1. LECTURE 15 Introduction to Functions

2. 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

3. Examples

4. 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

5. Using the function # Using a variable to “catch” the returned value ans = maxOf2(48, 35) print ans ans1 =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])

6. Maximum number in a list  Input: a list of numbers  Output: the value of the largest number in the list  Algorithm:

7. 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

8. #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 value ans = maxInList( [2,65,98,44,5,21,50,64]) print ans #Using the returned value directly print maxInList( ['Hal', 'Sally', 'George', 'Tim', 'Mike'])

9. 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

10. 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)

11. 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

12. #Defining the function in Python def 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 Python print compoundInterest(500,0.03,12,5)

13. Find the distance between points  Input: Two points (given as graphics objects)  Output: The distance between the points  Algorithm:

14. 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

15. #Define the function def 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 function print distance(Point(3,4), Point(0,0))

16. 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

17. 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

18. #Defining the function def 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 function 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)

19. Make a circle “blink” in new color  Input: a Circle object, the current color, a new color  Output: Nothing to return  Algorithm

20. 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

21. 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')