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Algorithms & Data Structures

BFS is a graph traversal algorithm that explores all vertices reachable from a source, visiting neighbors level by level using a FIFO queue.

DFS is a graph traversal algorithm that explores as far as possible along each branch before backtracking, using a LIFO stack.

Dijkstra's algorithm finds the shortest paths from a source node to all other nodes in a weighted graph with non-negative edge weights using a min-priority queue.

Topological Sort (Kahn's algorithm) orders the vertices of a Directed Acyclic Graph (DAG) such that for every directed edge u→v, u appears before v in the ordering.

Prim's algorithm finds a Minimum Spanning Tree (MST) for a weighted undirected graph by growing a tree one vertex at a time from an arbitrary start, always adding the cheapest edge that connects a tree vertex to a non-tree vertex.

Kruskal's algorithm finds a Minimum Spanning Tree (MST) by sorting all edges by weight and adding the cheapest edge that does not form a cycle, using the Union-Find data structure.

Bellman-Ford finds single-source shortest paths in a weighted graph and, unlike Dijkstra, supports negative edge weights. It works by relaxing all edges V−1 times and then checking for negative cycles.

Kosaraju's algorithm finds all Strongly Connected Components (SCCs) of a directed graph in linear time using two passes of DFS: one to order vertices by finish time, and one on the reverse graph to peel off components.

Floyd-Warshall computes the shortest paths between every pair of vertices in a weighted graph. It incrementally allows each vertex as an intermediate point and updates an all-pairs distance matrix.

An articulation point (cut vertex) is a vertex whose removal increases the number of connected components in a graph. Tarjan's algorithm finds all articulation points in a single DFS using discovery times and low-link values.