Consider the game tree given below: Here ◯ and ◻ represents MIN and MAX nodes…

2019

Consider the game tree given below:

Here ◯ and ◻ represents MIN and MAX nodes respectively. The value of the root node of the game tree is

  1. A.

    14

  2. B.

    17

  3. C.

    111

  4. D.

    112

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Correct answer: B

Solution: Evaluate the tree from bottom to top using the minimax algorithm.

Rules:

- MIN nodes choose the smaller value among their children.

- MAX nodes choose the larger value among their children.

Step 1: Evaluate the lowest-level MIN nodes

From the visible leaf values in the image:

- min(17, 19) = 17

- min(16, 111) = 16

- min(111, 112) = 111

- min(15, 14) = 14

Step 2: Evaluate the MAX nodes above them

- max(17, 16) = 17

- max(111, 112) = 112

- max(15, 14) = 15

Step 3: Evaluate the upper MIN nodes

- Left MIN node: min(17, 112) = 17

- Right MIN node: min(15, 14) = 14

Step 4: Evaluate the root MAX node

- max(17, 14) = 17

Final Answer: 17

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