Math Problem Statement
Consider the game tree shown below. Assuming both players act optimally, use alpha-beta pruning to find the value of the root node. The search goes from left to right; when choosing which child to visit first, choose the left-most unvisited child. In the first set of boxes below, enter the values of the labeled nodes. Then, select the leaf nodes that don't get visited due to pruning. Hint: Note that the value of a node where pruning occurs is not necessarily the maximum or minimum (depending on which node) of its children. When you prune on conditions V>β V>β or V<α V<α, assume that the value of the node is V V. game tree: D's children are A, B, and C. A's children are 8,4, and 9. B's children are 3, 5, and 6. C's children are 7, 2, and 1. D is maximizing. A, B, and C are minimizing.
What are the values of nodes A, B, C, and D? What leaf values that don't get visited due to pruning?
Solution
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Math Problem Analysis
Mathematical Concepts
Game Theory
Alpha-Beta Pruning
Minimax Algorithm
Formulas
Alpha-beta pruning conditions: V > β or V < α
Theorems
Minimax Theorem
Alpha-Beta Pruning Efficiency
Suitable Grade Level
Undergraduate-Level or Advanced High School
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