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# Your chance to review - PowerPoint PPT Presentation

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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• 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.

• Breadth First

• 1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11

• Depth First

• Trick Question

• 1, 2, 4, 8, 16, 32, ….

• Complete??

• Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces

• Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces

• Optimal??

• Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces

• Optimal?? No.

• Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces

• Optimal?? No.

• Time??

• 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

• 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??

• 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!

• Complete??

• Complete?? Yes (if b is finite)

• Complete?? Yes (if b is finite)

• Optimal??

• Complete?? Yes (if b is finite)

• Optimal?? Yes (if cost = 1 per step); not optimal in general

• Complete?? Yes (if b is finite)

• Optimal?? Yes (if cost = 1 per step); not optimal in general

• Time??

• 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

• 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??

• 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)

• 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.

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

• 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

• 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.

• 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.

• Expand least-cost unexpanded node

• Implementation:

• fringe = queue ordered by path cost

• Equivalent to breadth-first if step costs all equal

• Expand least-cost unexpanded node

• Implementation:

• fringe = queue ordered by path cost

• Equivalent to breadth-first if step costs all equal

• Complete??

• 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 

• 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??

• 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)

• 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??

• 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

• 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??

• 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*/)