ICS3U Grade 11 Computer Science

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ICS3U Modular Programming with Python

ICS3U Grade 11 Computer Science ICS3U Modular Programming with Python

ICS3U Learning Goals

In this ICS3U Grade 11 Computer Science lesson you will be learning to:

  • Understand the basic idea behind top down analysis
  • Take a larger problem and break it down into smaller modules
  • Create a function that accepts parameters and returns a value
  • Call functions from the main computer code and receive return values if necessary

Top Down Analysis

You are going to learn about a problem solving technique called Top Down Analysis and Stepwise Refinement.

Example of Modular Design

Suppose you were asked to find the median of a list of numbers. Remember the median is the middle number in an ordered list. The modules needed to solve the problem might be

  • Input the List
  • Sort the Data
    • Swap the Data
  • Pick the Middle Number
    • Find the average
  • Output the Middle Number

Input the list

  • Use a loop to get the data from the user
  • Store the data in an array

Sort The Data Module

  • Use a loop to cycle through each piece of data
  • Compare Current Value to Next Value, if out of order then call swap module
  • Repeat until the list is sorted

Swap Module

  • Store data in temp variable
  • Overwrite current value
  • Write temp variable to the array

Pick Middle Module

  • If list is odd -> Only one middle number, so pick it
  • If list is even -> Two middle numbers, find the average

Average Module

  • Add two numbers and divide by 2

Output Results

  • Print middle number to the screen

When using modular programming, your code will generally look as follows:

  • You define the modules at the top of your program
  • You define a “main” module for your program underneath them that uses all the functions and solves a particular problem

Writing Modules in Python

Usually we use the term function in python to represent a module. You might hear them called methods as well. (There is a difference, but it has to do with some more advanced topics in Object Oriented Programming, which is part of the ICS4U Course) You have already used a lot of python functions when writing your previous programs.

  • print()
  • input()
  • int()
  • len()
  • sqrt()
  • etc….

These are functions that execute code internally (that you can’t see) but you can learn how to use. The print function might have 20 lines of code in it, so imagine how long and confusing your programs would be if you had to write those 20 lines every time you wanted to print something.

We want to be able to create our own functions that accomplish very small and specific tasks.

Before a function can be usedd, it must be defined. That is, you define the rules of how the function will behave when used. – A function contains a header and a body

The Header

Sets up the name of the function, it might also have a parameter list

  • The name should reflect the task that the function performs. It should follow the same naming conventions that you would use for variables
  • The parameter list consists of the data the function needs to perform the task. The list is formed by specifying a variable to hold the data sent to it
    • For Example, the sqrt() function requires a number to be sent to it in order to work.
    • For Example, the len() function requires a list to be sent to it in order to work

The Body

Contains the code to accomplish the task of function.

  • It uses the parameter values that are sent to it to accomplish its tasks
  • The function might return a value back to the location at which it was called in order to be used in the main part of your program
    • Both the sqrt() and len() function send a result back to your program that you then store in a variable and use to solve a problem
  • The code for the body of the function must be indented (Similar if statements and loops)

Example - Slope Program

Suppose you wanted to create a program that calculates a bunch of slopes of different line segments.

It would be useful in this program to create a function that calculated the slope of a line given two points (x1,y1) and (x2,y2).  In order to accomplish this task, you would use the following formula

$$ x = \frac {y2-y1}{x2-x1} $$

The function needs to accept those 4 values to it and it needs to send the answer back to the main program so that answer could be used in some way afterwards

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor and run the program with different values for inputs

				
					#Function Definitions
def slope(x1,y1,x2,y2):
    m = (y2 - y1) / (x2 - x1)
    return m

#Main Program that solves a problem
def main():
    while True:
        
        #Get points from the user
        point1x = float(input("Enter x1: "))
        point1y = float(input("Enter y1: "))
        point2x = float(input("Enter x2: "))
        point2y = float(input("Enter y2: "))
        
        #Send values to the function to process and get answer
        userSlope = slope(point1x,point1y,point2x,point2y)
        
        #Output values
        print("Your line has a slope of: ", userSlope)
        
        #Stop?
        choice = input("Stop? Enter Yes, otherwise hit enter to continue")
        if choice.upper() == "YES":
            break
        

#Call the main function to start your code running
main()

The program reads all the function definitions at the top of the program first so when they are called in the future, it knows what to do with it.

The main part of the program is where you are solving a problem, just like you have always done.

  • The program gets 4  numbers from the keyboard
  • It sends the values of those numbers to the function named slope
    • It has effectively copied the values sent into the variables x1, y1, x2, y2
    • The order you send parameters to a function matters!!!
  • The slope function does the calculation for m, and the return function sends that calculation back to the location at which the function was called.
    • It basically replaces the function call with the value returned from the function
  • The variable userSlope then stores that returned value inside it to use as the rest of the program needs it to.

To start your program, you just have to call the main function.

  • main doesn’t have to have a parameter list and it doesn’t need return a value.
  • Just think of it as the starting point of your program
  • It doesn’t have to be called main (but conventions from other programming languages would dictate that is what you should do)

Functions without Return values or Parameters

Not all functions would necessarily need to return a value. Here is the definition of a function that prints out your credentials. This might be useful at the bottom of an email to save the user from having to type his contact information

				
					
def signature():
	print("Teacher Name")
	print("905 - 555 -5555")
	print("teacher@school.com")

Here is a definition of a function that prints out values of a list, one per line.

				
					
def printList(l):
    for i in range(0,len(l)):
        print(l[i])

They would be called just the same as every other function, but no need to assign them to a variable

				
					
#Main Program
def main():
    
    
    myList = [3,4,5,6,7]
    
    #Call printlist Function
    printList(myList)
    
    #Call signature Function
    signature()

Other Examples

Here are some other list and string functions that might be useful as well when solving problems

Changing a list to a String

  • This function accepts a list as a parameter
  • It creates a String using that list
  • The function returns that String value
				
					
def listToString(l):
	s = ""
	for i in range(0,len(l)):
		s = s + l[i]

	return s

Changing a String to a list

  • This function accepts a string as a parameter
  • It creates a list using the characters from the string
  • The function returns that list value
				
					
def stringToList(s):

	l = []
	for i in range(0, len(s)):
		l.append(s[i])

	return l

Exchanging the Position of items in a list

  • This function accepts a list as a parameter, along with two index values of the items wishing to be swapped positions.  
    • After the function call the item at position a will be at position b and the item that was at position b will be at position a
  • It stores the value of the first position in a temporary variable so it doesn’t get overwritten 
  • A simple swap like this wouldn’t work l[a] would swap but l[b] would not because position a was changed to b.  Need to store a in a separate variable first
    • l[a] = l[b]
    • l[b] = l[a] 
  • The function returns that swapped list
				
					
def swapList(l,a,b):
	
	temp = l[a]
	l[a] = l[b]
	l[b] = temp

	return l

Interactive Learning Activity - Grade 11 Computer Science

Copy the function definitions above into the Python Editor.  Write a main program that tests their function

				
					#Function Definitions
def listToString(l):
	s = ""
	for i in range(0,len(l)):
		s = s + l[i]

	return s

#Main Program to Test
def main():
    myList = ["H","i"]
    stringEquivalent = listToString(myList)
    print(stringEquivalent)
    
    
#Call main to start the program
main()
				
			
				
					#Function Definitions
def stringToList(s):

	l = []
	for i in range(0, len(s)):
		l.append(s[i])

	return l

#Main Program to Test
def main():
    myString = input("Enter a word: ")
    listEquivalent = stringToList(myString)
    print(listEquivalent)
    
    
#Call main to start the program
main()
				
			
				
					#Function Definitions
def swapList(l,a,b):
	
	temp = l[a]
	l[a] = l[b]
	l[b] = temp

	return l

#Main Program to Test
def main():
    
    myList = [20,30,70,50,60,100,10,40]
    
    #Swap 30 and 60
    myList = swapList(myList,1,4)
    print(myList)
    
    
#Call main to start the program
main()

Mixing Up a String

Suppose you have been asked to write a program that mixes up the characters in a String

The general solution could look something like this:

  • Swap two characters in the String and then repeat that swap several times until the String is significantly mixed up
  • You could make use of the 3 functions you just learned about to accomplish the task

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor and run the program with different values for inputs

				
					#Import statements
import random

#Function Definitions
def listToString(l):
	s = ""
	for i in range(0,len(l)):
		s = s + l[i]

	return s

def swapList(l,a,b):
	temp = l[a]
	l[a] = l[b]
	l[b] = temp

	return l

def stringToList(s):

	l = []
	for i in range(0, len(s)):
		l.append(s[i])

	return l

#Main Program to mix up a word
def main():
    
    word = input("Enter the Word to Mix Up: ")
    
    #Make swaps equal to the length of the word
    for i in range (0, len(word)):
    
        #Turn String into a list
    	charList = stringToList(word)
        
    	#Get Random Positions
    	position1 = random.randint(0,len(word)-1)
    	position2 = random.randint(0,len(word)-1)
    
    	#Swap Positions
    	swappedList = swapList(charList, position1, position2)
    
    	#Rebuild to a string
    	word = listToString(swappedList)
    
    #Output final mixed up word
    print("The mixed up word is: ", word)
    
#Call main to start the program
main()

The main strategy behind this program is that you 

  • Convert the String to a list
  • Get 2 random positions
  • Swap the entries in the list at those positions
  • Rebuild the list into a String

You can then repeat this process multiple times until you get it mixed up adequately.  I decided that mixing as many times as the length of the string was going to be good enough

This problem solving strategy is reflected in the main function

In order to accomplish that task, I wrote 3 functions

Function #1 – stringToList

  • This function starts with an empty list and then uses a loop to grab each character of the string and appends it to the list

Function #2 – swapList

  • This function takes a list and then 2 index value numbers and swaps the values at those position values

Function #3 – listToString

  • Takes a list and then uses a loop to take each element of the list and attach it to a blank string.  Effectively building up the new string each iteration of the loop.  

 

Video Summary

Watch a video of your teacher summarizing the learning content for this section

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Variable Scope

Not all variables can be accessed from anywhere in a program. The part of a program where a variable is accessible is called its scope.

  • There are two types of scope: Local Scope and Global Scope

Local Scope

Whenever you define a variable within a function, its scope lies ONLY within the function. It is accessible from the point at which it is defined until the end of the function and exists for as long as the function is executing. Which means its value cannot be changed or even accessed from outside the function.

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor, run the program and observe the error

				
					#Function Definitions
def sampleFunction():
    
    print(x)

#Main Program
def main():
    
    x = 5
    sampleFunction()
    
     
#Call main to start the program
main()

The variable x is created inside the main function.  Its scope is local to main.  No other function outside of main knows that it exists. 

  • If you want another function to know its value, then you must pass that value to it using the other function’s parameter list.

You can use the same variable names inside different functions.  Python treats those as completely separate variables even though they have the same name

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor, run the program and observe how the functions treat the variable x

				
					#Function Definitions
def sampleFunction():
    
    x = 3
    print("x is", x, "in the sample function")

#Main Program
def main():
    
    x = 5
    print("x is", x, "in main")
    sampleFunction()
    print("x is", x, "in main even after changing it in the function")
     
#Call main to start the program
main()

Global Scope

Whenever a variable is defined outside any function, it becomes a global variable, and its scope is anywhere within the program. Which means it can be used by any function.

  • Typically you define these global variables at the top of your program, before any function definitions.  
  • It isn’t great practice to use all global variables in your program.  Use them if needed, but prefer parameter passing.
 

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor, run the program and observe how the functions treat the variable x

				
					#Global Variables
x = 5

#Function Definitions
def sampleFunction():
    
    print("x is", x, "in the sample function")

#Main Program
def main():
    
    print("x is", x, "in main")
    sampleFunction()
         
#Call main to start the program
main()

Mixing Scope Variables

If there is a global variable and a local variable with the same name, then python will default to use the local scope version of that varaible

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor, run the program and observe how the functions treat the variable x

				
					#Global Variables
x = 5

#Function Definitions
def sampleFunction():
    
    x = 3
    print("x is", x, "in the sample function")

#Main Program
def main():
    sampleFunction()
    print("x is", x, "in main")
    
         
#Call main to start the program
main()

This can become a problem if you want to change the value of a global variable in a function.  If in the last example the goal was to change the value of the global variable x to 3, then it would fail.

  • To Fix this issue, you must declare x as global inside the function where you want to change it

Interactive Learning Activity - Grade 11 Computer Science

Type the following code into the Python Editor, run the program and observe how the functions treat the variable x

				
					#Global Variables
x = 5

#Function Definitions
def sampleFunction():
    global x
    x = 3
    print("x is", x, "in the sample function")

#Main Program
def main():
    
    sampleFunction()
    print("x is", x, "in main")
    
         
#Call main to start the program
main()

Video Summary

Watch a video of your teacher summarizing the learning content for this section

Play Video

ICS3U Coding Questions

Try to code the following ICS3U questions using an IDE of your choice (Spyder, IDLE, Pycharm, etc).  You will save those files on your computer for future reference. 

Each question has:

  • A video of your teacher live coding and explaining the solution
  • The final code used in the video.

Try your best to solve the problems yourself without looking at the solutions.

Make sure you test your programs with multiple different inputs to ensure it is functioning properly.

ICS3U Practice Question

Name Your File:  “ICS3UaddBetween.py” 

Write a function that calculates the sum of all the integers between 2 values (inclusive). Accept two numbers as parameters and retun the sum. Write a main program that illustrates the function working

				
					#Function Definitions
def sumBetween(a,b):
    total = 0
    for i in range(a,b+1):
        total = total + i
    return total

#Main Program
def main():
    start = int(input("Enter first value: "))
    end = int(input("Enter last value: "))
    added = sumBetween(start,end)
    print("The sum of the integers between those numbers is: ",added)
         
#Call main to start the program
main()

ICS3U Practice Question

Name Your File:  “ICS3UfactorialSum.py” 

Let’s take a look at a factorial

  • 5! = 5 x 4 x 3 x 2 x 1 = 120
  • 3! = 3 x 2 x 1 = 6

Write a program that calculates the sum of all factorials entered by the user. Your program should ask the user to enter as many factorials as they would like and add up the sum of all those factorials. (Entering zero should signal the program to stop)

For example, If the user entered 4 factorials: 3!, 5!, 8! And 2! It would add 6 + 120 + 40320 + 2 = 40448

You must write a function called factorial to accomplish this task. It should accept the number as a parameter and return the resultant factorial.

				
					#Function Definitions
def factorial(x):
    f = 1
    for i in range(2,x+1):
       f = f * i
    return f

#Main Program
def main():
    total = 0
    while True:
        num = int(input("Enter a number: (zero to stop) "))
        if num == 0:
            break
        else:
            total = total + factorial(num)
        
    print("\nThe sum of all the factorials is: ", total)
         
#Call main to start the program
main()

ICS3U Practice Question

Name Your File:  “ICS3UlowestTerms.py” 

Write a function that accepts a positive fraction “n/d” as a String and returns another fraction “n/d” in lowest terms

You are going to need to implement a Greatest Common Divisor Algorithm.  Don’t use the built in one.  Write one yourself that takes two numbers and finds the largest number that divides into both.

				
					#Function Definitions

#Finds the greatest common divisor between 2 integers
def gcd(a,b):
    
    #Largest divisor 1 -> if no other ones found
    g = 1
    
    #start search for divisors at the smallest number
    if a>b:
        start = b
    else:
        start = a
        
    #Count backwards to find the largest divisor
    for i in range (start,1,-1):
        
        #Found largest divisor so stop
        if a % i == 0 and b % i == 0:
            g = i
            break
    
    return g
        
#Converts a fraction to lowest terms (fraction is a string n/d) 
def convert(fraction):
   
    #Get the numbers from the string
    nd = fraction.split("/")
    numerator = int(nd[0])
    denominator = int(nd[1])
   
    #Calculate the greatest common divisor
    divisor = gcd(numerator,denominator)
    
    #Reduce the fraction
    numerator = numerator//divisor
    denominator = denominator//divisor
    
    #Return a new fraction as a string
    return str(numerator) + "/"+ str(denominator)

#Main Program
def main():
    f = input("Enter fraction (n/d): ")
    reduced = convert(f)
    print("Lowest Terms: ", reduced)
         
#Call main to start the program
main()

ICS3U Practice Question

Name Your File:  “ICS3UcountPrimes.py” 

Write a function that will determine if an integer is a prime number. It should accept an integer as a parameter and return either True or False if that number is prime. Use it to find the first 200 prime numbers

				
					#Function Definitions
def isPrime(x):
    
    #1 is not a prime #
    if x == 1:
        prime = False
    else:
        
        #Assume it's prime unless it finds a divisor
        prime = True
       
        for i in range(2,x):
            #If it finds a divisor its not prime
            if x % i == 0:  
                prime = False
                break
    return prime
   
#Main Program
def main():
    #The number of primes found
    count = 0
    
    #The number being tested for prime
    num = 1
    
    #loop until finding 200 prime #'s
    while count < 200:
        
        #Found a prime so increase count
        if isPrime(num):
            count = count + 1
            print(num)
        
        #Check next number
        num = num + 1 
         
#Call main to start the program
main()

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