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There are n gold coins placed at positions{1, . . . , n}on a line.The gold coin at position i has a positive weight wi. You can pick any of the n coins, except that if you pick the gold coin at position i then you cannot pick the adjacent ones, that is,the ones at positions i-1 and i+ 1. Design a dynamic programming algorithm to compute the maximum total weight of the coins you can collect.Also explain how to compute the sequence of coins to be taken.Make your algorithm as fast as you can.

For example, if n= 3 and the gold coins have weights w1= 20, w2= 30, w3= 15, then the maximum total weight is 20 + 15 = 35 and is obtained by picking the coins at positions 1 and 3.

Reference no: EM132329220

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