3. Consider the problem of moving k knights from k starting squares S₁,..., Sk to k goal squares 9₁,..., 9k, on an unbounded chessboard, subject to the rule that no two knights can land on the same square at the same time. Each action consists of moving up to k knights simultaneously. We would like to complete the maneuver in the smallest number of actions. a. What is the maximum branching factor in this state space, expressed as a function of k? b. Suppose h, is an admissible heuristic for the problem of moving knight i to goal g; by itself. Which of the following heuristics are admissible for the k-knight problem? Of those, which is the best? • min{h₁,..., hk} max{h₁,..., hk) • Σ=1ht c. Repeat (b) for the case where you are allowed to move only one knight at a time.

3. Consider the problem of moving k knights from k starting squares S₁,..., Sk to k goal squares 9₁,..., 9k, on an unbounded chessboard, subject to the rule that no two knights can land on the same square at the same time. Each action consists of moving up to k knights simultaneously. We would like to complete the maneuver in the smallest number of actions. a. What is the maximum branching factor in this state space, expressed as a function of k? b. Suppose h, is an admissible heuristic for the problem of moving knight i to goal g; by itself. Which of the following heuristics are admissible for the k-knight problem? Of those, which is the best? • min{h₁,..., hk} max{h₁,..., hk) • Σ=1ht c. Repeat (b) for the case where you are allowed to move only one knight at a time.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter14: Game Theory

Section14.3: Linear Programming And Zero-sum Games

Problem 9P

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