1. State Space Search 2 Chapter 3 Three Algorithms

2. Backtracking Suppose We are searching depth-first No further progress is possible (i.e., we can only generate nodes we’ve already generated) Backtrack

3. The algorithm: First Pass 1. Pursue path until goal is reached or dead end 2. If goal, quit and return the path 3. If dead end, backtrack until you reach the most recent node whose children have not been fully examined

4. BT maintains Three Lists and A State SL ◦List of nodes in current path being tried. If goal is found, SL contains the path NSL ◦List of nodes whose descendents have not been generated and searched DE ◦List of dead end nodes All lists are treated as stacks CS ◦Current state of the search

5. The Algorithm

6. State Space a b e g c a d h i j A as a child of C is intentional

7. Trace At Home Exercise: Trace with Goal j, Start A Show SL, NSL, DE, CS at each step of the algorithm

8. Depth-First: A Simplification of BT Eliminate saved path (SL) Results in Depth-First search ◦Goes as deeply as possible ◦Is not guaranteed to find a shortest path ◦Maintains two lists  Open List ◦ Contains states generated ◦ Children have not been examined (like NSL) ◦ Open is implemented as a stack  Closed List ◦ Contains states already examined ◦ Union of SL and DE

9. bool Depth-First(Start) { open = [Start]; closed = []; while (!isEmpty.open()) { CS = open.pop(); if (CS == goal) return true; else { generate children of CS; closed.push(CS); eliminate children from CS that are on open or closed; while (CS has more children) open.push(child of CS); } return false; }

10. Trace At Home Exercise: Trace graph on slide 6 with Goal j, Start a Show Open, Close, CS at each step of the algorithm

11. Breadth-First Search: DF but with a Queue bool Breadth-First(Start) { open = [Start]; closed = []; while (!isEmpty.open()) { CS = open.dequeue(); if (CS == goal) return true; else { generate children of CS; closed.enqueue(CS); eliminate children from CS that are on open or closed; while (CS has more children) open.enqueue(child of CS); } return false; }

12. Trace At Home Exercise: Trace graph on slide 6 with Goal j, Start a Show Open, Close, CS at each step of the algorithm

13. Both Algorithms 1. Open forms frontier of search 2. Path can be easily reconstructed  Each node is an ordered pair (x,y)  X is the node name  Y is the parent  When goal is found, search closed for parent, the parent of the parent, etc., until start is reached.

14. Breadth-First Finds shortest solution If branching factor is high, could require a lot of storage Depth-First If it is known that the solution path is long, DF will not waste time searching shallow states DF can get lost going too deep and miss a shallow solution DF and BF follow for the 8-puzzle

15. 8 Puzzle—DF (p. 105) Depth First Search of 8-Puzzle (p. 105) Depth Bound = 5