# graph

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A* Search Algorithm in Java: Heuristic Pathfinding

The A (A-Star) search algorithm is one of the most successful pathfinding algorithms in computer science. It is widely used in video games and robotics because it is both efficient and guaranteed to find the shortest pat…

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Bellman-Ford Algorithm in Java: Shortest Paths with Negative Weights

While Dijkstra's algorithm is faster for most shortest-path problems, it fails when the graph contains negative edge weights. For those scenarios, we use the Bellman-Ford algorithm. Not only does it handle negative weigh…

Dijkstra's Algorithm in Java: Finding the Shortest Path

Dijkstra's algorithm is the industry standard for finding the shortest path from a starting node to all other nodes in a graph with non-negative edge weights. Whether you are building a navigation system like Google Maps…

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Floyd-Warshall Algorithm in Java: All-Pairs Shortest Paths

While Dijkstra's algorithm finds the shortest path from a single source to all other nodes, the Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a weighted graph. It is a classic example…

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Kruskal's Algorithm in Java: Finding the Minimum Spanning Tree

Kruskal's algorithm is a famous greedy algorithm used to find the Minimum Spanning Tree (MST) of a connected, weighted, and undirected graph. An MST is a subset of edges that connects all vertices together, without any c…

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Lowest Common Ancestor (LCA) in Java: Binary Trees and DAGs

Introduction to Lowest Common Ancestor (LCA) The Lowest Common Ancestor (LCA) of two nodes p and q in a tree (or a Directed Acyclic Graph - DAG) is the lowest (i.e., deepest) node that has both p and q as descendants. A…

Apr 19, 202612 min read

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Prim's Algorithm in Java: Minimum Spanning Tree via Greedy Growth

While Kruskal's algorithm focuses on edges, Prim's algorithm takes a vertex-centric approach to finding the Minimum Spanning Tree (MST). It starts from an arbitrary node and "grows" the tree by always adding the cheapest…

Topological Sort in Java: Handling Dependencies with Kahn's Algorithm

Introduction to Topological Sort Topological Sort (or Topological Ordering) is an algorithm for ordering the vertices of a Directed Acyclic Graph (DAG) such that for every directed edge u -> v, vertex u comes before vert…

Apr 18, 20269 min read

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Union Find (DSU) in Java: Connectivity and Cycle Detection

Introduction to Union Find (Disjoint Set Union) The Union Find data structure, also known as Disjoint Set Union (DSU), is a powerful and efficient data structure that keeps track of a set of elements partitioned into a n…

Apr 18, 202610 min read