1. A* Path Finding
Ref: A-star tutorial

2. The Problem
start
target
wall
Find a path of lowest cost
Given

3. Terminology Node Traversal cost: F = G + H Open list & closed list
Parent node; current node
Traversal cost: F = G + H
G: movement cost from starting point
H: heuristic cost to the target (e.g., Manhattan distance)
Open list & closed list
Closed: traversal cost already determined
Heuristics: (wiki) experience-based techniques for problem solving, learning, and discovery.
Manhattan distance

4. A* Algorithm
Take the node of lowest cost from open list; switch it to closed list; name it current node
For its reachable and non-closed neighbors:
If not in open list, add them. Make current node their parent. Evaluate costs G & H.
Else (already in open), revise parent using G. update cost.
Stop when:
target is added to closed list
Open list is empty (fail to find target). No path

5. Example
Open: (0,1),(0,2),(0,3),(1,1),(1,3),(2,1),(2,2),(2,3)
Closed:(1,2)
(0,4)
(1,2)
(5,2)
(0,0)
(6,0)

6. Open: (0,1),(0,2),(0,3),(1,1),(1,3),(2,1),(2,3)
Closed: (1,2),(2,2)
(0,4)
10+10<14
(1,2)
(5,2)
(0,0)
(6,0)

7. Open: (0,1),(0,2),(0,3),(1,1),(1,3),(2,3),(1,0),(2,0)
Closed: (1,2),(2,2),(2,1)
(0,0)
(0,4)
(6,0)
This neighbor is NOT added
due to the “cut-corner” constraint

9. Finally,

10. Dijkstra, Best-first, A* Ref: url
Comparison
Dijkstra, Best-first, A*
Ref: url

11. Dijkstra Algorithm
Repeatedly examines the closest not-yet-examined vertex, adding its vertices to the set of vertices to be examined.
expands outwards from the starting point until it reaches the goal.
guaranteed to find a shortest path from the starting point to the goal

12. Best-First Search
Instead of selecting the vertex closest to the starting point, it selects the vertex closest to the goal.
(Greedy) Best-First-Search is not guaranteed to find a shortest path.

13. Dijkstra better than Best first

14. A* combines the advantages of both

15. Implementation (google code)