Java Graph Algorithms for Newbs

Introduce graph data structures with nodes and edges, classify graphs as directed, undirected, and weighted, and illustrate with webpages linking, social networks, and navigation maps.

Explore graph representations with adjacency matrix and adjacency list, using a football player example to show edge encoding with 1s and 0s, and compare space and time trade-offs.

Demonstrate an adjacency matrix in java using a v by v two-dimensional array to represent an undirected, unweighted graph with six vertices, marking edges as one and non-edges as zero.

Implement an adjacency list for an undirected graph using an array of linked lists for vertex connections, with bidirectional edges and adjacency printing.

Count all acyclic paths between two vertices using backtracking and a visited array in a Java graph, building an adjacency list and recursively exploring edges to yield the total paths.

Explore time and space complexity and big O notation. Compare best, average, and worst case analyses to understand how loops and input size shape algorithm efficiency.

Traverse a graph using breadth-first search by starting from a chosen node, marking visited nodes, and enqueuing neighbors into a queue to visit them in a first-in, first-out order.

Explore how breadth-first search powers web crawlers, GPS navigation, and social networks for friend suggestions. See how it reveals shortest paths and helps detect cycles and max-flow scenarios.

Learn to detect cycles in an undirected graph using BFS with an adjacency list, marking visited vertices, tracking parents, and outputting cycle presence.

Explore the Ford-Fulkerson algorithm to compute the maximum flow from source to sink by iteratively finding augmenting paths, respecting capacities, updating residual capacities, and stopping when no augmenting path remains.

Explore the Edmonds-Karp algorithm, a breadth-first search based implementation of Ford-Fulkerson to compute the maximum flow in a graph, highlighting capacity edges, source and sink in Java.

Explore how depth-first search traverses a graph in depth-first order, using a stack and a visited boolean array to backtrack and record the traversal path.

Master practical dfs applications: determine path existence, detect cycles, identify strongly connected components, test for bipartite graphs, and compute topological orderings in directed acyclic graphs.

Implement topological sorting for a directed graph using DFS and an adjacency list. Detect cycles to ensure a valid linear order of vertices using a stack.

Discover how Dijkstra's algorithm, the distress algorithm, finds the shortest paths from a source node to all other nodes in a graph by updating distances when shorter paths are found.

Implement and explain Dijkstra's algorithm to compute the shortest path distances from a source to all vertices in a graph, using adjacency matrix or adjacency list representations.

Explore the minimum spanning tree concept by inspecting a graph with four vertices and five edges, identifying connected, cycle-free subsets that cover all vertices and minimize total edge weight.

Learn prim's algorithm to find a minimum spanning tree of a graph by starting at a source node and avoiding cycles while minimizing total cost.