1. Algorithms for Exploration
Searches
Algorithms for Exploration

2. Graphs
How do we find the shortest path from NY to LA?

3. Graphs Graph representation: Nodes or Vertices : places you can be
Edges : routes between them

4. Graphs Graphs can represent any problem with connected states:
How do I turn cat into dog?

5. Graphs
Examples:

6. Breadth First Search
Explore all paths of length 1, then all paths of length 2, then all paths of length 3

7. BFS – Optimal Paths
Optimal Paths

8. Edge Weights
Edge Weights : Cost of taking a particular edge

9. Edge Weights Edge Weights : Cost of taking a particular edge
Optimal path may not have fewest edges:

10. Best First Search Best First Search
Maintain list of "places I know I can reach"
Always explore shortest remaining path
Stop when path to goal is shortest remaining path

11. Best First Search
Best First Search
Optimal path

12. Best First Search Best First Search Optimal path
Impossibly large number of paths to worry about
Given 20 branches per node:

13. Heuristic Heuristic : rule of thumb – guesstimation Heuristic Search :
Use a heuristic to guide your search – pick particular paths to explore first
Heurisitc adds "expected future cost" to each possible path

14. Sliding Puzzle

15. Sliding Puzzle State – where the tiles are
Edge – switch blank with neighbor

16. Sliding Puzzle
Goal: Fewest moves
Each move costs 1

17. Sliding Puzzle Goal: Fewest moves Each move costs 1
Heuristic : each out of place piece is 1 more cost
Total estimated cost = moves so far + pieces out of place

18. TicTacToe & Chess & Go

19. Game Difficulty https://www.youtube.com/watch?v=SUbqykXVx0A