In this lesson we will analyze some algorithmsin Python to check if a number belongs to the Fibonacci sequence.
In the previous lesson we studied how to print a Fibonacci sequence of variable length, each time decided by the user.
We have both an iterative and a recursive solution, using functions as well.
In this lesson instead ask the user to enter an integer and the program in Python will be able to tell if it is a Fibonacci number or not.
We will develop different solutions and analyze them.
Python Fibonacci – check if a number is Fibonacci
We study a first approach to a possible solution to the proposed problem.
The first thing that comes to mind, without knowing any rules, is to generate the Fibonacci numbers up to the input entered by the user and check if this number is contained in it.
We develop the solution using an iterative solution that will stop when the condition is satisfied, in our case when the entered number is found or numbers not greater than it are generated.
We create a sentinel variable, which we will call found for example, and set it to False. After that, this variable will change its value, becoming True only if the value is included in the sequence.
Here is a possible solution:
def check_fib(num):
found = False
a = 1
b = 1
c = a + b
print(a, end=' ')
print(b, end=' ')
while(c <= num):
print(c, end=' ')
a = b
b = c
c = a + b
if(c == num):
found = True
if(found):
print('Found')
else:
print('Not Found')
n = int(input('Insert a number: ' ))
check_fib(n)
Python Fibonacci - check if a number is Fibonacci - second solution
In this second solution we apply the well-known mathematical rules instead.
In particular, it is said that N is a Fibonacci number if and only if 5 N ^ 2 + 4 or 5 N ^ 2 - 4 is a square number.
We therefore develop an algorithm that satisfies these conditions by importing the math module in order to be able to use the square root (sqrt) function. If the square root is an integer then it means that it is a square number and therefore belongs to the sequence, otherwise it does not belong to it.
def check_fib(n):
import math
a = (5 * (n**2)) + 4
b = (5 * (n**2)) - 4
return (math.sqrt(a)).is_integer() or (math.sqrt(b)).is_integer()
n = int(input('Insert a number: ' ))
result = check_fib(n)
if (result):
print('The number is Fibonacci')
else:
print('The number is not Fibonacci')
Conclusion
In this lesson we learned how to check, in Python, if a number belongs to the Fibonacci sequence or not. In the next few lessons we will talk about lists in Python.
Fibonacci sequence in Python can have different implementation algorithms.
Recall that the Fibonacci sequence is a sequence of positive integers in which each number starting from the third is the sum of the previous two except the first two which are 1, 1.
For example, if N = 9, the terms of the sequence are: 1, 1, 2, 3, 5, 8, 13, 21, 34.
Fibonacci sequence in Python algorithm
So let’s create an algorithm that represents the Fibonacci sequence.
Take a number N as input and display the N terms of the Fibonacci sequence.
To implement this algorithm, first of all we take two variables a and b and assign the value 1 to both. We thus create the first two terms of the Fibonacci sequence that we will immediately print.
Then, we make a for loop to display the N terms with an index i ranging from 0 to N-1. After, within the cycle we calculate the third term c and then exchange a with b and b with c. Finally we print c.
Here is a possible solution:
n = int(input('How many numbers?: ' ))
a,b = 1,1
print(a)
print(b)
for i in range(n):
c = a+b
a = b
b = c
print(c, end=' ')
Once we understand the procedure, we rewrite the algorithm in a more elegant way, avoiding some instructions, such as the initial prints, and we carry out the exchange in a single line.
Here is the solution:
n = int(input('How many numbers?: ' ))
a,b = 1,1
for i in range(n):
print(a, end=' ')
a,b = b,a+b
print()
Fibonacci sequence in Python algorithm – with a function
We can also use a function to solve the algorithm.
def print_fibonacci(length):
a = 1
b = 1
for i in range (length):
print(a, end=" ")
a,b=b,a+b
n = int(input('How many numbers?: ' ))
print_fibonacci(n)
We can also add a control input. If a user insert a negative number the program can be request a new number.
def print_fibonacci(length):
a = 1
b = 1
for i in range (length):
print(a, end=" ")
a,b=b,a+b
n = int(input('How many numbers?: ' ))
while(n < 0):
n = int(input('How many numbers? Insert a positive number: ' ))
print_fibonacci(n)
Fibonacci sequence in Python algorithm – recursive solution
Here is the recursive solution to the algorithm. Remember that recursion is when you have a call directly to the function itself. In our case, in fact, we call the function rec_fib within the same function rec_fib.
def rec_fib(n):
if n > 1:
return rec_fib(n-1) + rec_fib(n-2)
return n
n = int(input('How many numbers?: ' ))
for i in range(1,n+1):
print(rec_fib(i))
Conclusion
In this lesson we studied how to develop a Fibonacci sequence algorithm in Python, in the next lesson we will see how to understand if a number is part of the sequence.
Random numbers are used for many purposes, let’s take some examples to better understand how are work.
First example about how to generate random numbers in Python
Write a program that generates n random numbers in an interval set by the user and displays them in output.
So, first of all, let’s import the random module.
Then we ask you to enter the interval values that we store in two variables, for example named x and y.
We also ask you to enter the amount of random numbers to be generated.
import random
x = int(input('Insert the first number : '))
y = int(input('Insert the first number : '))
n = int(input('How many numbers? : '))
Now we can generate the random numbers with the for loop, using randint in the interval (x, y).
import random
x = int(input('Insert the first number : '))
y = int(input('Insert the first number : '))
n = int(input('How many numbers? : '))
for i in range(n):
random_number = random.randint(x,y)
print(random_number,end=' ')
But be careful if the user enters the value of y smaller than x?
The program returns an error at the randint point (x, y) because the value of x must be less than the value of y.
Therefore, we can check the data entered by requesting the user to re-enter the data. Or you can also swap the two variables.
By exchanging the variables we therefore have:
import random
x = int(input('Insert the first number : '))
y = int(input('Insert the first number : '))
if x > y:
x,y = y,x
n = int(input('How many numbers? : '))
for i in range(n):
random_number = random.randint(x,y)
print(random_number,end=' ')
With an input check we could instead write like this:
import random
x = int(input('Insert the first number : '))
y = int(input('Insert the second number : '))
while x > y:
print('The first number must be smaller than second!')
x = int(input('Insert the first number : '))
y = int(input('Insert the second number : '))
n = int(input('How many numbers? : '))
for i in range(n):
random_number = random.randint(x,y)
print(random_number,end=' ')
Second example about how to generate random numbers in Python
Generate 100 random numbers from 1 to 200 in steps of 2, sum them and make the average.
In steps of 2 from 1 to 200-1, it means that only odd numbers from 1 to 199 are generated.
So let’s use the randrange function for this purpose which, unlike randint, also allows us to indicate the step.
Here, then, is the complete code of the algorithm on random numbers in Python:
import random
n = 100
sum = 0
for i in range(n):
random_number = random.randrange(1,200,2)
print(random_number,end=' ')
sum += random_number
average= sum / n
print('Average: ', average)
Clearly the calculation of the average is carried out as we have done many times with non-random numbers.
Conclusion
In this lesson we have developed some simple exercises on how to generate random numbers in Python, in the next lessons we will continue to practice again.
In this lesson we study ho to generate a Python random number.
Random numbers in Python, i.e. pseudorandom numbers, are used by first importing the random module. Then we just put in the script: import random.
If you also try to type help (‘random’) in interactive mode, you will see the specifications of this module, with the functions you can use in your scripts.
After importing the module then we can use all methods to generate the random numbers.
Python random number – random()
The random method generates a random decimal number between 0 and 1.
random.random()
Consequently, numbers with a comma between 0 and 1 are generated.
Python random number – Importing module
In Python it is possible to call only some elements of a module, thus avoiding to call an entire module.
For example, we can import only the functions we need using the keyword from followed by the name of the module, the import and the name of the method you want to import.
Here is a possible example:
from random import random
print(random())
As you can see, in this way it is no longer necessary to indicate random.random(), as in the previous example, but just random() is enough.
It is also possible to import all methods in this way as well:
from random import *
print(random())
print(randint(1,10))
Thus it is possible to use all methods without repeating random every time, but using only the name.
Python random number – randint()
The randint() method generates a random integer in a range specified in parentheses.
random.randint(1, 10)
In this example, random numbers between 1 and 10 are generated.
Python random number – randrange()
The randrange() method generates a random integer, in a range of values such as randint, but the step can be specified.
For example:
random.randrange(1, 10, 2)
In this case, only the odd numbers from 1 to 10 can be generated, therefore: 1, 3, 5, 7, 9.
The step is however optional, in the sense that it can also be indicated only:
random.randrange(1, 10)
And in this case the integers from 1 to 10 can be generated.
So, to generate a Python random number we can use also randrange().
seed()
With this method you can initialize the random number generator.
So let’s take an example:
random.randint(1, 100)
If we run this script we will get a different random number each time.
If instead we first set the seed:
random.seed(10)
random.randint(1, 100)
You will always get the same random number, in this case 74. Now try to change the value of the seed.
Conclusion
These are just some of the random number methods in Python, in the next lesson I will introduce some other methods.
How implement Machine Learning algorithms with Python?
Python is also one of the most used programming languages in the world.
In fact, this language offers essential libraries for making statistics, for processing images or even for data analysis.
Furthermore, Python is characterized by having a simple but feature-rich syntax. Certainly being an interpreted language it has a lower execution speed but many of its modules have been developed in C language.
Recall that Machine Learning is a branch of Artificial Intelligence and studies algorithms that are able to process the input data and then be able to make predictions. Today, these algorithms are very useful if you think about the large amount of data that exists on the web and offer an alternative to traditional algorithms.
The development community around Machine Learning in Python is increasingly large and therefore it is easy to find information or tutorials to get explanations. The modules and libraries are in large quantities and we will see them in detail in the next paragraph.
So we just have to start studying and have fun putting into practice what we have learned!
Machine Learning with Python – What Tools Do You Need?
So what are the tools we need in Pytnon?
Jupiter Notebook
First of all, a development environment like Jupyter Notebook, very easy to download and install.
In fact, on the installation page you will find the instructions:
pip install notebook
To execute it, just type:
jupyter notebook
Numpy
A module that allows you to do Machine Learning with Python is Numpy.
In fact, thanks to the many properties and methods for scientific calculation, it allows you to easily work with arrays and matrices.
It simply installs like this:
pip install numpy
In Linux systems it is necessary to write:
sudo apt-get install python3-numpy
The installation will not last long.
It is then used in Python scripts simply by writing:
import numpy
Pandas
One tool that allows you to easily manage DataFrame and Series is the Pandas library.
To install it simply write:
pip install pandas
It is then called in Python scripts like this:
import pandas
Matplotlib e Seaborn
As a tool for machine learning in Python, the Matplotlib and Seaborn libraries cannot be missing, which allow you to graphically view the processed data.
Installation takes place by writing on the command line:
pip install matplotlib
and we import it as before using import:
pip install seaborn
To be able to use them then I write:
import matplotlib
We then use import as usual:
import seaborn
Scikit-learn
The scikit-learn library implements Machine in Learning algorithms with Python.
Intuitively, the installation takes place as follows:
pip install scikit-learn
To use it, therefore, we import it:
import scikit-learn
Tensorflow
The tensorflow library implements Machine in Learning and Deep Learning algorithms in Python.
pip install tensorflow
We then import the library to be able to use it for our Python scripts:
import tensorflow
Conclusion
We have listed only some of the modules to do Machine Learning in Python, there are others that we will talk about later in the guide.
If you already have some basic Python I suggest you choose the module you don’t know, otherwise start with the basics. Here, then, is the link to the complete tutorial: Python language tutorial index.
Today we often hear about Machine Learning and Artificial Intelligence. Machine Learning algorithms are currently used in various fields. For example, we find applications in online shopping, in interactions with social media, in financial services, in health care, in the marketing sector to manage targeted advertising, etc.
Therefore it is essential to know the term of Machine Learning and understand where it is applied.
Machine Learning definition
Machine Learning, abbreviated ML, is a branch of Artificial Intelligence. The basic idea is that robots (or more generally systems) can perform actions as if they were humans or animals.
Knowledge is acquired through machine learning programs, as with humans who acquire knowledge based on experience.
Machine Learning algorithms use mathematical-computational methods that analyze data thanks to which the construction of analytical models is automated.
Machine Learning example
After giving the definition of Machine Learning, let’s analyze some examples.
After logging in at the time of the code, start the game which is based on the identification of waste by an Artificial Intelligence.
You will therefore be presented with an AI that must be trained. In fact, the Artificial Intelligence does not know if an object is a fish or a waste but we can give it instructions, labeling images or diagrams.
Each image can be labeled as fish or as waste. This acts as training and will then allow the Artificial Intelligence to recognize a refusal from a fish when new images are presented to it.
Machine Learning algorithms
We continue, in the context of Machine Learning, to give some other definitions by presenting the algorithms that determine the approach to a given problem.
The main types of algorithms are:
Supervised
Unsupervised
Semi supervised
For reinforcement
What is the difference? Simply in the way they acquire data to make predictions.
Supervised learning
In this type of algorithm, which is the most used one of Machine Learning algorithms, learning is managed just like a child memorizes animals by looking at some example images. As in the example seen on Program the future, where Artificial Intelligence is educated with images.
The algortimo therefore learns from a labeled data set. For example, this can be used in marketing, identifying products that the user may like based on the images he or she has chosen in the past. It is therefore based on experience.
Among these algorithms we will study, later in the guide, the linear and logistic regression algorithms.
Unsupervised learning
Unsupervised learning, on the other hand, is a Machine Learning alghoritm used on data that does not have a classification, that is, on non-labeled data.
Therefore, the right answer is not provided but the goal is to leave the algorithm to search for hidden characteristics or data.
The use of this algorithm occurs above all with transactional data. So, for example, the algorithm can identify users who have similar needs to address ad hoc marketing campaigns. In fact, by analyzing this data, for us human beings there may not be a sense that the algorithm is able to give.
Let’s take a purely explanatory example: the algorithm could identify that the population that buys more organic food needs less medical care (because for example they never buy drugs), therefore the algorithm could recommend a greater purchase of organic food, to safeguard health, to the people who need it most.
Semi Supervised Machine Learning
As we can easily guess, it is a ‘hybrid’ model that has the same applications as the supervised model, that is, a set of data is provided where certain inputs correspond to outputs, but also data with no output as in the unsupervised one.
An example of application is found for example in cameras that are able to identify a human face.
Machine Learning for Reinforcement
In this case we move on to a reinforcement learning according to which we learn from experiments and errors to reach a goal. The idea is to improve the functionality of the system by reinforcement, that is, the reward. Kind of like when you promise children candy if they reach a goal.
So when you reach the goal you have a reward, while if you don’t reach it, you don’t give anything or give you a punishment. The aim is to maximize the rewards by choosing the correct actions.
This type of approach is used in robotics and video games for example where a computer learns to beat an opponent based on the moves that have given him the most benefits previously.
Deep Learning algorithms are part of it.
Conclusion
In this lesson we talked about Machine Learning and we gave its definition by also talking about the different algorithms used in this sector. In future lessons I will continue to talk about this topic again.
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