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 = = = = = = = = = =