The greedy algorithm always gives the optimal solution if:
c_1 = 1, and
c_i >= 2*c_{i-1}, i = 2, 3, ..., n.
Dave
On Feb 7, 11:35 am, ziyuang <ziyu...@gmail.com> wrote:
> The classical coin-changing problem can be stated as follow:
> Given an integer set C={c_1, c_2, ... c_n} where c_1=1 and c_i < c_{i
> +1}, and an positive integer M,
> find the minimum of \sum_{i=1}^n x_i, where all x_i's are non-negative
> integers and subject to \sum_{i=1}^n x_i c_i = M
>
> And it is well known that the problem can be solved by dynamic
> programming. Further, in some special cases a greedy strategy also
> works.
> So my question is for what kind of C (the coin system) the problem
> stated above can only be done by dp, and in what cases the other
> method can also be adopted.
>
> Thank you.
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