[Verse 1] When graphs get weighted and paths need precision Dijkstra steps up with optimal decision Priority queue holds the shortest known distance While BFS treats every edge with resistance Breadth-first explores layer by layer neat But ignores the cost when weights compete Depth-first dives deep with recursive call But shortest paths? It misses them all [Chorus] Non-negative weights, Dijkstra's the king Greedy relaxation, optimal bring BFS for unweighted, DFS for traversal A-star adds heuristics, performance reversal Negative edges break the guarantee Bellman-Ford's the remedy [Verse 2] A-star brings heuristics to guide the search Manhattan distance helps it research Admissible functions never overestimate While Dijkstra explores without debate Both guarantee optimal when conditions align But A-star cuts search space, saves you time Dijkstra's exhaustive, explores every node A-star's selective, follows heuristic code [Chorus] Non-negative weights, Dijkstra's the king Greedy relaxation, optimal bring BFS for unweighted, DFS for traversal A-star adds heuristics, performance reversal Negative edges break the guarantee Bellman-Ford's the remedy [Bridge] When negative weights poison the well Dijkstra's assumption starts to rebel Relaxation order becomes critical Without it, results turn statistical Choose your weapon based on the terrain Weighted or not, positive or pain [Verse 3] Time complexity tells the real story Dijkstra's log-linear claims the glory BFS linear when edges are light DFS same speed for traversal flight A-star depends on heuristic quality Good estimates boost capability Space complexity matters in memory game Each algorithm stakes its claim [Chorus] Non-negative weights, Dijkstra's the king Greedy relaxation, optimal bring BFS for unweighted, DFS for traversal A-star adds heuristics, performance reversal Negative edges break the guarantee Bellman-Ford's the remedy [Outro] Graph structure dictates algorithm choice Let mathematics be your voice Dijkstra dominates the weighted scene When constraints are clean
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