Essentially algorithm definition: algorithms are finite sets of steps that can solve specific problems, and Turing machines are a specific depiction of what those steps entail. However, for more precise analysis of algorithm efficiency, Turing machines are not typically the best option.
As a random-access machine is a data processing device that can only access a finite number of items at a time, with the time it takes to do any particular operation being fixed. The order in which the items are processed is irrelevant. This means that some problems that are easy to solve on a standard computer are hard or impossible to solve on a random-access machine.
Essentials about computers
- Essentially, the one should have an understanding, how a computer executes programs and how this process can be improved through the use of parallelism.
- As computers can run multiple programs at once, which would result in faster execution times. This is due to the fact that basic operations, like arithmetic and comparisons, take a fixed amount of time to execute.
- Additionally, the amount of computer memory available is not unlimited, but is large enough to store all the data needed to solve a problem.
- Now that we have a basic understanding of algorithms and computer hardware, we can define a problem. A problem is a relation between input and output. The input is a set of data, and the output is a set of data that is a result of applying an algorithm to the input.
- Specifying a relation between inputs and outputs is more precise than it might sound. In a mathematical sense, a relation is a set of pairs. In our case, we’re specifying which outputs are acceptable for which inputs. This nails down our problem.
Elaborating with an example of sorting
The sorting problem is a way of organizing information by arranging it into sequences.
There are two sets of sequences in question: the input sequence and the output sequences. The input sequence is the information we are trying to organize, while the output sequences are the possible ways we could organize the information. The sorting problem requires that the elements of the result sequence be in increasing order, and that the resultant sequence consist of the same elements as the input sequence.
Problem solving is all about encoding inputs and running algorithms on those inputs. In order to encode an input, we need to know how much memory the input will take up. This is important because the time it takes to solve a problem increases exponentially with the size of the input. We can measure the size of a problem in terms of the amount of memory needed to encode it.
Why should You learn Python for Algorithms in coding?
No matter the language, if your program doesn’t scale well, it will be slow. This means that if one program takes twice as long as another to finish, it may not be a very good choice. Tweaking and optimizing can be costly in many ways and is not a task to be taken on lightly. What does matter, though, is how your program scales.
Doubling the size of the input will cause the running time to quadruple. If you add just one bit to the input, the running time may only increase by a small amount.
Python is an interpreted language, which makes it inherently slower than compiled languages like Java and C. However, there are ways to optimize Python code so that it runs more quickly. By taking advantage of the language’s features and by using the right data structures and algorithms, you can write code that is both efficient and fast.
Python is a great language for many purposes, but you may want to consider another language if you need to optimize your code for performance. Algorists don’t focus primarily on speed, so another language may work better for you if speed is your top priority.
Let’s understand algorithm examples:
Let’s do an experiment. Start an interactive Python interpreter, and enter the following:
count = 10**4
numbers = []
for i in range(count):
numbers.append(i)
numbers.reverse()This is more useful code. It starts by initializing a list with a few numbers. It then adds more numbers to the list as they come in, inserting them at the beginning so that the most recent ones are at the front. At the end, it prints out the list in reverse order.
Let’s do it in another way:
count = 10**4
numbers = []
for i in range(count):
numbers.insert(0, i)The above two codes analyzed in the way to calculate the sum of a list of numbers. The first code is faster, but the second code scales worse with the problem size. This means that as the list of numbers gets bigger. The first code finishes the calculation faster than the second code.
The differences in running time between two different code versions, are as; One that uses a loop to increase the count from 10**4 to 10**5, and one that uses an iterator. The loop is faster by a factor of about ten. But the iterator is slower by a factor of about two orders of magnitude.
Until now you could be able to get an idea regarding algorithm flowchart as well algorithm design. Algorithm meaning and data structures are so meaningful to a coder. However, We would provide our readers regarding full depth analysis of a few famous algorithms.
For example dijkstra, sorting algorithms, k means clustering, search algorithm in ai, binary search, binary search tree, random forest, xgboost, decision tree, svm, knn algorithm, dynamic programming, quick sort, bubble sort, insertion sort, selection sort, merge sort, algorithmic trading etc and especially Python Algorithms for machine learning in our algorithm series.
How to get Python on your system
Python is a programming language that you can use to do various things on a computer. It is already installed on some operating systems, like Mac OS X and Linux. And if it is not, you can install it using a package manager or from the Python web site.
Conclusion
This article talks about how important algorithms are in programming. And how some problems are harder(algorithm complexity is more) than others. It also provides some tips on how to approach harder algorithmic problems. We would love to share well-known algorithms and general principles that will help the reader create their own algorithms. We would suggest you to stick with category “Algorithms”. So that will help you to solve challenging problems and create programs that scale well.