Your chance to review

1. 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 and depth-first searches.

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

3. Properties of Depth-first Search • Complete??

4. 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

5. 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 • Optimal??

6. 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 • Optimal?? No.

7. 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 • Optimal?? No. • Time??

8. 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 • Optimal?? No. • Time?? O(bm): terrible if m is much larger than dbut if solutions are dense, may be much faster than breadth-first

9. 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 • Optimal?? No. • Time?? O(bm): terrible if m is much larger than dbut if solutions are dense, may be much faster than breadth-first • Space??

10. 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 • Optimal?? No. • Time?? O(bm): terrible if m is much larger than dbut if solutions are dense, may be much faster than breadth-first • Space?? O(bm), I.e., linear space!

11. Properties of Breadth-First Search • Complete??

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

13. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal??

14. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general

15. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • Time??

16. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1)= O( bd+1 ), ie, exp. in d

17. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • Time?? 1 + b + b2 + b3 + … + bd + b(bd – 1)= O( bd+1 ), ie, exp. in d • Space??

18. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • 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)

19. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • 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) • Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

20. Comparing bfs and dfs • bfs is preferred if • The branching factor is not too large (hence memory costs) • A solution appears at a relatively shallow level • No path is excessively deep • dfs is preferred if • The Tree is deep • The branching factor is not excessive • Solutions occur deeply in the tree

21. Questions?

22. 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

23. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • 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) • Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

24. Properties of Breadth-First Search • Complete?? Yes (if b is finite) • Optimal?? Yes (if cost = 1 per step); not optimal in general • 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) • Space is the big problem: can easily generate nodes at 10MB/sec, so 24hours = 860GB.

25. Problem Solving Agents

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

27. Problem Solving Agents

28. 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??

29. 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 

30. 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  • Optimal??

31. 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  • Optimal?? Yes – nodes expanded in increasing order of g(n)

32. 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  • Optimal?? Yes – nodes expanded in increasing order of g(n) • Time??

33. 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  • Optimal?? Yes – nodes expanded in increasing order of g(n) • Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution

34. 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  • Optimal?? Yes – nodes expanded in increasing order of g(n) • Time?? # of nodes with g  cost of optimal solution, O(b C*/) where C* is cost of optimal solution • Space??

35. 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  • Optimal?? Yes – nodes expanded in increasing order of g(n) • 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*/)