Kruskal’s Algorithm is a greedy algorithm used to find the minimum spanning tree of a weighted undirected graph. It works by sorting the edges of the graph in increasing order of weight and adding them to the tree one by one, provided that the edge does not create a cycle in the tree. The algorithm … Read more
Prim’s Algorithm is a greedy algorithm used to find the minimum spanning tree of a weighted undirected graph. It starts by selecting a random vertex from the graph and repeatedly adding the closest vertex that has not yet been added to the tree. The algorithm maintains a priority queue of edges with their weights and … Read more
DFS stands for Depth-First Search. It is a graph traversal algorithm that starts at a given source vertex and explores as far as possible along each branch before backtracking. In other words, it explores the vertices of a graph in depth-first order until there are no more vertices left to explore. To implement DFS, we … Read more
In this implementation, we define a Graph class that stores the graph as an adjacency list. The addEdge method adds an undirected edge between two vertices. The bfs method performs BFS starting from the given startVertex. We maintain a visited array to keep track of which vertices we have visited, and a queue to store … Read more
A binary tree can be represented using an array by assigning each node in the tree a unique index based on its level and position within the level. The root node is assigned index 1, and its left and right children are assigned indices 2 and 3, respectively. The left child of a node at … Read more
The Floyd-Warshall algorithm (also known as Warshall’s algorithm) is an algorithm used to find the shortest paths in a weighted graph with positive or negative edge weights. The algorithm was developed by Robert Floyd and Stephen Warshall in 1962. Here’s how the algorithm works: The floydWarshall function takes a 2D array graph representing the adjacency … Read more
Dijkstra’s algorithm is a popular algorithm used in computer science to find the shortest path between two nodes in a weighted graph. The algorithm was invented by Edsger W. Dijkstra in 1956. Here’s how the algorithm works: Dijkstra’s algorithm is commonly used in applications such as routing protocols in computer networks, finding shortest paths in … Read more
Detecting cycles in directed graphs is a bit more complicated than in undirected graphs because there are two types of edges – forward and backward – that need to be considered. One way to detect cycles in a directed graph is to use depth-first search (DFS) and maintain a stack of visited vertices. To detect … Read more
In an undirected graph, a cycle is a path that starts and ends at the same vertex, and consists of at least one other vertex that is visited more than once. To detect cycles in an undirected graph, one approach is to use the Depth-First Search (DFS) algorithm. The DFS algorithm starts at a vertex … Read more
