All-Pairs Shortest Path (APSP)

🔥 Floyd-Warshall Algorithm → Floyd–Warshall is a dynamic-programming algorithm that implements the APSP task by computing the full pairwise shortest-path distance (and optionally predecessor) matrix, handling negative edges and detecting negative cycles, especially suitable for dense graphs.

🔥 Dijkstra Algorithm → APSP defines the multi-source shortest-path objective and constraints; it specifies contexts (e.g., nonnegative edges, sparse graphs) where Dijkstra serves as the single-source subroutine within APSP solutions like repeated Dijkstra and Johnson’s algorithm, thereby enabling its correct application.

🔥 Johnson Algorithm → Johnson's algorithm is a specific method for solving APSP on sparse graphs with some negative edges; it relies on the APSP problem definition and expected outputs (all-pairs distance/predecessor matrices) to structure its reweighting plus repeated Dijkstra approach.

Single-Source Shortest Path →

Single-Pair Shortest Path →