1. Implementation: General Tree Search

2. Single-State Problem Formulation
A problem is defined by four items:
initial state
successor function (which actually defines all reachable states)
goal test
path cost (additive)

3. Your chance to review initial state successor function goal test
Si = 1
successor function
f(s) = 2s , f(s) = 2s+1
goal test
Sg = 11
path cost
Each transition costs one unit

4. Your chance to review
Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n+1.
Draw the portion of the state space for states 1 to 15.
Suppose the goal state is 11.
List the order in which nodes will be visited for breadth-first search.

5. Solution
Breadth First
1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11

6. Search Strategies
A strategy is defined by picking the order of node expansion
Strategies are evaluated along the following dimensions: completeness – does it always find a solution if one exists? time complexity – number of nodes generated/expanded space complexity – maximum number of nodes in memory optimality – does it always find a least-cost solution

7. Search Strategies
Time and space complexity are measured in terms of b – maximum branching factor of the search tree d – depth of the least-cost solution m – maximum depth of the state space (may be infinite)

8. Properties of Breadth-First Search
Complete??

9. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time??

10. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1) = O( bd+1 ), ie, exp. in d
Space??

11. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1) = O( bd+1 ), ie, exp. in d
Space?? O( bd+1 ) (keep every node in memory)
Optimal??

12. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1) = O( bd+1 ), ie, exp. in d
Space?? O( bd+1 ) (keep every node in memory)
Optimal?? Yes (if cost = 1 per step); not optimal in general
Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

13. Your chance to review
Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n+1.
Draw the portion of the state space for states 1 to 15.
Suppose the goal state is 11.
List the order in which nodes will be visited for depth-first search.

14. Solution Breadth First Depth First 1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11
Trick Question
1, 2, 4, 8, 16, 32, ….

15. Properties of Depth-first Search
Complete??

16. Properties of Depth-first Search
Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces
Time??

17. Properties of Depth-first Search
Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces
Time?? O(bm): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first
Space??

18. Properties of Depth-first Search
Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces
Time?? O(bm): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first
Space?? O(bm), i.e., linear space!
Optimal??

19. Properties of Depth-first Search
Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces
Time?? O(bm): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first
Space?? O(bm), I.e., linear space!
Optimal?? No.

20. Implementation: General Tree Search

21. Uninformed Search Strategies
Uninformed strategies use only information available in the problem definition
Breadth-first search
Uniform-cost search
Depth-first search
Depth-limited search
Iterative deepening search

22. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1) = O( bd+1 ), ie, exp. in d
Space?? O( bd+1 ) (keep every node in memory)
Optimal?? Yes (if cost = 1 per step); not optimal in general
Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

23. Properties of Breadth-First Search
Complete?? Yes (if b is finite)
Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1) = O( bd+1 ), ie, exp. in d
Space?? O( bd+1 ) (keep every node in memory)
Optimal?? Yes (if cost = 1 per step); not optimal in general
Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

24. Problem Solving Agents