Grossmont College Dynamic Programming Coins of Denomination Computer Science Task

Description

Given an unlimited supply of coins of denomination ?1,?2,??x1,x2,8n, we wish to make change for a value ?V.

We are seeking a dynamic programming algorithm with time complexity of ?(??)O(nV) for the following problem Input: ?1,?2,??;?x1,x2,8n;V, in which ??xi (i=1,.) and ?V are all integer numbers. Question: Decide whether it is possible to make change for value ?V using coins of denominations ?1,?2,??x1,x2,8n. Note that each ??xi can be used for unlimited times.

For instance, given the denomination {5,10}{5,10}, we can make change for 15=5+1015=5+10, and for 20=10+1020=10+10, but not for 1212.

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