[Verse 1]
Graph becomes a battlefield, nodes are cities to explore
Each connection has a weight, distance knocking at your door
Heuristic function guides us forward, crystal ball that never lies
Estimates the cost remaining, telescope that cuts through skies
F-score equals G plus H, mathematics in the mix
G tracks actual distance traveled, H predicts what we can fix
[Chorus]
A-star navigates the maze, best-first with a brain
Open list holds candidates, closed list breaks the chain
F-score low gets priority, queue sorts by the cost
Admissible heuristics guarantee we're never lost
Optimal solution guaranteed, shortest route we'll claim
A-star navigates the maze, algorithms hall of fame
[Verse 2]
Initialize with starting node, zero G and H computed
Open list receives first entry, search algorithm booted
Pop the lowest F-score winner, current node takes center stage
Generate its neighbor children, successors turn the algorithm page
Calculate their G and H values, parent path determines cost
Check if better routes exist, efficiency is never lost
[Chorus]
A-star navigates the maze, best-first with a brain
Open list holds candidates, closed list breaks the chain
F-score low gets priority, queue sorts by the cost
Admissible heuristics guarantee we're never lost
Optimal solution guaranteed, shortest route we'll claim
A-star navigates the maze, algorithms hall of fame
[Bridge]
Manhattan distance for the grid, Euclidean for the plane
Heuristic must never overestimate or optimality goes down the drain
Dijkstra with intelligence, breadth-first with direction
Time complexity manageable when heuristics show perfection
[Verse 3]
Closed list stores the visited, prevents the endless loops
Open list priority queue, min-heap keeps organized troops
Backtrack when goal discovered, parent pointers show the way
Reconstruction builds the answer, breadcrumb trail saves the day
Space complexity grows linear, time depends on branching factor
A-star solves the shortest route, pathfinding's main contractor
[Chorus]
A-star navigates the maze, best-first with a brain
Open list holds candidates, closed list breaks the chain
F-score low gets priority, queue sorts by the cost
Admissible heuristics guarantee we're never lost
Optimal solution guaranteed, shortest route we'll claim
A-star navigates the maze, algorithms hall of fame
[Outro]
F equals G plus H, remember this equation
A-star finds the optimal route through algorithmic innovation