[Verse 1]
Graph with weighted edges, need the shortest path to find
Dijkstra had the vision, brilliant algorithmic mind
Start with source vertex, mark distance as zero clean
All other nodes infinity, the largest you've ever seen
Priority queue ready, min-heap keeps us organized
Extract the smallest distance, that's how we optimize
[Chorus]
Select, relax, repeat - that's the Dijkstra beat
Never visit twice, greedy choice so neat
Distance gets smaller, neighbors get updated
Shortest path revealed when algorithm's completed
Select, relax, repeat - Dijkstra's guarantee
No negative weights allowed, positive paths only
[Verse 2]
Pull the minimum from queue, mark that vertex as done
Check each neighbor node, see if distance can be won
Current distance plus edge weight, compare it to what's stored
If it's smaller update parent, new best path explored
Push updated to the queue, let priority decide
Relaxation is the key, distances subside
[Chorus]
Select, relax, repeat - that's the Dijkstra beat
Never visit twice, greedy choice so neat
Distance gets smaller, neighbors get updated
Shortest path revealed when algorithm's completed
Select, relax, repeat - Dijkstra's guarantee
No negative weights allowed, positive paths only
[Bridge]
Time complexity big O, V squared with simple array
V log V plus E log V when binary heap's in play
Fibonacci heap improves it, V log V plus E straight
But implementation matters for the runtime fate
[Verse 3]
Visited set grows larger, unvisited shrinks down
When destination's processed, shortest path is found
Backtrack through the parents, reconstruct the route
From source to every vertex, optimal path pursuit
GPS navigation systems, network routing protocols
Dijkstra's algorithm working, solving real world goals
[Chorus]
Select, relax, repeat - that's the Dijkstra beat
Never visit twice, greedy choice so neat
Distance gets smaller, neighbors get updated
Shortest path revealed when algorithm's completed
Select, relax, repeat - Dijkstra's guarantee
No negative weights allowed, positive paths only
[Outro]
Greedy algorithm power, locally optimal choice
Leads to global solution, give Dijkstra your voice
Single source shortest path, the master of his trade
Graph traversal genius, foundation he has made