OnlineClasses

The category contains all the lectures as posts which teaches about Datastructures & Algorithms and Problem Solving

Shortest Path Using Bellman Ford Algorithm

Introduction This post about Bellman Ford Algorithm is a continuation of the post Shortest Path Using Dijkstra's Algorithm. While learning about the Dijkstra's way, we learnt that it is really efficient an algorithm to find the single source shortest path in any graph provided it has no negative weight edges and no negative weight cycles. The running time of the Dijkstra's Algorithm is also promising, O(E +VlogV) depending on our choice of data structure to implement the required Priority Queue. Why Bellman Ford Algorithm? There can be scenarios where a graph may contain negative weight ...
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Further Reading for Minimum Spanning Tree

Introduction This is a supplement to the posts for Minimum Spanning Tree and their Analysis. Check out the other related articles in the following section. Further Reading for Minimum Spanning Tree This section is meant to be read in conjunction to the post Minimum Spanning Tree - Prim's Algorithm The minimum spanning tree of a Graph is the union of minimum spanning trees of its connected components. This is a very important observation and it must be discussed in length and breadth because this will help us design our algorithm for MST in a better way. Why is it so important to underst...
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Minimum Spanning Tree Prim’s Algorithm

Introduction What is the minimum length of the network cable we require if we have to connect 100 computing machines in a building distributed across multiple floors? How do I guarantee that there can be no other minimum length possible than what I derive? Why is it even important to find the minimum length? The history of the problem You can read the classic problem solved by MST Applications of Minimum Spanning Tree Defining Spanning Trees A spanning tree is always defined for a weighted Graph G(V,E) where the weights are positive. This means that all the edges carry some positive we...
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Breadth First Traversal

Introduction This is the first article in the Graph Traversals – Online Classes. Dear Readers, these set of posts under Graph Traversals will make more sense if you have read the Graph Theory. Here is a quick brush up for the same. However, if you are familiar with Graph Theory and have a basic knowledge of what graphs are and how they are stored, you can dive into the traversals. Later in the series we will discover that the Graph Traversals are widely used in various application. Let me point out a couple of real world examples here: How can we conduct matches between teams in a C...
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Make anagrams from two Strings

Problem Statement Given two strings, find the total number of characters we need to delete from these strings to make them anagrams of each other. Understanding Anagrams Anagrams are defined with respect to a given string of characters (not necessarily characters in the English Alphabet) but a wider set of characters may be. Given two strings A and B, if the number of time each character occurs in both the string is exactly same, we say A and B are anagrams. However, the order in which the character appears may be different and doesn't matter. For example A = axbbxxcecdeedda B = abacb...
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Matrix Rotation and Matrix Transpose

Problem Definition – Matrix Rotation (by 90, 180, 270 degrees) This is a very famous interview question and has been asked numerous times. We are trying to solve the problem of matrix rotations where the inputs are as follows: A matrix of dimension M * N A number from the set (90, 180, ,270) by which we need to rotate the matrix. For simplicity we will consider a matrix to be a 2 dimensional array of integers. What does it mean to rotate a matrix? This can only be explained by nice diagrams. Just for a formal definition, I would say that matrix rotation is a structural re-arrangeme...
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Inorder Predecessor of node in Binary Tree Using Parent Pointer

Introduction This is the seventh article in the Tree Traversals - Online Classes. This article presents ways to find out inorder predecessor of node in binary tree. As we have already read about the Inorder Successor it wont take much effort to understand the predecessor. Definition - Inorder Predecessor of node in Binary Tree If a node K is called the inorder predecessor of node N then N must be visited immediately after K in a inorder traversal of the tree. Below is a more formal definition of Inorder Predecessor: If the node has a left sub-tree, then inorder predecessor is the ...
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