Coins come in a variety of values and weights. Consider a set of n coins, where each coin i has a specific value vi and a weight wi . All values are distinct. All input numbers are positive integers. When giving change that adds to a specific total T, we want to minimize the total weight of the coins given. The number available of each coin is unlimited. \

(a) Design and write, in pseudocode, a dynamic programming algorithm that will, given the information about n coins (values {vi} and weights {wi}) and a change amount T to be given, find the minimum total weight of coins whose values will add to exactly T (if such a set exists).

(b) Adapt your algorithm from (a) to find the number to be given of each coin that together produce the minimum.

(c) Analyse the running time of your algorithm from (a).