What is W3Schools? W3Schools is a website where you can find different types of courses to make your career. You can learn the ways of writing codes to develop online applications and web pages with the help of programming languages used for developing such applications. The platform also consists of a lot of tutorials which include of code examples. These examples can be modified for further learning and experiment. Price Plans of W3Schools W3Schools has four price plans whose details are given in the table below − Plan Cost Free $0 per month Basic ... Read More

In this tutorial, we will see how to model 2D heat conduction equation using Python. A 2D, steady, heat conduction equation with heat generation can be written in Cartesian coordinates as follows − $$\mathrm{\triangledown^{2} T \: + \: \frac{q_{g}}{k} \: = \: \frac{\partial^{2}T}{\partial x^{2}} \: + \: \frac{\partial^{2}T}{\partial y^{2}} \: + \: \frac{q_{g}}{k} \: = \: 0 \:\:\dotso\dotso (1)}$$ This has to be discretized to obtain a finite difference equation. Let us consider a rectangular grid as shown below. The index 𝑖 runs vertically i.e. row wise whereas the index 𝑗 runs horizontally i.e. column wise. Any inside node ... Read More

The Taylor Table method is a very efficient and elegant method of obtaining a finite difference scheme for a particular derivative considering a specific stencil size. To understand it one should be very much clear about what is a stencil. Suppose one wants to evaluate $\mathrm{\frac{d^{2}f}{dx^{2}}}$ then in finite difference method the starting point is the Taylor series. Consider the figure shown below for a better understanding of the method. The Taylor series expansion at the point $\mathrm{x_{i} \: + \: h}$ will be: $$\mathrm{f(x_{i} \: + \: h) \: = \: f(x_{i}) \: + \: hf'(x_{i}) \: + ... Read More

Introduction In this tutorial, we will understand different types of tries and their uses. Tries are tree-like data structures that are mostly used for operations like string searching. There are various types of trie and they are used as per the task requirement. Generally, trie tries are of three types: Standard trie, compressed trie, and suffix trie. We elaborate on the meaning of each type of trie. What is Trie A trie is a sorted binary tree also called a digital tree or a prefix tree. It has nodes that are used to store data or alphabets. Each node can ... Read More

Introduction In this tutorial, we implement an approach to sort a string on the basis of the number of matchsticks required for its representation. In this approach, we use N numbers of matchsticks and sort an array. The array can contain numbers, words, or both. Matchsticks are used to arrange them in the shape of a particular number or character. Demonstration 1 Input = Arr = ["1", "3", "4"] Output = The sorted array is 1 4 3 Explanation In the above input array, the array elements are 1, 3, and 4 Number of matchsticks required for ... Read More

Introduction This tutorial deals with the problem of sorting an array alphabetically while each number is converted into words. To translate numbers into words means changing numbers to their number names. Like, 65 is sixty-five. Here, we consider a numerical array, convert all array elements to words and arrange them alphabetically. Print the sorted array elements after converting words to their respective numbers. Demonstration 1 Input = Arr = {13, 1, 6, 7} Output = 1 7 6 13 Explanation The input array elements are 13, 1, 6, 7 The output with alphabetically sorted elements is 1 7 ... Read More

Introduction In this tutorial, we find an approach to find the range update Queries to XOR with 1 in a binary array. To implement the approach we use a binary array which is an array consisting of 0 and 1. The range update queries are the queries which are used to modify the binary array within the given upper and lower limit of a range. The upper and lower limits are the index of binary array elements. The elements lying in that range are updated with defined operations. XOR is one of the bitwise operations standing for exclusive OR. Its ... Read More

Introduction In this tutorial, the task is to use queries to search for an element in an array. It is to push to the front after every query in C++. To implement this task, it takes an array A with elements from 1 to 5 and a query array Q for finding the element in A and moving it to the front of the array. The output is the index number of the searched elements. We use two methods for moving array elements to the front as per the query array. Naive Approach − Iterate through the array of ... Read More

Introduction In this tutorial, we will learn about the istringstream and how to use it for processing strings. istringstream is an object of string class defined in the header file. It is used for reading from the stream strings. A stream is a flow of data (collection of characters) between input-output devices and programs. The header file defines 3 string class objects, which are as follows − istringstream ostringstream Stringstream All are used for separate operations, like istringstream is responsible for stream input, ostringstream is for stream output, and stringstream handles both input and output of ... Read More

Entropy is a property of a thermodynamic system that remains constant during a reversible adiabatic process. Moreover, we can also say that it is the degree of randomness or disorder in the system. If a system exchanges dQ heat from its surroundings at temperature T, then the chance in the entropy can be written as − $$\mathrm{ds \: = \: \frac{dQ}{T} \dotso \dotso \: (1)}$$ According to Clausius' inequality the cyclic integral of $\mathrm{\frac{dQ}{T}}$ along a reversible path is either less or equal to zero. Mathematically, it can be written as − $$\mathrm{\oint\frac{dQ}{T} \: \leq \: 0\dotso \dotso \: (2)}$$ ... Read More