[Verse 1] Picture a map where cities connect, dots on the grid represent Vertices hold the data we select, edges are roads that intersect Weight on each path shows the expense, distance or time that we dispense Graph theory breaks down the suspense, finding routes with confidence From LAX to JFK direct, flight connections architects Every junction we inspect, algorithms genuflect To the structure we perfect, shortest paths we can detect [Chorus] V for vertex, E for edge, W for weight upon the ledge Path is sequence, vertex pledge, memorize this sacred pledge Weighted graphs decode the maze, Dijkstra guides us through the haze Count the steps in countless ways, graph theory sets our minds ablaze [Verse 2] Airport terminals in the sky, flight networks multiply Each connection quantified, fuel costs can't deny Hub and spoke patterns apply, weighted edges specify Distance, price, or time to fly, algorithms ratify Social networks intertwine, friendship graphs by design Each relationship defined, weighted by how we align Trust and influence combine, shortest paths we can divine [Chorus] V for vertex, E for edge, W for weight upon the ledge Path is sequence, vertex pledge, memorize this sacred pledge Weighted graphs decode the maze, Dijkstra guides us through the haze Count the steps in countless ways, graph theory sets our minds ablaze [Bridge] Adjacency lists cascade, storing neighbors that we've made Matrix form alternatively displayed, connections never fade Sparse or dense, the choice we've weighed, efficiency parade [Verse 3] Bellman-Ford handles negative weights with grace While Dijkstra dominates the positive space Floyd-Warshall finds all pairs' embrace A-star heuristics accelerate the race From source to destination traced, optimal solutions placed Graph traversal interlaced, computational taste [Outro] Vertices, edges, weights aligned Shortest paths by math designed Graph theory expands your mind Leave no optimal route behind
← What is Dijkstra's Algorithm? | How Dijkstra's Algorithm Works →