Introduction FTP, or File Transfer Protocol, is a standard network protocol used to transfer files from one host to another over a TCP-based network, such as the internet. In Linux, FTP is a vital tool for transferring files between servers or between a local machine and a server. It allows users to manage and organize files on their Linux system without having to be physically present at that location. Understanding the Default FTP Port in Linux FTP (File Transfer Protocol) is an essential component of any Linux server. It allows users to transfer files between the local machine and remote ... Read More
Introduction In Linux, file permissions determine who can access, modify, or execute files and directories. They play a crucial role in ensuring the security and integrity of a system. Without proper file permissions, unauthorized users can gain access to sensitive data or execute malicious code that can damage a system. To understand why file permissions matter in Linux, it's important to know that every file and directory has an owner and a group associated with it. The owner is the user who created the file or directory, while the group is a collection of users with similar permissions. By assigning ... Read More
Introduction As a system administrator managing a remote Ubuntu Server, it can be hard to focus on the console's small and default font style. Moreover, in some cases, the default font can be unreadable or unattractive. Therefore, you might need to change the console font of your server to something more pleasant and easier to read. The Benefits of Changing Console Fonts There are several reasons why changing console fonts can be necessary or beneficial. Better Readability The default Ubuntu Server console font is small and may not be easy to read especially if you are working on an old ... Read More
Permutations and Combinations refer to the arrangements of objects in mathematics. Permutation − In permutation, the order matters. Hence, the arrangement of the objects in a particular order is called a permutation. Permutations are of two types − Permutation with repetition Suppose we have to make a three-digit code. Some possible numbers are 123, 897, 557, 333, 000, and 001. So how many numbers can we make like this? Let us look at it this way− In the once place, we have ten options − 0-9 Similarly, at the tenth and the hundredth place also, we have ten options. 0-9. ... Read More
HCF or the Highest common factor of two or more numbers refers to the highest number which divides them. A rational number is the quotient p/q of two numbers such that q is not equal to 0. Problem Statement Given an array with fractional numbers, find the HCF of the numbers. Example 1 Input [{4, 5}, {10, 12}, {24, 16}, {22, 13}] Output {2, 3120} Explanation The fractional numbers given are: 4/5, 10/12, 24/16 and 22/13 2/3120 is the largest number that divides all of them. Example 2 Input [{18, 20}, {15, 12}, {27, 12}, {20, 6}] ... Read More
In mathematics, a Stella Octangula number is a figurate number based on the Stella Octangula, of the form n(2n2 − 1). Stella Octangula numbers which are perfect squares are 1 and 9653449. Problem Statement Given a number n, check whether it is the Stella Octangula number or not. The sequence of Stella Octangula numbers is 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990 Example1 Input x = 14 Output Yes Explanation $$\mathrm{For\: n = 2, expression \:n\lgroup 2n^2 – 1\rgroup is\: 14}$$ Example2 Input n = 22 Output No Explanation $$\mathrm{There \:is\: no\: ... Read More
According to Nicomachus’ Theorem, the sum of the cubes of the first n integers is equal to the square of the nth triangular number. Or, we can also say − The sum of cubes of first n natural numbers is equal to square of sum of first natural numbers. Putting it algebraically, $$\mathrm{\displaystyle\sum\limits_{i=0}^n i^3=\lgroup \frac{n^2+n}{2}\rgroup^2}$$ Theorem $$1^3 = 1$$ $$2^3 = 3 + 5$$ $$3^3 = 7 + 9 + 11$$ $$4^3 = 13 + 15 + 17 + 19\vdots$$ Generalizing $$n^3 =\lgroup n^2−n+1\rgroup+\lgroup n^2−n+3\rgroup+⋯+\lgroup n^2+n−1\rgroup$$ Proof By Induction For all n Ε Natural ... Read More
In this problem, we will learn to implement the unrolled linked list. The unrolled linked list is a specialized version of the linked list. The normal linked list contains a single element in a single node, but the unrolled linked list contains a group of elements in each node. Also, insertion, deletion, and traversal in the unrolled linked list work the same as the typical linked list. The linear search is faster in the array than in the linked list. So, we can add elements in the array and an array in each node of the linked list. Also, ... Read More
In this problem, we need to implement Vizing's Theorem. Vizing's Theorem is used with graphs. Theorem statement - For any undirected graph G, the value of the Chromatic index is equal to the d or d + 1, where d is the maximum degree of the graph. The degree for any vertex is the total number of incoming or outgoing edges. Problem statement - We have given a graph and need to implement Vizing's Theorem to find the Chromatic index of the graph. Note - The chromatic index is a positive integer, requiring a ... Read More
The Schonhage-Strassen algorithm is useful when we need to multiply large decimal numbers. As Java supports the 1018 size of integers, and if we need to multiply the digits of more than 1018, we need to use the Schonhage-Strassen algorithm, as it is one of the fastest multiplication algorithms. It uses the basic rules for the multiplication of two numbers. It first performs the linear convolution and then performs the carry to get the final result. Problem statement - We have given mul1 and mul2 large decimal numbers and need to implement the Schonhage-Strassen algorithm to multiply both ... Read More
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