Effective Search Algorithms for State Spaces

1. State Space Search 2Chapter 3 Three Algorithms

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

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

4. 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 BT maintains Three Lists and A State

5. The Algorithm

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

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

8. 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 Depth-First: A Simplification of BT

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

11. 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; } Breadth-First Search: DF but with a Queue

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

13. Open forms frontier of search • 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. Both Algorithms

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