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Your chance to review

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.

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Your chance to review

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  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*/)

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