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Re: Turning a Sequence into a List?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg130643] Re: Turning a Sequence into a List?
*From*: Dana DeLouis <dana01 at me.com>
*Date*: Sun, 28 Apr 2013 01:01:19 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-outx@smc.vnet.net
*Delivered-to*: mathgroup-newsendx@smc.vnet.net
> Hello, I'm playing with a problem with minimum coins to make change.
> Here's a problem spot where I look at ways to make up 52 and 53 cents
> <snip>
> (later I'll use v = Range[1,99].
Hi. This doesn't quite answer your question, but I've always found this interesting.
One can find All combinations, say up to 100, very quickly with the following.
Then, a specific combination is quickly found because all the hard work is already done.
Here's the generating function for all combinations:
gf = 1 / Times@@(1-{p,n,d,q} *x^{1,5,10,25});
// Find them all up to 100:
equ=ExpandAll[Series[gf,{x,0,100}]];
// Here are all the ways to make 11.
// (d p means 1 dime and 1 penny)
// (n^2 p means 2 nickels and one penny)
List@@Coefficient[equ,x,11]
{d p,n^2 p,n p^6,p^11}
The 49 combinations for 52 are:
List@@Coefficient[equ,x,52]
{d^5 p^2,d^4 n^2 p^2,d^3 n^4 p^2,=85 <snip > ,p^27 q,p^2 q^2}
The smallest number of coins has the smallest sum of exponents.
ie q^2 p^2 -> 2+2 = 4
Again=85 just interesting.
= = = = = = = = = =
HTH :>)
Dana DeLouis
Mac & Mathematica 9
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