[Verse 1] Started with a graph problem, need to find the way Shortest path from A to Z, algorithms at play Dijkstra's got that greedy mind, always picks the best Priority queue keeps it clean, never second guess Single source to everywhere, non-negative weights Relaxation technique smooth, updates all the states But when the weights go negative, Dijkstra starts to break Bellman-Ford steps in strong, whatever time it takes [Chorus] D-I-J-K-S-T-R-A, greedy choice will lead the way Positive weights only, that's the price you gotta pay A-star heuristic guidance, Floyd-Warshall all pairs Choose your algorithm right, based on what your problem shares Shortest path solutions, pick the tool that really cares [Verse 2] A-star brings intelligence, heuristic guides the search Manhattan distance, Euclidean, helps you leave the lurch Admissible function key, never overestimate Goal-directed strategy, optimal results create Dijkstra's just A-star when heuristic equals zero But A-star cuts the search space, makes it move like hero Game maps and GPS routing, A-star takes the crown When you know where you're headed, it won't let you down [Chorus] D-I-J-K-S-T-R-A, greedy choice will lead the way Positive weights only, that's the price you gotta pay A-star heuristic guidance, Floyd-Warshall all pairs Choose your algorithm right, based on what your problem shares Shortest path solutions, pick the tool that really cares [Verse 3] Bellman-Ford runs slower, but handles negative edge Detects those cycles too, keeps you from the ledge N minus one iterations, relax every single time Dynamic programming flow, complexity's not prime Floyd-Warshall goes all out, every pair gets checked O of N cubed running time, what did you expect When you need all shortest paths, Floyd's the way to go Matrix multiplication style, watch the distances flow [Bridge] Time complexity matters when the data gets large Dijkstra's N log N when priority's in charge Space versus time trade-offs, memory allocation Choose based on your constraints, graph size calculation [Outro] Dijkstra for the positive, A-star when you know the goal Bellman-Ford for negatives, Floyd when you want it all Path-finding algorithms, each one has its place Pick the right solution and you'll win the shortest race
← How Dijkstra's Algorithm Works | Implementation and Time Complexity →