4. Coins-in-a-line game: an even number, n, of coins, of various denominations from various countries, are placed in a line. Two players, who we will call Alice and Bob, take turns removing one of the coins from either end of the remaining line of coins. That is, when it is a player's turn, he or she removes the coin at the left or right end of the line of coins and adds that coin to his or her collection. The player who removes a set of coins with larger total value than the other player wins, where we assume that both Alice and Bob know the value of each coin in some common currency, such as dollars. $6 $5 $2 $7 $3 $5

Operations Research : Applications and Algorithms
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ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter17: Markov Chains
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Create an efficient java code to solve the problem by using dynamic programming

4. Coins-in-a-line game: an even number, n, of coins, of various
denominations from various countries, are placed in a line. Two players,
who we will call Alice and Bob, take turns removing one of the coins from
either end of the remaining line of coins. That is, when it is a player's
turn, he or she removes the coin at the left or right end of the line of coins
and adds that coin to his or her collection. The player who removes a set
of coins with larger total value than the other player wins, where we
assume that both Alice and Bob know the value of each coin in some
common currency, such as dollars.
$6
$5
$2
GAMES
3
$7
$3
1
2
Alice: (1, $6), (6, $5), (4, $7)
Bob: (2, $5), (5, $3), (3, $2)
Design a winning strategy for Alice (the first player).
Total value = $18
Total value = $10
10
5
$5
6
Transcribed Image Text:4. Coins-in-a-line game: an even number, n, of coins, of various denominations from various countries, are placed in a line. Two players, who we will call Alice and Bob, take turns removing one of the coins from either end of the remaining line of coins. That is, when it is a player's turn, he or she removes the coin at the left or right end of the line of coins and adds that coin to his or her collection. The player who removes a set of coins with larger total value than the other player wins, where we assume that both Alice and Bob know the value of each coin in some common currency, such as dollars. $6 $5 $2 GAMES 3 $7 $3 1 2 Alice: (1, $6), (6, $5), (4, $7) Bob: (2, $5), (5, $3), (3, $2) Design a winning strategy for Alice (the first player). Total value = $18 Total value = $10 10 5 $5 6
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