Computers and Technology, 06.05.2020 03:05 yeehaw777
Consider the problem of making change for n cents using the fewest number of coins. Assume that each coin's value is an integer.
a. Suppose that the available coins are in the denominations that are powers of c, i. e., the denominations are c0 ; c1; …; ck for some integers c > 1 and k _ 1. Show that the greedy algorithm of picking the largest denomination first always yields an optimal solution. You are expected to reason about why this approach gives an optimal solution. (Hint: Show that for each denomination ci, the optimal solution must have less than c coins.)
b. Design an Ο(nk) time algorithm that makes a change for any set of k different coin denominations, assuming that one of the coins is 3 cents in value.
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