问题
We usually the following recurrence relation for the coin change problem:
(P is the total money for which we need change and d_i is the coin available)
But can't we make it like this:
(V is the given sorted set of coins available, i and j are its subscripts with Vj being the highest value coin given)
C[p,Vi,j] = C[p,Vi,j-1] if Vj > p
= C[p-Vj,Vi,j] + 1 if Vj <=p
Is there anything wrong with what I wrote? Though the solution is not dynamic but isn't it more efficient?
回答1:
Consider P = 6, V = {4, 3, 1}. You would pick 4, 1, 1 instead of 3, 3, so 3 coins instead of the optimal 2.
回答2:
What you've written is similar to the greedy algorithm that works only under certain conditions. (See - How to tell if greedy algorithm suffices for finding minimum coin change?).
Also, in your version you aren't actually using Vi within the recurrence, so it's just a waste of memory
来源：https://stackoverflow.com/questions/13075242/coin-change-dynamic-programming