A topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge UV from vertex u to vertex v, u comes before v in the ordering. This only makes sense in directed graphs.There are many places where topological sort makes a lot of sense. For example, let's say you're following a recipe, in this, there are some steps that are must for going to the next steps. But some of these can be performed in parallel. In a similar fashion, during college when selecting courses, there are some prerequisites ... Read More

DFS visits the child vertices before visiting the sibling vertices; that is, it traverses the depth of any particular path before exploring its breadth. A stack (often the program's call stack via recursion) is generally used when implementing the algorithm.Following is how a DFS works −Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)Repeat Rule 1 and Rule 2 until the stack is empty.Let us ... Read More

BFS visits the neighbor vertices before visiting the child vertices, and a queue is used in the search process. Following is how a BFS works −Visit the adjacent unvisited vertex. Mark it as visited. Display it. Insert it in a queue.If no adjacent vertex is found, remove the first vertex from the queue.Repeat Rule 1 and Rule 2 until the queue is empty.Let us look at an illustration of how BFS Traversal works:StepTraversalDescription1Initialize the queue.2We start by visiting S (starting node) and mark it as visited.3We then see an unvisited adjacent node from S. In this example, we have three ... Read More

Graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals are classified by the order in which the vertices are visited.

We'll be creating a graph class that supports weights and both directed and undirected types. This will be implemented using an adjacency list. As we move to more advanced concepts, both weights and directed nature of the graphs will come in handy.An adjacency list is an array A of separate lists. Each element of the array Ai is a list, which contains all the vertices that are adjacent to vertex i. We're defining it using 2 members, nodes and edges.Let's set up the graph class by defining our class and some methods that we'll use to add nodes and edges ... Read More

A graph is a pictorial representation of a set of objects where some pairs of objects are connected by links. The interconnected objects are represented by points termed as vertices, and the links that connect the vertices are called edges.Formally, a graph is a pair of sets (V, E), where V is the set of vertices and E is the set of edges, connecting the pairs of vertices. Take a look at the following graph −In the above graph, V = {a, b, c, d, e} E = {ab, ac, bd, cd, de}TerminologyMathematical graphs can be represented in the data ... Read More

Here is the complete implementation of the AVL Tree Class −Exampleclass AVLTree {    constructor() {       // Initialize a root element to null.       this.root = null;    }    getBalanceFactor(root) {       return this.getHeight(root.left) - this.getHeight(root.right);    }    getHeight(root) {       let height = 0;       if (root === null || typeof root == "undefined") {          height = -1;       } else {          height = Math.max(this.getHeight(root.left), this.getHeight(root.right)) + 1;       }     ... Read More

We can learn how we can insert a node in an AVL Tree. Insertions in AVL trees are the same as BST, we just need to perform one extra step called balance tree during insert whenever we move down the tree.This requires calculating the balance factor which we already saw before. And according to the configurations, we need to call appropriate rotation methods. These are pretty intuitive with the help of the above explanation.We again create a class method and a helper function for recursive calls − Exampleinsert(data) {    let node = new this.Node(data);    // Check if the tree ... Read More

To balance itself, an AVL tree may perform the following four kinds of rotations −Left rotationRight rotationLeft-Right rotationRight-Left rotationThe first two rotations are single rotations and the next two rotations are double rotations. To have an unbalanced tree, we at least need a tree of height 2. With this simple tree, let's understand them one by one.Left RotationIf a tree becomes unbalanced, when a node is inserted into the right subtree of the right subtree, then we perform a single left rotation −In our example, node A has become unbalanced as a node is inserted in the right subtree of ... Read More

AVL tree checks the height of the left and the right sub-trees and assures that the difference is not more than 1. This difference is called the Balance Factor.For example, in the following trees, the first tree is balanced and the next two trees are not balanced −In the second tree, the left subtree of C has height 2 and the right subtree has height 0, so the difference is 2. In the third tree, the right subtree of A has height 2 and the left is missing, so it is 0, and the difference is 2 again. AVL tree ... Read More