a.

A solution with a loop over indices

def sum_list_v2(a): (list)->num

list_sum = 0 i = 0 for i in range(len(a)):

list_sum = list_sum + a[i] return list_sum 8

Task 4 and Programming Exercise 1

1.After studying the previous four fundamental functions, how would you modify them to only sum odd numbers (or odd list elements)? Try yourself and then see next step for solutions.

2.Open the file called four_functions.py Copy/paste, one by one, Example 1 to 4 into Python visualizer. Run through each example and understand how the solutions work and how the variables change in the loops. As always, you can find python visualizer here (make sure you choose Python 3)

http://www.pythontutor.com/visualize.html#mode=edit

3. Programming exercise: Write a function called ah(l,x,y) that given a list l, and integers x and y such that x <=y, returns two numbers. The first is the number of elements of l that are between x and y (including x and y). The second number is the minimum element of l that is between x and y (including x and y). Example test:

>>> t=[5, 1, -2.5, 10, 13, 8]

>>> ah(t, 2,11) (3, 5)

Recall that you can return two numbers referred by variables a and b by just returning a tuple (a,b)

9

Task 5

How many stars does the following program print?

1. a) 0 b) 15 c) 45 d) 48 e) 68

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Intermission: print function revisited

Built-in function print, when its completes printing, enters a new line. For example:

print(This is) print(Lab 5) Prints:

This is

Lab 5

As mentioned in the last lab, this default behavior of the print function can be changed by specifying what we want print function to end with. For example:

print(This is, end=***)

print(Lab 5.) Would This is***Lab 5

print(This is, end=) Print This isLab 6

print(Lab 6, end=
) This is Lab 7

print(This is, end= ) =>

print(Lab 7)

In other words, unless specified otherwise, the default end for the print function is end=

Introduction to Computing Using Python by Lj. Perkovic

More examples of use of print function

Function print prints, by default,

a newline character after printing its arguments

Task 6

1. What does this print?
2. What does this print?
3. What does this print?

Task 7

What does the following program print?

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Programming Exercise 2: Experiment with Perfect Numbers

• A positive integer is called a perfect number if it is equal to the sum of all of its positive divisors, excluding itself. For example, 6 is perfect number since 6=1+2+3. The next is 28=1+2+4+7+12. There are four perfect numbers less than 10,000. Write a program that prints all these four
• Your program should have a function called is_perfect that takes as input a positive integers and returns True if it is perfect and False
• Once you are Modify your program so that it looks for all perfect numbers smaller than 35 million. What do you notice? Assuming that you computer can do a billion instructions in a sec, can you figure out how long, roughly, will it take your computer to find 5^th perfect number (it is 33,550,336). Is the answer roughly: couple of minutes, couple of hours, couple of days, weeks, months, years ?
• ₁₅ What if you wanted to wait until it prints 6^th perfect number, which is 8,589,869,056?

Programming Exercise 3a:

Arithmetic progression

Recall that a sequence of numbers forms an arithmetic progression if the difference between every pair of consecutive numbers is the same. For example: -5, -1, 3, 7, 11 forms an arithmetic progression since the difference between every pair of consecutive numbers is 4. On the contrary 5, 10, 15, 24, 29 is not an arithmetic progression since the difference between some consecutive pairs is 5 and some 4. A sequence that has exactly one number is considered arithmetic, too.

• Write a function called arithmetic that takes as input a list of numbers and returns True if the numbers of the list form arithmetic And False otherwise

Testing:

>>> arithmetic( [-5, -1, 3, 7, 11] )

True

>>> arithmetic([0, -1, 3, 7, 11])

False

>>> a = [5, 10, 15, 24, 29]

>>> arithmetic(a)

False

>>> arithmetic(a[:3])

True

Programming Exercise 3b: and now is it sorted?

Now modify your method arithmetic slightly so that instead it tests if the numbers in the give lists are ordered for smallest to largest. Call the new function is_sorted

Testing:

>>> is_sorted([1, 1, 1, 7, 7])

True

>>> is_sorted([-10, -1, 3, 7, 100])

True

>>> is_sorted([0, 3, 1, 7, 11])

False

>>> a = [5, -10, 15, 24, 29]

>>> is_sorted(a)

False

>>> is_sorted(a[1:4])

True

Task 6: Flow of execution

The the following two multiple choice questions:

https://runestone.academy/runestone/static/thinkcspy/Functions/FlowofExecutionSummary.html