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Re: Turning a Sequence into a List?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130501] Re: Turning a Sequence into a List?
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Tue, 16 Apr 2013 04:22:24 -0400 (EDT)
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v = Range[24,30]; 
sol = Reduce[25q + 10d + 5n + p == # && 0 <= p < 5 && 0 <= n < 2 && 
             0 <= d < 3 && 0 <= q < 4, {q,d,n,p}, Integers]& /@v

{q == 0 && d == 2 && n == 0 && p == 4,
 (q == 0 && d == 2 && n == 1 && p == 0) || (q == 1 && d == 0 && n == 0 && p == 0),
 (q == 0 && d == 2 && n == 1 && p == 1) || (q == 1 && d == 0 && n == 0 && p == 1),
 (q == 0 && d == 2 && n == 1 && p == 2) || (q == 1 && d == 0 && n == 0 && p == 2),
 (q == 0 && d == 2 && n == 1 && p == 3) || (q == 1 && d == 0 && n == 0 && p == 3),
 (q == 0 && d == 2 && n == 1 && p == 4) || (q == 1 && d == 0 && n == 0 && p == 4),
 q == 1 && d == 0 && n == 1 && p == 0}

ToRules@If[ Head@# === And, #, If[ 
  Plus@@#[[1,All,2]] < Plus@@#[[2,All,2]], #[[1]], #[[2]] ] ]& /@ sol

{{q -> 0, d -> 2, n -> 0, p -> 4},
 {q -> 1, d -> 0, n -> 0, p -> 0},
 {q -> 1, d -> 0, n -> 0, p -> 1},
 {q -> 1, d -> 0, n -> 0, p -> 2},
 {q -> 1, d -> 0, n -> 0, p -> 3},
 {q -> 1, d -> 0, n -> 0, p -> 4},
 {q -> 1, d -> 0, n -> 1, p -> 0}}

On Mon, Apr 15, 2013 @ 09:35 PM, Rob <rob at piovere.com> wrote:

> 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 
> (later I'll use v =  Range[1,99].
> 
> v=Range[52,53];
> sol=(Reduce[25q+10d+5n+p==# &&0<=p<5 &&0<=n<2 &&0<=d<3 
> &&0<=q<4,{q,d,n,p},Integers])& /@v
> 
> (* which gives {(q == 1 && d == 2 && n == 1 && p == 2) || (q == 2 &&
>      d == 0 && n == 0 && p == 2), (q == 1 && d == 2 && n == 1 &&
>      p == 3) || (q == 2 && d == 0 && n == 0 && p == 3)} *)
> 
> There are two cases for each coin and I need to pick the one with the 
> smallest number of coins. But the only way I know to begin that is with 
> a list of rules. I can get a Sequence for the first element of the List 
> sol but I can't figure how to get the Sequence to a list.
> 
> x = (sol[[1]]) // ToRules
> (* Sequence[{q -> 1, d -> 2, n -> 1, p -> 2}, {q -> 2, d -> 0, n -> 0,  
> p -> 2}] *)
> 
> I've always had problems figuring out what a Sequence is and the HELP 
> doesn't really help me. Can someone please suggest how I can use this 
> sequence to select the {q,d,n,p} set that has the minimum coin count? 
> It's got me stumped. Thanks.



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