Data Structure II Assignment PDF

## Difference between DFS and BFS - DFS stands for Depth - BFS stands for Breadth ## Define: ### Graph - A graph is a non-linear data structure consisting of a set of vertices (or nodes) and a set of edges connecting them. - Each vertex in a graph represents an entity or a concept, while each edge...

## Difference between DFS and BFS - DFS stands for Depth - BFS stands for Breadth ## Define: ### Graph - A graph is a non-linear data structure consisting of a set of vertices (or nodes) and a set of edges connecting them. - Each vertex in a graph represents an entity or a concept, while each edge represents a relationship or a connection between two vertices. - Graphs can be directed or undirected. - In a directed graph, the edges have a direction from one vertex to another, while in an undirected graph, the edges are bidirectional. - Graphs are commonly used to model complex systems, such as social networks, transportation networks, and computer networks. - They are also used in various algorithms, such as the shortest path algorithm and minimum spanning tree algorithms, to find optimal solutions to various problems. ### Cyclic Graph - A cyclic graph is a data structure where a node can have a path to itself through a sequence of edges. - This means that there is at least one cycle or loop in the graph. - Cyclic graphs are different from acyclic grafts which do not contain any cycles. - In an acyclic graph, each node has a unique path to every other node in the graph. - However, dealing with cyclic graphs can be more complex than dealing with acyclic graphs. - Algorithms that work on acyclic graphs may not work on cyclic graphs or may need to be modified to handle the presence of cycles. - For example, traversing a cyclic graph requires detecting and avoiding cycles to avoid getting stuck in an infinite loop. ### Adjacency Matrix - An adjacency matrix is a data structure used to represent a graph. - It is a square matrix where the rows and columns represent the nodes of the graph, and each element in the matrix represents an edge between two nodes. - If node i is adjacent to node j, then the element at the intersection of row i and j will be 1; otherwise, it will be 0. ### Loop - This is a programming construct that allows the repetition of a set of instructions until a certain condition is met. - In the context of data structures, a loop refers to a situation where a particular sequence of instructions or an operation is repeated multiple times, usually for a certain number of iterations or until a particular condition is met. - Loops are commonly used in data structures to traverse, access, or manipulate data elements repeatedly. - For example, in a linked list, a loop can be used to traverse the list and perform a specific operation on each element until the end of the list is reached. - Similarly, in an array, a loop can perform a certain operation on it. - Loops are an important and powerful tool in computer programming and data structures as they allow for efficient and automated repetition of code and are often used in conjunction with conditional statements and other control structures to create complex algorithms and applications. ## Algorithm for Merge Sort ``` Algorithm MergeSort(A, I, h); if (l < h) { mid = (l + h) / 2; MergeSort(A, l, mid); MergeSort (A, mid + 1, h); Merge(A, l, mid, h); } ```