Examples of Functions¶

Example: Reporting the Square of a Number¶

In this example, we will write a function called square_message(). The function should take one argument, n, and should print the message:

The square of [n] is [n**2].

def square_message(n):
    print("The square of ", n, " is ", n**2, ".", sep='')

In the cell below, we have a loop that applies the function square_message() to every element of the list A.

A = [12, 34, 89, 17, 23, 49, 87, 34, 89, 71]

for i in range(0, len(A)):
    square_message(A[i])

The square of 12 is 144.
The square of 34 is 1156.
The square of 89 is 7921.
The square of 17 is 289.
The square of 23 is 529.
The square of 49 is 2401.
The square of 87 is 7569.
The square of 34 is 1156.
The square of 89 is 7921.
The square of 71 is 5041.

Example: Summing the First `n` Positive Integers¶

In the following cell, we write a function called sum_first() that takes a single parameter n, and returns the sum of the first n positive integers.

def sum_first(n):
    
    total = 0
    
    for i in range(1,n+1):
        total = total + i
        
    return total

We now call sum_first() on 100, and also on 237, printing the return value for each function call.

print(sum_first(100))
print(sum_first(237))

5050
28203

Example: Factorials¶

We will now write a function called fact() that takes in one argument, assumed to be an integer, and returns the factorial of that integer.

def fact(n):
    
    product = 1
    
    for i in range(1,n+1):
        product = product * i
        
    return product

We will use our function calculate the factorials of 3, 5, 10, and 20.

print(fact(3))
print(fact(5))
print(fact(10))
print(fact(20))

6
120
3628800
2432902008176640000

Example: `sum_power` Function¶

In the cell below, we create a function called sum_power. The function has two parameters, x and n. The parameter x is intended to be a list. The parameter n should be an int with a default value of 1. The function should raise each element to the power of n, sum the resulting values, and then return this sum.

def sum_power(x, n=1):
    total = 0
    
    for i in range(0, len(x)):
        total += x[i]**n
        
    return total 

We test our function in the cell below.

A = [4,-3,1]
print(sum_power(A))
print(sum_power(A, 2))
print(sum_power(A, 3))
print(sum_power(A, 7))

Example: `find_item` Function¶

In the cell below, we define a function called find_item that has three parameters, x, item, and first. The parameter x is expected to be a list. The parameter first should have a default value of True. The function should behave as follows:

If first == True, then the function should search for the first time that item appears in x, and should return the index of that occurrence.
If first == False, then the function should search for the last time that item appears in x, and should return the index of that occurrence.
If item does not appear in x, then the function should return None.

def find_item(x, item, first=True):
    idx = None
    for i in range(0, len(x)):
        if x[i] == item:
            idx = i
            if first:
                return idx
    return idx

After defining your function, use the following lines of code to test it.

letter_list = ['B', 'C', 'A', 'D', 'A', 'C', 'B', 'A', 'D']

print(find_item(letter_list, 'A'))
print(find_item(letter_list, 'A', first=False))
print(find_item(letter_list, 'D'))
print(find_item(letter_list, 'D', first=False))
print(find_item(letter_list, 'E'))
print(find_item(letter_list, 'E', first=False))

2
7
3
8
None
None

Example: Division with Remainder¶

Write a function div_w_remainder() that takes two arguments, num and div, and returns the number of times that div evenly divides num (i.e. the quotient), as well as the remainder of num after division by div. Coerce the remainder into an integer.

def div_w_remainder(num, div):
    
    quotient = int(num/div)
    remainder = num % div
    
    return (quotient, remainder)

We will now consider several examples to test our function.

q, r = div_w_remainder(17, 3)
print('Quotient: ', q)
print('Remainder:', r)

Quotient:  5
Remainder: 2

q, r = div_w_remainder(459, 17)
print('Quotient: ', q)
print('Remainder:', r)

Quotient:

 27
Remainder: 0

q, r = div_w_remainder(6237, 13)
print('Quotient: ', q)
print('Remainder:', r)

Quotient:  479
Remainder: 10

Example: Locating Elements in a List¶

Write a function called locate. The function should take two arguments: a list called x, and another variable called item.

The function should return two values: A list of indices at which the element in x is equal to item, and a count of the number of times that item appears in x.

def locate(x, item):
   
    index_list = []

    for i in range(0, len(x)):
        if x[i] == item:
            index_list.append(i)

    return (index_list, len(index_list))

A list of student grades is provided in the cell below. Call locate() five times. In each function call, pass in grades for x. For item, use each of the following values: 'A', 'B', 'C', 'D', and 'F'.

For each function call, print out a message of the following form:

A: indices = [......], count = ##

grades = ['A', 'D', 'A', 'C', 'B', 'F', 'A', 'D', 'C', 'B', 'F', 'A', 'C', 
          'B', 'A', 'B', 'B', 'C', 'B', 'F', 'D', 'D', 'A', 'C', 'B']

for letter in ['A', 'B', 'C', 'D', 'F']:
    idx, c = locate(grades, letter)
    print(str(letter) + ': indices = ' + str(idx) + ', count = ' + str(c) )

A: indices = [0, 2, 6, 11, 14, 22], count = 6
B: indices = [4, 9, 13, 15, 16, 18, 24], count = 7
C: indices = [3, 8, 12, 17, 23], count = 5
D: indices = [1, 7, 20, 21], count = 4
F: indices = [5, 10, 19], count = 3

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