A graph is a non-linear data structure consisting of a set of vertices or nodes and a set of edges that connect such pairs. Unlike linear data structures such as arrays, linked lists or hierarchical ones like trees, graphs represent complex relationships where any node can be connected to any other node. They are incredibly versatile and used to model real world scenarios like social networks, road maps, and electrical circuits.
Breadth-first search is a graph traversal algorithm that explores a graph level by level, starting from a designated source node. It systematically visits all the vertices at a certain distance from the source before moving on to vertices that are further away, effectively finding the shortest path in an unweighted graph. BFS utilizes a queue to manage the order of exploration, ensuring that nodes are visited in order of their distance from the starting point. This makes it particularly useful for finding the shortest path or determining connectivity between nodes in a graph
Depth-First Search (DFS) is a graph traversal algorithm that explores a graph by going as deep as possible along each branch before backtracking. Starting from a chosen root node, DFS explores as far as it can along one path before moving to the next available path, effectively traversing the graph in a depthward manner. It uses a stack, explicitly or implicitly through recursion to keep track of the path and backtrack when a dead end is reached. DFS is useful for tasks like finding connected components, detecting cycles, and solving mazes