Take a look at this paper:
http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.0400v1.pdf
Dave
On Feb 7, 1:51 pm, ziyuang <ziyu...@gmail.com> wrote:
> Thank you. But can you offer your proof?
>
> On Feb 8, 3:02 am, Dave <dave_and_da...@juno.com> wrote:
>
>
>
> > 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.- Hide quoted text -
>
> - Show quoted text -
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