Problems Problem Spaces Problems, Problem Spaces, and Search Ahmed - - PowerPoint PPT Presentation

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Problems Problem Spaces Problems, Problem Spaces, and Search Ahmed - - PowerPoint PPT Presentation

Mar 03, 2024 216 likes •311 views

Problems Problem Spaces Problems, Problem Spaces, and Search Ahmed Rafea Ahmed Rafea Problem Solving Steps Problem Solving Steps Define the Problem precisely Analyze the problem Analyze the problem Isolate and represent the task

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SLIDE 1

Problems Problem Spaces Problems, Problem Spaces, and Search

Ahmed Rafea Ahmed Rafea

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SLIDE 2

Problem Solving Steps Problem Solving Steps

  • Define the Problem precisely
  • Analyze the problem

Analyze the problem

  • Isolate and represent the task knowledge
  • Choose the best problem solving technique
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Defining the Problem as a State Space Search

E l W t J P bl

  • Example ‐ Water Jug Problem
  • You are given two jugs, a 4‐gallon one and a 3‐

gallon one gallon one.

  • Neither has any measuring markers on it.

Th i h b d fill h j

  • There is a pump that can be used to fill the jugs

with water. H t tl 2 ll f t i t

  • How can you get exactly 2 gallons of water into

the 4‐gallon jug?

  • initial state (0 0)
  • initial state (0,0)
  • goal state (2,n)
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SLIDE 4

Operators Operators

1 if <4 > (4 ) 1. if x<4 ‐> (4,y) 2. if y<3 ‐> (x,3) 3. if x>0 ‐> (x‐d,y) 4. if y>0 ‐> (x,y‐d) 5. if x>0 ‐> (0,y) 6 if y>0 > (x 0) 6. if y>0 ‐> (x,0) 7. if x+y>=4 and y>0 ‐> (4,y‐(4‐x)) 8. if x+y>=3 and x>0 ‐> (x‐(3‐y),3) 9. if x+y<=4 and y>0 ‐> ((x+y),0)

  • 10. if x+y<=3 and x>0 ‐> (0,x+y)

11 (0 2) ‐> (2 0)

  • 11. (0,2) > (2,0)
  • 12. (2,y) ‐> (y,2)
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Algorithm : Breadth First Search Algorithm : Breadth‐First Search

(0,0)

  • |

| (4.0) (0,3) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ | | | | | | (4,3) (0,0) (3,1) (3,0) (4,3) (0,0)

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Algorithm : Depth First Search Algorithm : Depth‐First Search

(0,0)

  • |

| (4.0) (0,3) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ | | | (4,3) (0,0) (3,1)

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Advantage of Depth First Search Advantage of Depth‐First Search

  • Less Memory
  • By chance, it may find a solution without

By chance, it may find a solution without examining much of the search space at all

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Advantage of Breadth‐First Search

  • It will not get trapped exploring a blind alley
  • If there is a solution then BFS is guaranteed to

If there is a solution then BFS is guaranteed to find it If h l i l l i i i l

  • If there are multiple solution, a minimal

solution will be found