1. Uninformed Search Strategies
What are the four things known in the problem definition?

2. Uninformed Search Strategies
What are the four things known in the problem definition?
Start State
Successor Functions
Goal State
Path Cost

3. 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

4. With a neighbor
List the type of search domain where breadth first is a good solution.
A bad solution
List the type of search domain where depth first sear is a good solution.

5. 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

6. 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.

7. 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.

8. Problem Solving Agents

9. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal

10. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete??

11. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 

12. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time??

13. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution

14. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution
Space??

15. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution
Space?? # of nodes with g  cost of optimal solution, O(b C*/)

16. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution
Space?? # of nodes with g  cost of optimal solution, O(b C*/)
Optimal??

17. Uniform-cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete?? Yes, if step cost 
Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution
Space?? # of nodes with g  cost of optimal solution, O(b C*/)
Optimal?? Yes – nodes expanded in increasing order of g(n)

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?? No

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. Depth-limited Search
= depth-first search with depth limit L, i.e., nodes at depth L have no successors
Recursive implementation:

21. Iterative Deepening Search

22. Iterative Deepening Search l = 0
Limit = 0

23. Iterative Deepening Search l = 1
Limit = 1

24. Iterative Deepening Search l = 2
Limit = 2

25. Iterative Deepening Search l = 3
Limit = 3

26. Properties of Iterative Deepening Search
Complete??

27. Properties of Iterative Deepening Search
Complete?? Yes
Time??

28. Properties of Iterative Deepening Search
Complete?? Yes
Time?? (d+1)b0 + db1 + (d-1)b2 + … + bd = O(bd)
Space??

29. Properties of Iterative Deepening Search
Complete?? Yes
Time?? (d+1)b0 + db1 + (d-1)b2 + … + bd = O(bd)
Space?? O(bd)
Optimal??

30. Properties of Iterative Deepening Search
Complete?? Yes
Time?? (d+1)b0 + db1 + (d-1)b2 + … + bd = O(bd)
Space?? O(bd)
Optimal?? Yes, if step cost = 1 Can be modified to explore uniform-cost tree Numerical comparison for b=10 and d=5, solution at far right: N(IDS) = , , ,000 = 123,450 N(BFS) = , , , ,990 = 1,111,100

31. So let’s try it again…
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.
Suppose the goal state is 11.
List the order in which nodes will be visited in depth limited search with limit 4
For iterative deepening.

32. Solution Depth Limited, l=3 Iterative Deepening
1, 2, 4, 8, 16, 17, 9, 18, 19, 5, 10, 20, 21, 11
Iterative Deepening
1, 1, 2, 3, 1, 2, 4, 5, 3, 6, 7, 1, 2, 4, 8, 9, 5, 10, 11

33. Summary of algorithms

34. PA #1 Light’s Out Turn off all of the lights.
But switching one light switches all lights immediately adjacent to it.

35. PA#1 You can play a version online at:

36. PA #1 READ the specific requirements
Can use any language that I can run in the labs. (But I strongly suggest python or Java).
Should print an optimal path, the number of nodes considered so far, and the number of nodes in memory at the end.
Must follow naming conventions listed in assignment. (File named LightsOut, method named search)

37. PA #1

38. PA #1