🥑 Graph Traversal | Data Structures & Algorithms

#DataStructures #Algorithms #GraphTheory #BFS #DFS This video covers the fundamental algorithms for Graph Traversal, the process of systematically exploring a graph's vertices and edges. Presented by Hayden Smith, this lecture explains the two primary traversal strategies: Depth-First Search (DFS) and Breadth-First Search (BFS). 🧭 Two Main Strategies: BFS and DFS Graph traversal is essential for finding paths, searching for items, or exploring the entire structure of a graph. The two main algorithms for this are: * Depth-First Search (DFS): This strategy explores a graph by going as "deep" as possible down one path. When it hits a dead end, it backtracks to the last junction and explores the next available branch. * Breadth-First Search (BFS): This strategy explores the graph "wide" or level by level. It starts at a source node, visits all of its immediate neighbors, then visits all of their neighbors, and so on. ⚙️ How They Work To avoid getting stuck in infinite loops in graphs with cycles, both algorithms must keep track of which vertices have already been visited. While both can be implemented iteratively, the key difference lies in the data structure used: BFS uses a Queue, while DFS uses a Stack. DFS can also be implemented very elegantly using recursion. ⏱️ Performance and Properties For a graph implemented with an adjacency list, both BFS and DFS have a time complexity of O(V + E), where V is the number of vertices and E is the number of edges. A critical difference is that BFS will always find the shortest path (in terms of the number of edges) between two nodes in an unweighted graph. DFS makes no such guarantee. 🌳 Spanning Trees A full traversal of a connected graph using either BFS or DFS will produce a spanning tree. This is a subgraph that includes all of the original graph's vertices but contains no cycles. View the full playlist: https://www.youtube.com/playlist?list=PLi2pCZz5m6GEftzPIxVH1ylwytux9WOGN