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Breadth-First Search (BFS) Algorithm

Breadth-First Search (BFS) is one of the fundamental graph traversal algorithms used in computer science. It is particularly effective for searching or traversing tree or graph data structures, exploring nodes level by level from a starting point. BFS is commonly used in scenarios such as finding the shortest path in unweighted graphs, peer-to-peer networks, web crawlers, and more.

Depth-First Search (DFS) Algorithm

Depth-First Search (DFS) is a classic algorithm used to explore nodes and edges of a graph. It proceeds by exploring as far along a branch as possible before backtracking, which contrasts with Breadth-First Search (BFS) that explores neighbors level by level. DFS can be implemented using either recursion or an explicit stack and is a fundamental tool in fields such as artificial intelligence, compiler design, and topological sorting.

Graphs in Computer Science: Theory, Algorithms, and Applications

Graphs are fundamental data structures in computer science, used to model pairwise relations between objects. They are ubiquitous in applications ranging from social networks and the web to transportation, compiler construction, and bioinformatics.

Shortest Path Using Dijkstra's Algorithm

Finding the shortest path in a graph is a foundational problem in computer science and operations research. It is crucial in network routing, geographical mapping, artificial intelligence, and logistics. One of the most well-known and efficient algorithms for finding the shortest path from a source node to all other nodes in a graph with non-negative edge weights is Dijkstra’s Algorithm.

Bellman-Ford Algorithm for Shortest Path

The Bellman-Ford algorithm is a fundamental single-source shortest path algorithm used in graph theory. Unlike Dijkstra’s algorithm, Bellman-Ford can handle graphs with negative weight edges, making it versatile for a broader class of problems. It was first proposed by Richard Bellman and Lester Ford in 1958.