Tag Archives for " the "

Top four real algorithms that dominate our world


If you are an algorithm beginner, then you must be wondering who we can explain them, what are they and how they impact our society? In fact, algorithms are all around us, and they make the digital world functional. It is essential to mention that algorithms aren’t only used in computing sciences but they are a mathematical entity. They were first discovered in 1600 BC, but the modern use started around 1930s. In this article, we will explain the top four algorithms that rule the world and why without them our life wouldn’t be possible.

Merge sort, quick sort, and heap sort

post6aWhat is the best algorithm to manage elements? It all depends on what you need, and that’s why we put the three more frequently used algorithms which are used to sort items. Maybe you have preferences, but three of them are equally good. The merge sort algorithm is one of the essential algorithms nowadays. It uses divide and conquers approach to solve problems. John von Neumann invented this algorithm in 1945. The quicksort has a different approach to sorting issues. It can use in-place partition algorithms, but the problem with them is that they aren’t stable sort, except for sorting RAM-based arrays. The last one is the heap sort which uses priority queue that decreases time in the data.

Fourier Transform and Fast Fourier Transform

Our entire digital world uses three simple, but very potent algorithms, which change signals form their time domain into their frequency domain and vice versa. In fact, you are seeing and reading this articles thanks to these algorithms. The internet, Wi-Fi connection, smartphones, PCs, satellites and other devices have a computer inside and use these algorithms to function, and you can’t get a degree in science without studying this type of algorithms.

post6bDijkstra’s algorithm

It is safe to say that internet wouldn’t be functional without this algorithm. This graph search algorithm is used in various applications and, in this case, the problem can be modeled and presented as a graph, and you have to find the shortest path between two nodes. Considering that science has advanced, and today we can use better solutions of finding the shortest route, but Dijkstra’s algorithm is still used because of its stability in systems which require it.

RSA algorithm

If there weren’t cryptography and cybersecurity, then the internet wouldn’t be as important as it is today. The security can be observed from different perspectives, you may think security in the era of NSA and other intelligence agencies or are you really that naïve to believe that you are safe on the Internet. People need to be safe to spend their money. After all, you wouldn’t fill out your credit card number on the web, if you know it’s not secure. In this case, RSA algorithm remains as the most important in the field of cryptography. It shapes who cryptography works, and it’s a solution to a simple, but also challenging problems.

The freeze app – What is this app and does it exist

Nowadays, you can find apps for almost anything, and some of them will freeze your phone, maybe they are infected, or it’s just the negligence of the developer. For instance, the app might try to perform some math operation, such as dividing five by 0. On the other hand, your math teacher will tell you that 5/0 does not make sense, but when a modern computer meets this expression it will freeze and in the worst-case scenario, crashing your operating system with it. Once your phone freezes, there is not much you can do, but to restart the device and after that remove the app from your smartphone.

But, then the main questing is, why such bad apps exit in the first place and can you test them for such behavior before the use.

The Freeze App

post4aLet’s imagine that some software company managed to solve this issue, where there is a Freeze app who will test all other apps and determine whether they will freeze your phone. This type of app might work by performing experiments for the suspicious apps in a simulated environment, without stopping your phone. Or, it will just deduce the input app’s behavior from inspecting its source code. For average users, it’s not relevant how Freeze app manages what it promises. Its use would be straightforward to use. First, you will have to select the suspicious app you want to test, and it has to be installed on your smartphone. Then Freeze app will do its analytics, which might take a couple of minutes and present you the final result.

The paradox app

As soon as Freeze app gets to store, developers will try to build a Paradox app, and its primary purpose will be to rectify mistakes the Freeze app makes. So, here is how it should look like: you run the Freeze app to in inspect the Paradox, if it turns out OK, then freeze your phone, for instance by computing five by 0. On the other hand, if the Freeze shows not OK, then declare Freeze detected that Paradox freezes and terminate the process.post4b

Why doesn’t Freeze app exist?

There are a couple of reason why this type of app doesn’t exist. Either the Paradox app is malicious and freezes your phone, or it’s not. But, we will show you both cases. For example, let’s assume that Paradox is corrupted and freezes your phone. In this case, the Freeze app will detect this condition, and in Paradox’s code, computation proceeds from line one to three and Paradox will show the information “Freeze detected that Paradox freezes” and it will end this process. According to our assumptions, the phone did not freeze, and we can reject this proposition.

In the second example, the Paradox doesn’t freeze our phone. The Freeze app will determine this and Paradox’s computation will continue with line two and freeze the phone, which again contradicts our assumptions. Based on this, we can end our discussion stating that Freeze app doesn’t exist.


Shouryya Ray and the press

A German 16-year old has become a worldwide phenomenon and the first person who managed to solve a mathematical problem that Sir Isaac Newton posed more than 300 years ago. Shouryya Ray worked on how to calculate the precise path of a projectile under gravity and subject to air resistance. The Indian-borne teen reposted to have solved the problem while working on a school project. German society awarded the young man by giving him a prize for contribution to the science and labeled him as a genius. Considering he solved the math problem while doing a school project his research is put down to curiosity and student’s naivety.

His family moved to Germany when he was 12 years old. The boy’s father got a job as an engineer at a technical college and he that his father had a significant influence on his, showing him love towards math and taught this calculus when he was six years old. Even Mr. Ray’s father told the media that his son’s mathematical powers quickly surpassed his own, showing considerable knowledge and progress, which is rare for such a young boy. The father said that Ray never discussed the project with him and that he used math equations that are even beyond his reach.

post2bNewton posed this problem 300 years ago, which relates to movement of projectiles through the air. Before Mr. Ray’s solution, mathematicians and scientist were able to offer an only partial answer, but no one managed to solve the problem in full. That’s why the public became shocked when a young man offered a solution. If that wasn’t enough, Mr. Ray also managed to solve an additional problem which involves the collision of a body with a wall, that was posed in the 19th century. Experts and scientists say that these solutions will contribute to better precision in areas as ballistics.

On the other hand, a university professor Jürgen Voigt states that Newton never posed a problem. He said that the movement of the body or object under the influence of gravity and friction in the air is managed by a specific differential equation. Moreover, the theory of average differential equations yields that equation can be solved and that solution is presented in particular form. When he says average equation, he thinks that textbooks contain this approach and it is taught in third-year courses at the university. He and his coworkers published a four-page report where they tried to contextualize Ray’s work. Voigt emphasized that Ray deserved a prize for his work and that his solution should be appreciated, considering it’s coming from a 16-year old boy. We are left to see, what kind of discoveries will Ray make in the future.