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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.

Solution

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

- Depth First
- Trick Question
- 1, 2, 4, 8, 16, 32, ….

Properties of Depth-first Search

- Complete??

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

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??

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.

Properties of Depth-first Search

- Optimal?? No.
- Time??

Properties of Depth-first Search

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

Properties of Depth-first Search

- 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??

Properties of Depth-first Search

- 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!

Properties of Breadth-First Search

- Complete??

Properties of Breadth-First Search

- Complete?? Yes (if b is finite)

Properties of Breadth-First Search

- Complete?? Yes (if b is finite)
- Optimal??

Properties of Breadth-First Search

- Complete?? Yes (if b is finite)
- Optimal?? Yes (if cost = 1 per step); not optimal in general

Properties of Breadth-First Search

- Complete?? Yes (if b is finite)
- Optimal?? Yes (if cost = 1 per step); not optimal in general
- Time??

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

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??

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)

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.

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 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

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.

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.

Uniform-cost Search

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

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??

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

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??

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)

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??

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

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??

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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