CS 331: Artificial Intelligence function MAX-VALUE( state , , ) - - PDF document

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CS 331: Artificial Intelligence function MAX-VALUE( state , , ) - - PDF document

4/19/2019 ALPHA-BETA Pseudocode function ALPHA-BETA-SEARCH( state ) returns an action inputs : state , current state in game v MAX -VALUE( state , - , +) return the action in SUCCESSORS( state ) with value v CS 331: Artificial


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CS 331: Artificial Intelligence Alpha-Beta Practice

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ALPHA-BETA Pseudocode

function ALPHA-BETA-SEARCH(state) returns an action inputs: state, current state in game v ← MAX-VALUE(state, -∞, +∞) return the action in SUCCESSORS(state) with value v function MAX-VALUE(state, , ) returns a utility value inputs: state, current state in game , the value of the best alternative for MAX along the path to state , the value of the best alternative for MIN along the path to state if TERMINAL-TEST(state) then return UTILITY(state) v ← -∞ for a, s in SUCCESSORS(state) do v ← MAX(v, MIN-VALUE(s, , )) if v ≥  then return v  ← MAX(, v) return v

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ALPHA-BETA Pseudocode

function MIN-VALUE(state, , ) returns a utility value inputs: state, current state in game , the value of the best alternative for MAX along the path to state , the value of the best alternative for MIN along the path to state if TERMINAL-TEST(state) then return UTILITY(state) v ← +∞ for a, s in SUCCESSORS(state) do v ← MIN(v, MAX-VALUE(s, , )) if v ≤  then return v  ← MIN(, v) return v

Run Alpha-Beta Pruning

MAX MIN 7 MAX 6 8

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2 1

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Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞)

5

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞)

6

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SLIDE 2

4/19/2019 2

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞)

7

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7

8

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞)

9

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7

10

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7)

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Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
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(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7)

12

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SLIDE 3

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Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8

13

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8

14

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7

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Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞)

16

Solution

MAX MIN 7 MAX 6 8

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2 1

  • 15
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(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞)

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A B C D E F G

Solution

MAX MIN 7 MAX 6 8

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2 1

  • 15
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(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞) (7, +∞)

18

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SLIDE 4

4/19/2019 4

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞) (7, +∞) (7, +∞)

19

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞) (7, +∞) (7, +∞) 2

20

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞) (7, +∞) (7, +∞) 2 2

21

Solution

MAX MIN 7 MAX 6 8

  • 10

2 1

  • 15
  • 10

(−∞, +∞) (−∞, +∞) (−∞, +∞) 7 (7, +∞) 7 (−∞, 7) (−∞, 7) 8 7 (7, +∞) (7, +∞) (7, +∞) 2 2

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