A* Search Algorithm Demo

Real GPS data: Optimal pathfinding with f(n) = g(n) + h(n)

Combines actual cost + heuristic estimate • Guaranteed optimal solution
A* Search Algorithm

A* uses the evaluation function f(n) = g(n) + h(n) where:

  • g(n): Actual cost from start to current node
  • h(n): Heuristic estimate from current node to goal
  • f(n): Total estimated cost of path through this node
A* guarantees optimal solutions when using admissible heuristics (never overestimate).

A* with Real GPS Data

This demo uses actual road distances for g(n) and straight-line GPS distances for h(n):

  • g(n): Real road distances (408km Riyadh↔Qassim, 849km Riyadh↔Jeddah, etc.)
  • h(n): GPS straight-line distances (Riyadh=645km, Jeddah=65km to Makkah, etc.)
  • f(n): g(n) + h(n) guides the search toward optimal paths

A* will find the cheapest total distance route, not just the fewest hops!

f(n) = g(n) + h(n)
g(n) = actual cost from start to n
h(n) = heuristic cost from n to goal
f(n) = total estimated cost through n
Step Controls
Legend
Start/Path
Goal
Exploring
Explored
Frontier
Ready to Start

Click "Next Step" to begin A* search from Riyadh to Makkah, or click "Auto Play" for automatic visualization.

Current Status: Ready

Algorithm Comparison Compare with Greedy Heuristic Basics
Pseudocode
Data Structures
Frontier (Priority Queue by f-value):
Empty
Explored:
Empty
Performance Metrics
0
Steps
0
Explored
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Path Cost
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Path Length
Algorithm Comparison
Algorithm Function Optimal?
BFS Fewest hops Unweighted only
Dijkstra g(n) only Yes
Greedy h(n) only No
A* g(n) + h(n) Yes*
*With admissible heuristic

Understanding A* Search Algorithm

How A* Works
Best of Both Worlds:
  • Like Dijkstra: Considers actual cost g(n)
  • Like Greedy: Uses heuristic guidance h(n)
  • Optimal: Guarantees shortest path with admissible h(n)
  • Efficient: Explores fewer nodes than Dijkstra
Our Saudi Cities Result:

A* will find the optimal 929km route (Riyadh → Jeddah → Makkah) because:

  • f(Jeddah) = 849 + 65 = 914
  • f(Qassim) = 408 + 620 = 1028
  • Lower f-value = higher priority
A* Properties
Requirements for Optimality:
  • Admissible heuristic: h(n) ≤ true cost to goal
  • Consistent heuristic: h(n) ≤ c(n,n') + h(n')
  • Non-negative costs: All edge weights ≥ 0
Our GPS Heuristic:
  • Straight-line distance is admissible
  • Never overestimates road distance
  • Manhattan distance would also work
Why A* is Popular: Perfect balance of optimality and efficiency for pathfinding!
Real-World A* Applications
Navigation & Routing:
  • GPS Navigation: Google Maps, Waze (shortest time/distance)
  • Delivery Services: UPS, FedEx route optimization
  • Autonomous Vehicles: Self-driving car pathfinding
  • Flight Planning: Aircraft route optimization
Gaming & AI:
  • Video Games: NPC pathfinding (RPGs, strategy games)
  • Puzzle Solving: 15-puzzle, sliding block puzzles
  • Robotics: Robot navigation and motion planning
  • Network Routing: Internet packet routing protocols
Key A* Takeaways
  • Optimal + Efficient: Best combination for pathfinding
  • Heuristic quality matters: Better h(n) = fewer explored nodes
  • Admissibility crucial: Overestimating breaks optimality
  • Industry standard: Most widely used pathfinding algorithm
  • Flexible framework: Works with any admissible heuristic
  • Perfect for students: Combines multiple AI concepts