Functions¶

If a task has to be performed in a program many times, it is better to code that task as a function. Function is a piece of reusable code that can be invoked(called) from anywhere. They perform the intended task with supplied parameters and return the result if needed.

Python function has several advanatages over C functions and Java methods: - Functions can take variable number of arguments. This is supported natively - Functions can have named arguments (you had seen it in print()) - Functions can return multiple values - If you need a helper function for a function, you can define it inside the function

Defining a function¶

The syntax for defining a function is as follows

def function_name(argument_list):
    statement_1
    statement_2
    ...
    statement_n
    return values

Let’s write a function for calculating $Fib(n)$ , $n$ ‘th Fibonacci Number, defined by

$Fib(n) = Fib(n-1) + Fib(n-2)$ , where $Fib(0) = a$ and $Fib(1) = b$

First implementation uses $a = 0,b = 1$ . Further implementations include options for modifying $a$ and $b$

In [2]:

def fibonacci_first(n):
    first,second = 0,1
    while n != 0:
        n, first, second = n - 1, second, first + second
    return first

In [3]:

fibonacci_first(10)       # Function call

Out[3]:

Let’s have an option to choose $a$ and $b$

In [4]:

def fibonacci_second(n,a,b):
    first,second = a,b
    while n != 0:
        n, first, second = n - 1, second, first + second
    return first

In [5]:

fibonacci_second(9,1,1)

Out[5]:

Let $a$ and $b$ have the default values $0$ and $1$ respectively

In [6]:

def fibonacci_third(n,a=0,b=1):
    first,second = a,b
    while n != 0:
        n, first, second = n - 1, second, first + second
    return first

In [7]:

fibonacci_third(10)  # behaves like fibonacci_first()

Out[7]:

In [8]:

fibonacci_third(9,1) # behaves like fibonacci_second(9,1,1)

Out[8]:

In [9]:

fibonacci_third(9,1,2) # Run with fully different parameters

Out[9]:

You can also change one default value. You can do this by passing named argument to function

In [10]:

fibonacci_third(9,b=3)

Out[10]:

What we have to do if we want $n$ Fibonacci Numbers instead of $n$ th Fibonacci Number?¶

One soulution is to return a list of $n$ numbers. We will see that once we learn about Lists in next chapter
What we can do now is return an iterable object, that iterates through $n$ Fibonacci nuumbers. Instead of returning a number, we can simply yield it to construct a genertor. The resulting Generator object can be used with for loop. (remember range object)

In [11]:

def fibonacci_generator(n,a=0,b=1):
    first,second = a,b
    while n != 0:
        yield first
        n, first, second = n - 1, second, first + second

In [12]:

for num in fibonacci_generator(10):
    print(num,end=',')

0,1,1,2,3,5,8,13,21,34,

You can now also use in operator to check the membership of an element in the Generator Object

In [13]:

8 in fibonacci_generator(10)

Out[13]:

True

In [14]:

10 in fibonacci_generator(10)

Out[14]:

False

Let’s modify above loop in order to print Fibonacci Numbers with numbering

In [16]:

for i,num in enumerate(fibonacci_generator(10,a = 2, b = 3)):
    print('Fib({})={}'.format(i,num))

Fib(0)=2
Fib(1)=3
Fib(2)=5
Fib(3)=8
Fib(4)=13
Fib(5)=21
Fib(6)=34
Fib(7)=55
Fib(8)=89
Fib(9)=144

enumerate() function takes an iterable object as an argument and returns an iterator which is the original iterator enumerated.

Functions¶

Defining a function¶

What we have to do if we want Fibonacci Numbers instead of th Fibonacci Number?¶

What we have to do if we want $n$ Fibonacci Numbers instead of $n$ th Fibonacci Number?¶