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Data Structure Articles
Page 43 of 164
Centered Octahedral Number
What do you mean by a Centered octahedral number? Let’s decode. Firstly, what is an Octahedron? An octahedron is an eight−sided, equilateral triangle−shaped three−dimensional geometric shape. With 8 vertices, 12 edges, and 6 square faces, it is a polyhedron. One of the five Platonic solids, which are regular, convex polyhedra with symmetrical vertex arrangements and identical faces, is the octahedron. The octahedron has a variety of fascinating characteristics and uses, including crystallography, where it is used to describe the structure of certain crystals, and computer graphics, where it is used to model objects in three dimensions. Numerous other natural phenomena, ...
Read MoreCentered Heptagonal Number
What do you understand by the term centered hepatgonal number? Let’s decode in this article. First of all, what is a heptagonal number? A heptagonal number is a figurate number representing the number of dots that can be arranged to form a regular heptagon (a seven−sided polygon). The formula for the nth heptagonal number is: n(5n−3)/2, where n must be a positive integer. The first few heptagonal numbers, for example, are: 1 is the first heptagonal number (corresponding to a heptagon with one dot). 7 is the second heptagonal number (corresponding to a heptagon with 7 dots). 18 is ...
Read MoreCake Number
What do you understand by the term `Cake Number`? Let's decode it in this article. The term "cake number" describes a concept of discrete geometry and combinatorics−related mathematical idea. It is built on the concept of the Lazy caterer's sequence. What is the Lazy Caterer's Sequence? The maximum number of pieces a disk (cake or pizza) can be sliced into using a specific number of straight slices is known as the Lazy caterer's sequence. Although it mentions a disk, we will consider a cake in our example. One straight cut can divide a cake into two pieces, two straight cuts ...
Read MoreMinimum Number of Operations to move all Uppercase Characters before all Lower Case Characters
You are given a string 'str' that contains both uppercase and lowercase letters. Any lowercase character can be changed to an uppercase character and vice versa in a single action. The goal is to print the least possible instances of this process that are necessary to produce a string containing at least one lowercase character, followed by at least one uppercase character. Input Output Scenarios First possible solution: the first 4 characters can be converted to uppercase characters i.e. “TUTORial” with 4 operations. Input str = “tutoRial” Output 1 Second possible solution: the third character ...
Read MoreFirst Come, First Serve ñ CPU Scheduling | (Non-preemptive)
FCFS CPU Scheduling (First Come, First Serve) is a fundamental CPU scheduling mechanism that executes programs in the order they are added to the ready queue. In other words, the first process to come will be carried out first, and so on. Since it uses a non−preemptive scheduling technique, a process that has been allocated to the CPU will keep running until it is finished or enters a waiting state. Scenario 1 Let's take a look at an example to understand FCFS CPU scheduling in more detail. Suppose we have three processes with the following arrival times and burst times: ...
Read MoreFinding Optimal Page Size
Operating system has a concept known as the optimal page size that is affected by a number of variables, such as the system architecture, the amount of physical memory at hand, and the workload of the running applications. Steps/ Approach The following steps can be used to find the ideal page size: Step 1: Establish the system's design:Different CPU designs support varied page sizes. For instance, x86 CPUs typically offer 4KB page sizes, whereas ARM CPUs support 4KB, 16KB, or 64KB page sizes. Step 2: Calculate the physical memory capacity:The ideal page size depends on the physical memory capacity. Larger ...
Read MoreFind time taken to Execute the Tasks in A Based on the Order of Execution in B
The goal is to determine the minimum time required to complete the tasks in queue A based on the order of execution in queue B, given two queues A and B, each of size N, where: Pop this task and run it if the task identified at the head of queue B is also at the head of queue A. Pop the current task from queue A and push it at the end if the task discovered at the front of queue B is not also found at the front of queue A. One unit of time is ...
Read MoreFind the Time Taken Finish Processing of given Processes
Given are N processes and two N−sized arrays, arr1[] and arr2[]. A process's time in the critical section is recorded in arr1[], and it’s time to finish processing after leaving the critical part is recorded in arr2. The goal is to determine how long it will take for each process to finish processing (both inside and outside of the critical section) in any given order. Input Output Scenarios Assume we have 3 arrays as shown below Input N = 3, arr1[] = {1, 4, 3}, arr2[] = {2, 3, 1} Output 9 The first process, at ...
Read MoreAdvantages and Disadvantages of Three-tier Architecture
A 3−tier application architecture is a modular client−server architecture that consists of a presentation tier, an application tier, and a data tier. The presentation tier is a graphical user interface (GUI) that interacts with the other two tiers; the data tier stores information; the application tier manages logic. A 3−tier architecture has pros in terms of better horizontal scalability, performance, and availability. When there are three layers, each component can be produced concurrently by a separate team of programmers using a different programming language than the developers of the other levels. The 3−tier paradigm makes it simpler for an organization ...
Read MoreLargest Component Size in a Graph Formed by Connecting Non-Co-Prime Nodes
Introduction In this tutorial, we discuss the problem of finding the largest component size in a graph generated by connecting non-co-prime nodes through C++. Graphs are formed by nodes connected by edges. The components of the graph are a subset of values that form nodes. There is an array a[] which forms graph G. The components of the graph are a subset of values that form nodes. The non-coprime numbers are the numbers that have a HCF (Highest Common Factor) other than 1, that means they have some other common factors. We solve the problem statement in this tutorial using ...
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