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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(.)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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(.) expression for the running time of your algorithm.
Transcribed Image Text: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(.) expression for the running time of your algorithm.
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