Re: Efficient algorithm?
- From: "Mitch" <maharri@xxxxxxxxx>
- Date: 19 Mar 2007 13:02:46 -0700
On Mar 18, 9:12 pm, "Ez_Alg" <virtualreal...@xxxxxxxxx> wrote:
Given an unlimited supply of coins of denominations x1; x2; : : : ;
xn, we wish to make change for a value v using at most k coins; that
is, we wish to find a set of k coins whose total value is v.
This might not be possible: for instance, if the denominations are 5
and 10 and k = 6, then we can make change for 55 but not for 65. what
is an efficient dynamic-programming algorithm for the following
problem.
Input: x1; : : : ; xn; k; v.
Question: Is it possible to make change for v using at most k coins,
of denominations x1; : : : ; xn?
any help would be appriciated.
Dynamic programming means remember results on (structured) subsets of
the input. Often (as is probably best in this case) you'll remember it
in a table. What do you think your table should look like?
Now... how do you fill out that table? Consider denomination 'xn'.
There's a solution for v using a single coin of size xn if...what?
(that's gives you your recursive function to help compute the table).
Mitch
.
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