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Given an unlimited supply of coins of denominations x1, x2, . . . , xn, we wish to make change for a value v; that is, we wish to find a set of coins whose total value is v. This might not be possible: for instance, if the denominations are 5 and 10 then we can make change for 15 but not for 12. Give an O(nv) dynamic-programming algorithm for the following problem.
Input: x1,...,xn;v.
Question: Is it possible to make change for v using coins of denominations x1, . . . , xn?
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