Alice and Bob want to play the following game by alternating turns: They have access to a row of n coins of values v1,..., Vn, where n is even. In each turn, a player selects either the first or the last coin from the row, removes it from the row, and receives the value of the coin. Alice starts the game. Devise a dynamic programming algorithm to determine the maximum possible amount of money Alice can definitely win (assume that Bob will play in such a way to maximize the amount he gets). State a O(.)

Alice and Bob want to play the following game by alternating turns: They have access to a row of n coins of values v1,..., Vn, where n is even. In each turn, a player selects either the first or the last coin from the row, removes it from the row, and receives the value of the coin. Alice starts the game. Devise a dynamic programming algorithm to determine the maximum possible amount of money Alice can definitely win (assume that Bob will play in such a way to maximize the amount he gets). State a O(.)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 12RP

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