1. Hristian Hristov Telerik Corporation http:/telerikacademy.com

2. 1. Dijkstra algorithm 2. Greedy search 3. A*  Heuristics  Admissible heuristics  Consistent heuristic 4. Additional information 2

3. Short Revision

4.  Uninformed search - We do not know where the goal is! - Guaranteed to find the goal!

5.  Short explanation 1. Start from a certain state and add onto fringe 2. Pop the state with highest priority from the fringe, mark as used and add its unmarked successors to the fringe 3. If fringe is empty - end the algorithm, else go to step 2  Complexity – O(nlogn) 5

6. 6

8.  We are informed for the goal  Use some greedy function to reach the goal  Does NOT always work!

9.  Short explanation For the labyrinth example: 1. Start from certain state 2. Move towards the goal minimizing the Manhattan distance. 3. If cannot move – end algorithm, else go to step 2

12. Why not mixing greedy and Dijkstra? 12

13. How to mix them? - Hello heuristic functions! -admissible heuristics - consistant heuristics 13

14. What is a heuristic? 14

15.  Some interesting values for graph search h(n) – heuristic of state n C(n) – actual minimum cost from n g(n) – cost to current state from start f(n) – evaluation function c(n, p) – edge between states n and p f(n) = g(n) + h(n) 15

16.  Admissible heuristics for every state n: C(n) >= f(n) 16

17. Consistent heuristic for every n and its successor a: h(n) <= c(n, a) + h(a) and h(goal)=O 17

18. Let’s use the heuristics! - Basically same idea as Dijkstra - Instead of the distance travelled we use the heuristics - Heuristics should be admissible and consistent 18

19. Pseudocode 1. Push start state with its heuristics onto the fringe 2. While fringe is not empty or goal is not reached: - Pop highest-priority state from the fringe - Push its non-visited successors onto the fringe calculating their heuristics and mark current state as parent 3. Print the path if needed 19

20. Live demo

21.  Dijkstra ALgorithms: “Programming = ++Algorithms” by P. Nakov; http://en.wikipedia.org/wiki/Dijkstra's_algorit hm http://en.wikipedia.org/wiki/Dijkstra's_algorit hm http://en.wikipedia.org/wiki/Dijkstra's_algorit hm  Heuristics: http://en.wikipedia.org/wiki/Heuristic; http://en.wikipedia.org/wiki/Admissible_heuris tic http://en.wikipedia.org/wiki/Consistent_heuris tic http://en.wikipedia.org/wiki/Heuristic http://en.wikipedia.org/wiki/Admissible_heuris tic http://en.wikipedia.org/wiki/Consistent_heuris tic http://en.wikipedia.org/wiki/Heuristic http://en.wikipedia.org/wiki/Admissible_heuris tic http://en.wikipedia.org/wiki/Consistent_heuris tic 21

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