1. A function is a block of code that performs a specific task when the function is called (invoked). You can use functions to make your code reusable, better organized, and more readable. Functions can have parameters and return values.

2. There are at least four basic types of functions in Python:

built-in functions which are an integral part of Python (such as the print() function). You can see a complete list of Python built-in functions at https://docs.python.org/3/library/functions.html.
the ones that come from pre-installed modules.
user-defined functions which are written by users for users – you can write your own functions and use them freely in your code,
the lambda functions

3. You can define your own function using the def keyword and the following syntax:

def your_function(optional parameters):
   # the body of the function

1 2	def your_function(optional parameters): # the body of the function

You can define a function which doesn’t take any arguments, e.g.:

def message(): # defining a function
   print("Hello") # body of the function

message() # calling the function

def message(): # defining a function

print("Hello") # body of the function

message() # calling the function

You can define a function which takes arguments, too, just like the one-parameter function below:

def hello(name): # defining a function
   print("Hello,", name) # body of the function

name = input("Enter your name: ")

hello(name) # calling the function

def hello(name): # defining a function

print("Hello,", name) # body of the function

name = input("Enter your name: ")

hello(name) # calling the function

4. You can pass information to functions by using parameters. Your functions can have as many parameters as you need.

An example of a one-parameter function:

def hi(name):
   print("Hi,", name)

hi("Greg")

def hi(name):

print("Hi,", name)

hi("Greg")

An example of a two-parameter function:

def hi_all(name_1, name_2):
   print("Hi,", name_2)
   print("Hi,", name_1)

hi_all("Sebastian", "Konrad")

def hi_all(name_1, name_2):

print("Hi,", name_2)

print("Hi,", name_1)

hi_all("Sebastian", "Konrad")

An example of a three-parameter function:

def address(street, city, postal_code):
   print("Your address is:", street, "St.,", city, postal_code)

s = input("Street: ")
p_c = input("Postal Code: ")
c = input("City: ")

address(s, c, p_c)

def address(street, city, postal_code):

print("Your address is:", street, "St.,", city, postal_code)

s = input("Street: ")

p_c = input("Postal Code: ")

c = input("City: ")

address(s, c, p_c)

5. You can pass arguments to a function using the following techniques:

positional argument passing in which the order of arguments passed matters (Ex. 1),
keyword (named) argument passing in which the order of arguments passed doesn’t matter (Ex. 2),
a mix of positional and keyword argument passing (Ex. 3).

Ex. 1
def subtra(a, b):
print(a - b)

subtra(5, 2) # outputs: 3
subtra(2, 5) # outputs: -3

Ex. 2
def subtra(a, b):
print(a - b)

subtra(a=5, b=2) # outputs: 3
subtra(b=2, a=5) # outputs: 3

Ex. 3
def subtra(a, b):
print(a - b)

subtra(5, b=2) # outputs: 3
subtra(5, 2) # outputs: 3

Ex. 1

def subtra(a, b):

print(a - b)

subtra(5, 2) # outputs: 3

subtra(2, 5) # outputs: -3

Ex. 2

def subtra(a, b):

print(a - b)

subtra(a=5, b=2) # outputs: 3

subtra(b=2, a=5) # outputs: 3

Ex. 3

def subtra(a, b):

print(a - b)

subtra(5, b=2) # outputs: 3

subtra(5, 2) # outputs: 3

It’s important to remember that you have to put positional arguments before keyword arguments. Positional arguments mustn’t follow keyword arguments. That’s why if you try to run the following snippet:

def subtra(a, b):
print(a - b)

subtra(5, b=2) # outputs: 3
subtra(a=5, 2) # Syntax Error

def subtra(a, b):

print(a - b)

subtra(5, b=2) # outputs: 3

subtra(a=5, 2) # Syntax Error

Python will not let you do it by signalling a SyntaxError.

6. You can use the keyword argument passing technique to pre-define a value for a given argument:

def name(first_name, last_name="Smith"):
print(first_name, last_name)

name("Andy") # outputs: Andy Smith
name("Betty", "Johnson") # outputs: Betty Johnson (the keyword argument replaced by "Johnson")

def name(first_name, last_name="Smith"):

print(first_name, last_name)

name("Andy") # outputs: Andy Smith

name("Betty", "Johnson") # outputs: Betty Johnson (the keyword argument replaced by "Johnson")

7. You can use the return keyword to tell a function to return some value. The return statement exits the function, e.g.:

def multiply(a, b):
   return a * b
print(multiply(3, 4)) # outputs: 12

def multiply(a, b):
   return
print(multiply(3, 4)) # outputs: None

def multiply(a, b):

return a * b

print(multiply(3, 4)) # outputs: 12

def multiply(a, b):

return

print(multiply(3, 4)) # outputs: None

8. The result of a function can be easily assigned to a variable, e.g.:

def wishes():
   return "Happy Birthday!"

w = wishes()

print(w) # outputs: Happy Birthday!

def wishes():

return "Happy Birthday!"

w = wishes()

print(w) # outputs: Happy Birthday!

Look at the difference in output in the following two examples:

# Example 1
def wishes():
   print("My Wishes")
   return "Happy Birthday"

wishes() # outputs: My Wishes

# Example 2
def wishes():
   print("My Wishes")
   return "Happy Birthday"

print(wishes())

# outputs: My Wishes
#          Happy Birthday

# Example 1

def wishes():

print("My Wishes")

return "Happy Birthday"

wishes() # outputs: My Wishes

# Example 2

def wishes():

print("My Wishes")

return "Happy Birthday"

print(wishes())

# outputs: My Wishes

# Happy Birthday

9. You can use a list as a function’s argument, e.g.:

def hi_everybody(my_list):
   for name in my_list:
      print("Hi,", name)

hi_everybody(["Adam", "John", "Lucy"])

def hi_everybody(my_list):

for name in my_list:

print("Hi,", name)

hi_everybody(["Adam", "John", "Lucy"])

10. A list can be a function result, too, e.g.:

def create_list(n):
   my_list = []
   for i in range(n):
      my_list.append(i)
   return my_list

print(create_list(5))

def create_list(n):

my_list = []

for i in range(n):

my_list.append(i)

return my_list

print(create_list(5))

11. You can use the return keyword to tell a function to return some value. The return statement exits the function, e.g.:

def multiply(a, b):
  return a * b

print(multiply(3, 4)) # outputs: 12

def multiply(a, b):
  return

print(multiply(3, 4)) # outputs: None

def multiply(a, b):

return a * b

print(multiply(3, 4)) # outputs: 12

def multiply(a, b):

return

print(multiply(3, 4)) # outputs: None

12. The result of a function can be easily assigned to a variable, e.g.:

def wishes(): 
  return "Happy Birthday!" 

w = wishes() 
print(w) # outputs: Happy Birthday!

def wishes():

return "Happy Birthday!"

w = wishes()

print(w) # outputs: Happy Birthday!

Look at the difference in output in the following two examples:

# Example 1
def wishes():
  print("My Wishes")
  return "Happy Birthday"

wishes() # outputs: My Wishes

# Example 2
def wishes():
  print("My Wishes")
  return "Happy Birthday"

print(wishes())

# outputs: My Wishes
# Happy Birthday

# Example 1

def wishes():

print("My Wishes")

return "Happy Birthday"

wishes() # outputs: My Wishes

# Example 2

def wishes():

print("My Wishes")

return "Happy Birthday"

print(wishes())

# outputs: My Wishes

# Happy Birthday

13. You can use a list as a function’s argument, e.g.:

def hi_everybody(my_list):
  for name in my_list:
    print("Hi,", name)

hi_everybody(["Adam", "John", "Lucy"])

def hi_everybody(my_list):

for name in my_list:

print("Hi,", name)

hi_everybody(["Adam", "John", "Lucy"])

14. A list can be a function result, too, e.g.:

def create_list(n):
  my_list = []
  for i in range(n):
    my_list.append(i)
  return my_list

print(create_list(5))

def create_list(n):

my_list = []

for i in range(n):

my_list.append(i)

return my_list

print(create_list(5))

15. A variable that exists outside a function has a scope inside the function body (Example 1) unless the function defines a variable of the same name (Example 2, and Example 3), e.g.:

Example 1:

var = 2 
def mult_by_var(x): 
  return x * var 

print(mult_by_var(7)) # outputs: 14

var = 2

def mult_by_var(x):

return x * var

print(mult_by_var(7)) # outputs: 14

Example 2:

def mult(x): 
  var = 5 
  return x * var 

print(mult(7)) # outputs: 35

def mult(x):

var = 5

return x * var

print(mult(7)) # outputs: 35

Example 3:

def mult(x): 
  var = 7 
  return x * var

var = 3 
print(mult(7)) # outputs: 49

def mult(x):

var = 7

return x * var

var = 3

print(mult(7)) # outputs: 49

16. A variable that exists inside a function has a scope inside the function body (Example 4), e.g.:

Example 4:

def adding(x): 
  var = 7 
  return x + var 

print(adding(4)) # outputs: 11 
print(var) # NameError

def adding(x):

var = 7

return x + var

print(adding(4)) # outputs: 11

print(var) # NameError

17. You can use the global keyword followed by a variable name to make the variable’s scope global, e.g.:

var = 2
print(var) # outputs: 2

def return_var():
  global var
  var = 5
  return var

print(return_var()) # outputs: 5
print(var) # outputs: 5

var = 2

print(var) # outputs: 2

def return_var():

global var

var = 5

return var

print(return_var()) # outputs: 5

print(var) # outputs: 5

18. Is it worth checking how it works with lists (do you recall the peculiarities of assigning list slices versus assigning lists as a whole?).

The following example will shed some light on the issue:

def my_function(my_list_1):
  print("Print #1:", my_list_1)
  print("Print #2:", my_list_2)
  my_list_1 = [0, 1]
  print("Print #3:", my_list_1)
  print("Print #4:", my_list_2)

my_list_2 = [2, 3]
my_function(my_list_2)
print("Print #5:", my_list_2)

def my_function(my_list_1):

print("Print #1:", my_list_1)

print("Print #2:", my_list_2)

my_list_1 = [0, 1]

print("Print #3:", my_list_1)

print("Print #4:", my_list_2)

my_list_2 = [2, 3]

my_function(my_list_2)

print("Print #5:", my_list_2)

The code’s output is:

Print #1: [2, 3]
Print #2: [2, 3]
Print #3: [0, 1]
Print #4: [2, 3]
Print #5: [2, 3]

Print #1: [2, 3]

Print #2: [2, 3]

Print #3: [0, 1]

Print #4: [2, 3]

Print #5: [2, 3]

It seems that the former rule still works.

Finally, can you see the difference in the example below:

def my_function(my_list_1):
  print("Print #1:", my_list_1)
  print("Print #2:", my_list_2)
  del my_list_1[0] # Pay attention to this line.
  print("Print #3:", my_list_1)
  print("Print #4:", my_list_2)

my_list_2 = [2, 3]
my_function(my_list_2)
print("Print #5:", my_list_2)

def my_function(my_list_1):

print("Print #1:", my_list_1)

print("Print #2:", my_list_2)

del my_list_1[0] # Pay attention to this line.

print("Print #3:", my_list_1)

print("Print #4:", my_list_2)

my_list_2 = [2, 3]

my_function(my_list_2)

print("Print #5:", my_list_2)

We don’t change the value of the parameter my_list_1 (we already know it will not affect the argument), but instead modify the list identified by it.

The output may be surprising. Run the code and check:

Print #1: [2, 3] 
Print #2: [2, 3] 
Print #3: [3] 
Print #4: [3] 
Print #5: [3]

Print #1: [2, 3]

Print #2: [2, 3]

Print #3: [3]

Print #4: [3]

Print #5: [3]

Let’s explain it :

if the argument is a list, then changing the value of the corresponding parameter doesn’t affect the list (remember: variables containing lists are stored in a different way than scalars),
but if you change a list identified by the parameter (note: the list, not the parameter!), the list will reflect the change.

19. A function can call other functions or even itself. When a function calls itself, this situation is known as recursion, and the function which calls itself and contains a specified termination condition (i.e., the base case – a condition which doesn’t tell the function to make any further calls to that function) is called a recursive function.

20. You can use recursive functions in Python to write clean, elegant code, and divide it into smaller, organized chunks. On the other hand, you need to be very careful as it might be easy to make a mistake and create a function which never terminates. You also need to remember that recursive calls consume a lot of memory, and therefore may sometimes be inefficient.

When using recursion, you need to take all its advantages and disadvantages into consideration.

The factorial function is a classic example of how the concept of recursion can be put in practice:

def factorial_function(n):
    if n < 0:
        return None
    if n < 2:
        return 1
    return n * factorial_function(n - 1)

print(factorial(4)) # 4 * 3 * 2 * 1 = 2

def factorial_function(n):

if n < 0:

return None

if n < 2:

return 1

return n * factorial_function(n - 1)

print(factorial(4)) # 4 * 3 * 2 * 1 = 2

Factorial without recursion:

def factorial_function(n):
    if n < 0:
        return None
    if n < 2:
        return 1
    
    product = 1
    for i in range(2, n + 1):
        product *= i
    return product


for n in range(1, 6):  # testing
    print(n, factorial_function(n))

def factorial_function(n):

if n < 0:

return None

if n < 2:

return 1

product = 1

for i in range(2, n + 1):

product *= i

return product

for n in range(1, 6): # testing

print(n, factorial_function(n))

Exercise 1

What is the output of the following snippet?

def intro(a="James Bond", b="Bond"):
   print("My name is", b + ".", a + ".")

intro()

def intro(a="James Bond", b="Bond"):

print("My name is", b + ".", a + ".")

intro()

# My name is Bond. James Bond.

Exercise 2

What is the output of the following snippet?

def intro(a="James Bond", b="Bond"):
   print("My name is", b + ".", a + ".")

intro(b="Sean Connery")

def intro(a="James Bond", b="Bond"):

print("My name is", b + ".", a + ".")

intro(b="Sean Connery")

# My name is Sean Connery. James Bond.

Exercise 3

What is the output of the following snippet?

def intro(a, b="Bond"):
   print("My name is", b + ".", a + ".")

intro("Susan")

def intro(a, b="Bond"):

print("My name is", b + ".", a + ".")

intro("Susan")

# My name is Bond. Susan.

Exercise 4

What is the output of the following snippet?

def add_numbers(a, b=2, c):
   print(a + b + c)

add_numbers(a=1, c=3)

def add_numbers(a, b=2, c):

print(a + b + c)

add_numbers(a=1, c=3)

# SyntaxError – a non-default argument (c) follows a default argument (b=2)

A non-default arguments must be before a default arguments.

Exercise 5

What is the output of the following snippet?

def hi():
   return
   print("Hi!")

hi()

def hi():

return

print("Hi!")

hi()

# the function will return an implicit None value

Exercise 6

What is the output of the following snippet?

def is_int(data):
if type(data) == int:
   return True
elif type(data) == float:
   return False

print(is_int(5))
print(is_int(5.0))
print(is_int("5"))

def is_int(data):

if type(data) == int:

return True

elif type(data) == float:

return False

print(is_int(5))

print(is_int(5.0))

print(is_int("5"))

True

False

None

Exercise 7

What is the output of the following snippet?

def even_num_lst(ran):
   lst = []
   for num in range(ran):
      if num % 2 == 0:
         lst.append(num)
   return lst

print(even_num_lst(11))

def even_num_lst(ran):

lst = []

for num in range(ran):

if num % 2 == 0:

lst.append(num)

return lst

print(even_num_lst(11))

[0, 2, 4, 6, 8, 10]

Exercise 8

What is the output of the following snippet?

def list_updater(lst):
   upd_list = []
   for elem in lst:
      elem **= 2
      upd_list.append(elem)
   return upd_list

foo = [1, 2, 3, 4, 5]
print(list_updater(foo))

def list_updater(lst):

upd_list = []

for elem in lst:

elem **= 2

upd_list.append(elem)

return upd_list

foo = [1, 2, 3, 4, 5]

print(list_updater(foo))

[1, 4, 9, 16, 25]

Exercise 9

What is the output of the following snippet?

def hi(): 
  return print("Hi!") 

hi()

def hi():

return print("Hi!")

hi()

the function will return an implicit None value

Exercise 10

What is the output of the following snippet?

def is_int(data): 
  if type(data) == int: 
    return True 
  elif type(data) == float: 
    return False 

print(is_int(5)) 
print(is_int(5.0)) 
print(is_int("5"))<code class="codep ">

def is_int(data):

if type(data) == int:

return True

elif type(data) == float:

return False

print(is_int(5))

print(is_int(5.0))

print(is_int("5"))<code class="codep ">

True FalseNone

Exercise 11

What is the output of the following snippet?

def even_num_lst(ran): 
  lst = [] 
  for num in range(ran): 
    if num % 2 == 0: 
      lst.append(num) 
  return lst 

print(even_num_lst(11))

def even_num_lst(ran):

lst = []

for num in range(ran):

if num % 2 == 0:

lst.append(num)

return lst

print(even_num_lst(11))

[0, 2, 4, 6, 8, 10]

Exercise 12

What is the output of the following snippet?

def list_updater(lst): 
  upd_list = [] 
  for elem in lst: 
    elem **= 2 upd_list.append(elem) 
  return upd_list foo = [1, 2, 3, 4, 5] 

print(list_updater(foo))

def list_updater(lst):

upd_list = []

for elem in lst:

elem **= 2 upd_list.append(elem)

return upd_list foo = [1, 2, 3, 4, 5]

print(list_updater(foo))

[1, 4, 9, 16, 25]

Exercise 13

What will happen when you try to run the following code?

def message(): 
  alt = 1 
  print("Hello, World!") 

print(alt)

def message():

alt = 1

print("Hello, World!")

print(alt)

The NameError exception will be thrown (NameError: name 'alt' is not defined)

Exercise 14

What is the output of the following snippet?

a = 1 
def fun(): 
  a = 2 
  print(a) 

fun() 
print(a)

a = 1

def fun():

a = 2

print(a)

fun()

print(a)

Exercise 15

What is the output of the following snippet?

a = 1 
def fun(): 
  global a 
  a = 2 
  print(a) 

fun() 
a = 3 
print(a)

a = 1

def fun():

global a

a = 2

print(a)

fun()

a = 3

print(a)

Exercise 16

What is the output of the following snippet?

a = 1 
def fun(): 
  global a 
  a = 2 
  print(a) 

a = 3 
fun() 
print(a)

a = 1

def fun():

global a

a = 2

print(a)

a = 3

fun()

print(a)

Exercise 17

What will happen when you attempt to run the following snippet and why?

def factorial(n): 
  return n * factorial(n - 1) 

print(factorial(4))

def factorial(n):

return n * factorial(n - 1)

print(factorial(4))

The factorial function has no termination condition (no base case) so Python will raise an exception (RecursionError: maximum recursion depth exceeded)

Exercise 18

What is the output of the following snippet?

def fun(a): 
if a > 30: 
  return 3 
else: 
  return a + fun(a + 3) 

print(fun(25))

def fun(a):

if a > 30:

return 3

else:

return a + fun(a + 3)

print(fun(25))

56

Exercise 19

What is the output of the following snippet?

def fun(in=2, out=3):
  return in*out

print (fun(3))

def fun(in=2, out=3):

return in*out

print (fun(3))

invalid syntax

in is a keyword, you can not use in as a name of parametr

Ex. 20

What is the output of the following code snippet?

x = 10

def fun():
  global x
  if x >= 10:
    x += 100

print(x)

x = 10

def fun():

global x

if x >= 10:

x += 100

print(x)

10

The code does not call the fun() function. As a result, the program does not execute the body of the function and the content of the variable x does not change. Therefore, the print statement returns 10 on the screen.

Ex. 21

What is the output of the following code snippet?

def fun(x, y = 1):
  return x * y

print(fun('3', 2))

def fun(x, y = 1):

return x * y

print(fun('3', 2))

33

Ex. 22

What is the output of the following code snippet?

def rectangle(b, h):
  perimeter = (b + h) * 2
  area = b * h
  return b, h, area, perimeter

print(rectangle(10, 3)[2])

def rectangle(b, h):

perimeter = (b + h) * 2

area = b * h

return b, h, area, perimeter

print(rectangle(10, 3)[2])

Correct answer

30

Scenario

Your task is to write and test a function which takes one argument (a year) and returns True if the year is a leap year, or False otherwise.

To determine if a year is a leap year, we apply a simple rule: if the year is divisible by 4, it’s a leap year, except for end-of-century years, which must also be divisible by 400. For instance, the year 2000 was a leap year, while 1900 was not.

def is_year_leap(year):
    x = year % 4
    y = year % 100
    z = year % 400
    
    if (x == 0 and y != 0) or (y == 0 and z == 0):
        print (" x=",x, " y=", y, " z=", z, sep="")
        return True
    else:
        print (" x=",x, " y=", y, " z=", z, sep="")
        return False


test_data = [1900, 2000, 2016, 1987]
test_results = [False, True, True, False]
for i in range(len(test_data)):
	yr = test_data[i]
	print(yr,"->",end="")
	result = is_year_leap(yr)
	if result == test_results[i]:
		print("OK")
	else:
		print("Failed")

def is_year_leap(year):

x = year % 4

y = year % 100

z = year % 400

if (x == 0 and y != 0) or (y == 0 and z == 0):

print (" x=",x, " y=", y, " z=", z, sep="")

return True

else:

print (" x=",x, " y=", y, " z=", z, sep="")

return False

test_data = [1900, 2000, 2016, 1987]

test_results = [False, True, True, False]

for i in range(len(test_data)):

yr = test_data[i]

print(yr,"->",end="")

result = is_year_leap(yr)

if result == test_results[i]:

print("OK")

else:

print("Failed")

Scenario

Your task is to write and test a function which takes two arguments (a year and a month) and returns the number of days for the given month/year pair (while only February is sensitive to the year value, your function should be universal).

The initial part of the function is ready. Now, convince the function to return None if its arguments don’t make sense.

def is_year_leap(year):
    x = year % 4 
    y = year % 100 
    z = year % 400 
    if (x == 0 and y != 0) or (y == 0 and z == 0): 
        return True 
    else: 
        return False

def days_in_month(year, month):
    even = month % 2 == 0
    if month == 2:
        if is_year_leap(year):
            return 29
        else:
            return 28
    elif month <= 7:
        if even:
            return 30
        else:
            return 31
    elif month > 7:
        if even:
            return 31
        else:
            return 30
    
test_years = [1900, 2000, 2016, 1987]
test_months = [2, 2, 1, 11]
test_results = [28, 29, 31, 30]
for i in range(len(test_years)):
	yr = test_years[i]
	mo = test_months[i]
	print(yr, mo, "->", end="")
	result = days_in_month(yr, mo)
	if result == test_results[i]:
		print("OK")
	else:
		print("Failed")

def is_year_leap(year):

x = year % 4

y = year % 100

z = year % 400

if (x == 0 and y != 0) or (y == 0 and z == 0):

return True

else:

return False

def days_in_month(year, month):

even = month % 2 == 0

if month == 2:

if is_year_leap(year):

return 29

else:

return 28

elif month <= 7:

if even:

return 30

else:

return 31

elif month > 7:

if even:

return 31

else:

return 30

test_years = [1900, 2000, 2016, 1987]

test_months = [2, 2, 1, 11]

test_results = [28, 29, 31, 30]

for i in range(len(test_years)):

yr = test_years[i]

mo = test_months[i]

print(yr, mo, "->", end="")

result = days_in_month(yr, mo)

if result == test_results[i]:

print("OK")

else:

print("Failed")

Scenario

Your task is to write and test a function which takes three arguments (a year, a month, and a day of the month) and returns the corresponding day of the year, or returns None if any of the arguments is invalid.

def is_year_leap(year):
    x = year % 4 
    y = year % 100 
    z = year % 400 
    if (x == 0 and y != 0) or (y == 0 and z == 0): 
        return True 
    else: 
        return False

def days_in_month(year, month):
    even = month % 2 == 0
    if month == 2:
        if is_year_leap(year):
            return 29
        else:
            return 28
    elif month <= 7:
        if even:
            return 30
        else:
            return 31
    elif month > 7:
        if even:
            return 31
        else:
            return 30

def day_of_year(year, month, day):
    count=0
    for month in range (1,month):
        count+=days_in_month(year, month)
        #print(month, count)
    count+=day
    return count

print(day_of_year(2001, 12, 31))

def is_year_leap(year):

x = year % 4

y = year % 100

z = year % 400

if (x == 0 and y != 0) or (y == 0 and z == 0):

return True

else:

return False

def days_in_month(year, month):

even = month % 2 == 0

if month == 2:

if is_year_leap(year):

return 29

else:

return 28

elif month <= 7:

if even:

return 30

else:

return 31

elif month > 7:

if even:

return 31

else:

return 30

def day_of_year(year, month, day):

count=0

for month in range (1,month):

count+=days_in_month(year, month)

#print(month, count)

count+=day

return count

print(day_of_year(2001, 12, 31))

Scenario

A natural number is prime if it is greater than 1 and has no divisors other than 1 and itself.

Complicated? Not at all. For example, 8 isn’t a prime number, as you can divide it by 2 and 4 (we can’t use divisors equal to 1 and 8, as the definition prohibits this).

On the other hand, 7 is a prime number, as we can’t find any legal divisors for it.

Your task is to write a function checking whether a number is prime or not.

The function:

is called is_prime;
takes one argument (the value to check)
returns True if the argument is a prime number, and False otherwise.

Hint: try to divide the argument by all subsequent values (starting from 2) and check the remainder – if it’s zero, your number cannot be a prime; think carefully about when you should stop the process.

def is_prime(num):
    if num > 1:
        flag = 1
        for divider in range (2,10):
            if num % divider == 0 and num != divider and num>divider:
               # print(num, divider, sep=" -> ")
                flag=0
    return flag

for i in range(1, 100):
	if is_prime(i + 1):
			print(i + 1, end=" ")
print()

def is_prime(num):

if num > 1:

flag = 1

for divider in range (2,10):

if num % divider == 0 and num != divider and num>divider:

# print(num, divider, sep=" -> ")

flag=0

return flag

for i in range(1, 100):

if is_prime(i + 1):

print(i + 1, end=" ")

print()

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

Fibonacci numbers

Are you familiar with Fibonacci numbers?

They are a sequence of integer numbers built using a very simple rule:

the first element of the sequence is equal to one (Fib₁ = 1)
the second is also equal to one (Fib₂ = 1)
every subsequent number is the the_sum of the two preceding numbers:
(Fib_i = Fib_i-1 + Fib_i-2)

Here are some of the first Fibonacci numbers:

fib_1 = 1
fib_2 = 1
fib_3 = 1 + 1 = 2
fib_4 = 1 + 2 = 3
fib_5 = 2 + 3 = 5
fib_6 = 3 + 5 = 8
fib_7 = 5 + 8 = 13

What do you think about implementing this as a function?

Let’s create our fib function and test it. Here it is:

def fib(n):
    if n < 1:
        return None
    if n < 3:
        return 1

    elem_1 = elem_2 = 1
    the_sum = 0
    for i in range(3, n + 1):
        the_sum = elem_1 + elem_2
        elem_1, elem_2 = elem_2, the_sum
    return the_sum


for n in range(1, 10):  # testing
    print(n, "->", fib(n))

def fib(n):

if n < 1:

return None

if n < 3:

return 1

elem_1 = elem_2 = 1

the_sum = 0

for i in range(3, n + 1):

the_sum = elem_1 + elem_2

elem_1, elem_2 = elem_2, the_sum

return the_sum

for n in range(1, 10): # testing

print(n, "->", fib(n))

Recursion version:

def fib(n):
    if n < 1:
        return None
    if n < 3:
        return 1
    return fib(n - 1) + fib(n - 2)

def fib(n):

if n < 1:

return None

if n < 3:

return 1

return fib(n - 1) + fib(n - 2)