LECTURE 15

Introduction to Functions

Informal idea of a function

A function converts an input to an output The inputs are called actual parameters

or arguments The output is called the return value.

Input

function

output

Examples

Name: maxOf2

Input: two numbers Output: the value of the largest one Defining the function in Python

def maxOf2(n1, n2): # n1 and n2 are numbers #returns the largest

if n1 >= n2: return n1 else: return n2

Using the function

# Using a variable to “catch” the returned valueans = maxOf2(48, 35)print ansans1 =maxOf2(45.6, 78.3)print ans1

# Printing the returned value immediately# Note that sometimes the function may work for values of the actual # parameters that were not intended! Don’t count on it!

print maxOf2("Dan", "Don")print maxOf2([1,2,3], [4,5,6])

Maximum number in a list

Input: a list of numbers Output: the value of the largest number

in the list Algorithm:

Maximum number in a list

Input: a list of numbers Output: the value of the largest number

in the list Algorithm:

Let biggestSoFar be the first item in the list Loop through all items in the list

If you find some item larger than biggestSoFar, set biggestSoFar to this new value

#Defining the function in Python

def maxInList(aList): #aList is a non empty list of numbers #returns the largest item on the list

biggestSoFar = aList[0] for item in aList[1:]: if item > biggestSoFar: biggestSoFar = item return biggestSoFar

#Using the function#A variable to “catch” the returned valueans = maxInList( [2,65,98,44,5,21,50,64])print ans#Using the returned value directlyprint maxInList( ['Hal', 'Sally', 'George', 'Tim', 'Mike'])

Compute simple interest

Input: Principal, rate, years Output: The amount of interest earned

on the principal after the given number of years

Defining the function in Python

def simpleInterest(principal, rate, years): #rate is given as a decimal so a 2% annual rate #would be given as 0.02 #Returns the total amount of interest on the principate at rate #for this many years

interest = principal*rate*years return interest

#Using the function in Python

print simpleInterest(500, 0.03, 5)

Compound Interest

Input: principal, annual rate, number of compounding periods per year, number of years

Output: The total interest earned Algorithm:

Figure out the rate per compounding period Figure out the number of compounding

periods Compute the final value of the investment Compute and return the interest

#Defining the function in Pythondef compoundInterest(principal, rate, n, years): #returns the interest gained on the principal after years #where the interest is compounded n times per year #rate is the annual rate given as a decimal

#compute the number of compounding periods p = n * years #compute the interest rate per compounding period r = rate/n #calculate the final value of the investment value = principal for i in range(p): value = value + value*r #calculate the difference between the initial investment and #the current value interest = value - principal return interest

#Using the function in Pythonprint compoundInterest(500,0.03,12,5)

Find the distance between points Input: Two points (given as graphics

objects) Output: The distance between the

points Algorithm:

Find the distance between points Input: Two points (given as graphics

objects) Output: The distance between the

points Algorithm:

Find the x and y coordinates of the first point

Find the x and y coordinate of the second point

Use the distance formula to calculate the distance

Return the distance

#Define the functiondef distance(p1, p2): #p1 and p2 are Point objects #returns the distance between the points

x1 = p1.getX() y1 = p1.getY() x2 = p2.getX() y2 = p2.getY() dist = math.sqrt( (x1 - x2)**2 + (y1 - y2)**2) return dist

#Use the functionprint distance(Point(3,4), Point(0,0))

Tell if point is inside a circle

Input: Point object and Circle object Output: True or False depending on

whether the point is inside the circle Algorithm

Tell if point is inside a circle

Input: Point object and Circle object Output: True or False depending on

whether the point is inside the circle Algorithm

Get the center of the circle Get the radius of the circle Calculate the distance of the point to the

center of the circle If it is less that the radius return True Otherwise return False

#Defining the functiondef isInside(myPoint, myCircle): #returns True if myPoint is inside myCircle; otherwise False

p1 = myCircle.getCenter() r = myCircle.getRadius() dis = distance(myPoint,p1) #use the other function I defined if dis <=r: return True else: return False

#Using the functionwin = GraphWin("Testing Functions", 400, 400)win.setCoords (0,0,5,5)c = Circle(Point(2,3), 0.5)c.draw(win)c.setFill("yellow")p1 = Point(2,4)p1.draw(win)print isInside(p1, c)

Make a circle “blink” in new color Input: a Circle object, the current color,

a new color Output: Nothing to return Algorithm

Make a circle “blink” in new color Input: a Circle object, the current color,

a new color Output: Nothing to return Algorithm

set fill to new color Sleep for one minute Set fill to the original color

def flash (myCircle, oldColor, newColor): #expects a circle whose fillColor is oldColor #changes the color of myCircle to new color, waits 1 sec\ #and changes back to old color

myCircle.setFill(newColor) time.sleep(1) myCircle.setFill(oldColor) return

win = GraphWin("Testing Functions", 400, 400)win.setCoords (0,0,5,5)c = Circle(Point(2,3), 0.5)c.draw(win)c.setFill("yellow")p1 = Point(2,4)p1.draw(win)print isInside(p1, c)flash(c, "yellow", "green")time.sleep(1)flash(c, "yellow", 'pink')