Lab 5 User-defined Modules Solution

We have used several built-in modules or libraries like math, turtle, and sys. In this lab you will build several user-defined modules or libraries. A module or library allows you to logically organize

your Python code. Grouping related code into a module makes the code easier to understand and use. In its simplest form, a module is a file consisting of Python code. A module can define functions, variables, and classes (we will look at classes in the last third of CS8). A module can also include
runnable code!

Part A

Create a module named cone.py. Define three functions with arguments r (radius) and h (height): volume(r, h), surface_area(r, h), and printstats(r, h) to calculate the volume and surface area of a cone with radius r and height h. printstats(r, h) displays to two decimal places both the volume and surface_area. Don’t forget to document each function by describing its purpose (this is used by Python’s help() function to display information about a function). For example to document the volume() function do as follows,

def volume(r, h):

'''

volume(r,h) computes the volume of a right-circular cone with radius r and height h.
'''

…


Now test the cone module as illustrated in the Python Shell. Note what gets displayed when help(volume) is called.

Part B

Create a module named specialsums.py. Define three functions with one argument n, an integer:
gauss(n), sumofsqs(n), and sumofcubes(n). Note that the caller provides the value for n.

gauss(n) computes the sum:

1 + 2 + 3 + ... + n

sumofsqs(n) computes:

1 + 22 + 32 + ... + n2

sumofcubes(n) computes:

1 + 23 + 33 + ... + n3

Make sure your functions work properly, that is, returns 0 when n is 0 or a negative integer. Now test the specialsums module as illustrated in the Python Shell.





















By placing a description at the beginning of this module (use ' ' ' document here ' ' ') anyone using it can ask for help(specialsums) to display each function and their description.






















Exercise: Implement the fourth function sumconsecutive(m,n) described above.
The dir( ) Function

The dir() built-in function returns a sorted list of strings containing the names defined by a module. The list contains the names of all the modules, variables and functions that are defined in the specified module. Here is an example for you to run.














Here is the output produced:










Timing Code in Python

In computer science, one way to test the efficiency of a function or program segment is to time the execution of the function call or program segment on different argument values and/or on different sets of data.

The time() function returns the time (in seconds) from January 1, 1970 (This is when time began, because the Unix operating system was created then). Here is an outline of how function calls and program segments are timed.

import time

start = time.time()

    • code to be timed goes here (place function call here)

stop = time.time()

print('%1.2f seconds' % (stop - start))

Part C

Two ways to compute the cube of a number u is to use the exponentiation operator to form u**3 or to use repeated multiplication to form u*u*u. Time the function sumofcubes(N) using these two ways of calculating a cube of a number, for the following values of N.

sumofcubes(N) with u**3
|
sumofcubes(N) with u*u*u
|----------
|------------

|----------
|------------
|
| N
| Time (sec) |
| N
| Time (sec) |
|----------
|------------
|
|----------
|------------
|
|5000000
|
|
|5000000
|
|
|----------
|------------
|
|----------
|------------
|
|10000000
|
|
|10000000
|
|
|----------
|------------
|
|----------
|------------
|
|15000000
|
|
|15000000
|
|
|----------
|------------
|
|----------
|------------
|
|20000000
|
|
|20000000
|
|
|----------
|------------
|
|----------
|------------
|
|25000000
|
|
|25000000
|
|
|----------
|------------
|
|----------
|------------
|