[Verse 1] Started with a problem, need to find the way From vertex A to B, what's the cost to pay Graph theory fundamentals, let me break it down Nodes connected by edges, weights all around Shortest path algorithms, that's the game we play Dijkstra's got the method, BFS for the day When all edges equal one, breadth-first is clean But weighted graphs need more, know what I mean [Chorus] D-I-J-K-S-T-R-A, greedy choice every day Pick the minimum distance, never go astray B-F-S for unweighted, level by level we go Shortest paths in graphs, that's how we flow Distance arrays and queues, priority maintains Graph theory mastery running through our veins [Verse 2] Dijkstra starts with source, distance zero set All other nodes infinity, algorithm's bet Priority queue holding vertices by their cost Extract minimum each time, efficiency not lost Relax the neighbors, update distance when we find A shorter path exists, optimization refined Mark visited nodes, never process them twice Single source shortest paths, algorithm precise [Chorus] D-I-J-K-S-T-R-A, greedy choice every day Pick the minimum distance, never go astray B-F-S for unweighted, level by level we go Shortest paths in graphs, that's how we flow Distance arrays and queues, priority maintains Graph theory mastery running through our veins [Bridge] Bellman-Ford for negative weights, iterate V minus one Floyd-Warshall all pairs, dynamic programming done A-star heuristic guidance, informed search refined Graph representations matter, adjacency defined Matrix or list structure, space and time combined [Verse 3] Breadth-first exploration, queue-based traversal clean Process level by level, shortest paths between Unweighted graph guarantee, minimum hops achieved FIFO queue mechanics, distance retrieved Mark nodes as visited, prevent infinite loops Parent tracking backwards, reconstruct the groups Path reconstruction easy, follow parent chain Graph algorithms mastered, knowledge in the brain [Chorus] D-I-J-K-S-T-R-A, greedy choice every day Pick the minimum distance, never go astray B-F-S for unweighted, level by level we go Shortest paths in graphs, that's how we flow Distance arrays and queues, priority maintains Graph theory mastery running through our veins [Outro] From source to destination, algorithms guide Shortest path solutions, computer science pride Graph theory foundations, pathfinding complete West coast optimization, can't accept defeat
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