We have been working on some structures on python such as, variables (int, float, str, list), operators (Arithmetic: +, -, *, /, **, //; Logical: !, and, or; Comparison: >, <, ==,!=), control structures (if, for), so we are ready to learn one of the most useful therefore important structures, the functions.
A function is a segment of code that usually is going to be used several times during the program, or you want to leave appart so that your code doesn't look messy.
As you have noticed so far, sometimes read code gets very complicated and it is very ofter to have specific sections of the code that gets repeated, here is where functions take place.
def function(a,b):
c=a*b
return c
Here we can see the basic structure, it MUST initiate with def, after the name of the function, then in parenthesis the parameters that it function recive and then the : and the indentation in the same way we do with if or for, and at the end we have a return.
Parameters and return are optional.
To use a function, we write the name and give the parameters,
a1=2
b1=3
print(function(a1,b1))
6
Look that the names of the variables are not the same we used when defining the function. They do not have to coincide, in fact it is better if they dont.
One of the advantages of python when compared with different programming languages, is that it is possible to use the same function with different data types,
a2=2
b2=[1,2,3,4]
print(function(a2,b2))
[1, 2, 3, 4, 1, 2, 3, 4]
A function can have two different behaviours in terms of the parameters,
There are two different ways to give the parameters to functions, and
pythondoes this automatically depending on the data type
- By value
- By reference
Let us explore the difference.
Here, we define a function that recieve a value a, create a variable and save there a+1, then return the value of that varialbe
def function2(a):
temporal=a+1
return temporal
print(a1,function2(a1))
2 3
The variable temporal is created locally inside de function, so that outside it doesn't exist
print(temporal)
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-6-154d002d4153> in <module> ----> 1 print(temporal) NameError: name 'temporal' is not defined
We can save the result of a function on a variable, for example,
b=function2(a1)
print(b)
3
But, what if we do not use an auxiliar variable?
def function3(a):
a=a+1
return a
a=2
print(a,function3(a))
2 3
print(a)
2
It didn't change!
And if we do not use the return?
def function4(a):
a=a+1
print(a)
2
function4(a)
print(a,function4(a))
2 None
It does the calculation, but when the function is finished the result is not used.
On the prevous examples, python created a copy of the variable and work with the copy without changing the parameter, this is called Parameter passed by value.
On the other hand, we have a different behaviour when working with lists
def function5(list1):
list1.append(2)
lista=[1]
function5(lista)
print(lista)
[1, 2]
The main difference here is that lists are passed by value or reference.
a=[1,2]
b=a
print(b)
[1, 2]
b.append(3)
print(a)
[1, 2, 3]
c=a.copy()
print(c)
[1, 2, 3]
c.append(4)
print(a)
[1, 2, 3]
print(c)
[1, 2, 3, 4]
Recursivity solves the queston:
How can we use a function inside itself?
It is not always possible, and it has a particular structure.
For example they can be used to compute,
- Sum of the smaller integers
- Factorial
- Fibonacci numbers
- Pascal Triangle
On class we discussed the calculation of the sum of the smaller numbers (int), for example for 10
if we think this operation as sum(n), we can see this as n+sum(n-1) or n+(n-1)+sum(n-2) until n+(n-1)+...+0, lets program this.
We need to separate two cases, the first one, indicates that the recursion is finished!, and the second implements the recursion
def sum_n(n):
if n == 0:
return 0
else:
return n + sum_n(n-1)
print(sum_n(10))
55
Let see a more complex problem,
We are going to program the Sieve of Eratosthenes.
This is an algorithm for finding prime numbers in a given interval.
The method work as follows,
import math as m
def sieve(n):
primes = list(range(2,n+1))
maxi = m.sqrt(n)
num = 2
while num < maxi:
i = num
while i <= n:
i += num
if i in primes:
primes.remove(i)
for j in primes:
if j > num:
num = j
break
return primes
data=sieve(100)
print(data)
[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]