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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
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31
Task/Topswops/00DESCRIPTION
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Topswops is a card game created by John Conway in the 1970's.
Assume you have a particular permutation of a set of n cards numbered 1..n on both of their faces, for example the arrangement of four cards given by [2, 4, 1, 3] where the leftmost card is on top. A round is composed of reversing the first m cards where m is the value of the topmost card. rounds are repeated until the topmost card is the number 1 and the number of swaps is recorded. For our example the swaps produce:
<pre> [2, 4, 1, 3] # Initial shuffle
Assume you have a particular permutation of a set of &nbsp; n &nbsp; cards numbered &nbsp; 1..n &nbsp; on both of their faces, for example the arrangement of four cards given by &nbsp; [2, 4, 1, 3] &nbsp; where the leftmost card is on top.
A round is composed of reversing the first &nbsp; m &nbsp; cards where &nbsp; m &nbsp; is the value of the topmost card.
Rounds are repeated until the topmost card is the number &nbsp; 1 &nbsp; and the number of swaps is recorded.
For our example the swaps produce:
<pre>
[2, 4, 1, 3] # Initial shuffle
[4, 2, 1, 3]
[3, 1, 2, 4]
[2, 1, 3, 4]
[1, 2, 3, 4]</pre>
For a total of four swaps from the initial ordering to produce the terminating case where 1 is on top.
[1, 2, 3, 4]
</pre>
For a total of four swaps from the initial ordering to produce the terminating case where &nbsp; 1 &nbsp; is on top.
For a particular number <code>n</code> of cards, <code>topswops(n)</code> is the maximum swaps needed for any starting permutation of the n cards.
For a particular number &nbsp; <code> n </code> &nbsp; of cards, &nbsp; <code> topswops(n) </code> &nbsp; is the maximum swaps needed for any starting permutation of the &nbsp; <code>n</code> &nbsp; cards.
;Task:
The task is to generate and show here a table of <code>n</code> vs <code>topswops(n)</code> for n in the range 1..10 inclusive.
The task is to generate and show here a table of &nbsp; <code> n </code> &nbsp; vs &nbsp; <code> topswops(n) </code> &nbsp; for &nbsp; <code> n </code> &nbsp; in the range &nbsp; 1..10 &nbsp; inclusive.
;Note:
[[oeis:A000375|Topswops]] is also known as [http://www.haskell.org/haskellwiki/Shootout/Fannkuch Fannkuch] from the German Pfannkuchen meaning [http://youtu.be/3biN6nQYqZY pancake].
[[oeis:A000375|Topswops]] is also known as &nbsp; [http://www.haskell.org/haskellwiki/Shootout/Fannkuch Fannkuch] &nbsp; from the German Pfannkuchen meaning &nbsp; [http://youtu.be/3biN6nQYqZY pancake].
;Cf.
;Related tasks:
* [[Number reversal game]]
* [[Sorting algorithms/Pancake sort]]
<br><br>

121
Task/Topswops/360-Assembly/topswops.360 Normal file
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* Topswops optimized 12/07/2016
TOPSWOPS CSECT
USING TOPSWOPS,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) prolog
ST R13,4(R15) " <-
ST R15,8(R13) " ->
LR R13,R15 " addressability
MVC N,=F'1' n=1
LOOPN L R4,N n; do n=1 to 10 ===-------------==*
C R4,=F'10' " *
BH ELOOPN . *
MVC P(40),PINIT p=pinit
MVC COUNTM,=F'0' countm=0
REPEAT MVC CARDS(40),P cards=p -------------------------+
SR R11,R11 count=0 |
WHILE CLC CARDS,=F'1' do while cards(1)^=1 ---------+
BE EWHILE . |
MVC M,CARDS m=cards(1)
L R2,M m
SRA R2,1 m/2
ST R2,MD2 md2=m/2
L R3,M @card(mm)=m
SLA R3,2 *4
LA R3,CARDS-4(R3) @card(mm)
LA R2,CARDS @card(i)=0
LA R6,1 i=1
LOOPI C R6,MD2 do i=1 to m/2 -------------+
BH ELOOPI . |
L R0,0(R2) swap r0=cards(i)
MVC 0(4,R2),0(R3) swap cards(i)=cards(mm)
ST R0,0(R3) swap cards(mm)=r0
AH R2,=H'4' @card(i)=@card(i)+4
SH R3,=H'4' @card(mm)=@card(mm)-4
LA R6,1(R6) i=i+1 |
B LOOPI ----------------------------+
ELOOPI LA R11,1(R11) count=count+1 |
B WHILE -------------------------------+
EWHILE C R11,COUNTM if count>countm
BNH NOTGT then
ST R11,COUNTM countm=count
NOTGT BAL R14,NEXTPERM call nextperm
LTR R0,R0 until nextperm=0 |
BNZ REPEAT ---------------------------------+
L R1,N n
XDECO R1,XDEC edit n
MVC PG(2),XDEC+10 output n
MVI PG+2,C':' output ':'
L R1,COUNTM countm
XDECO R1,XDEC edit countm
MVC PG+3(4),XDEC+8 output countm
XPRNT PG,L'PG print buffer
L R1,N n *
LA R1,1(R1) +1 *
ST R1,N n=n+1 *
B LOOPN ===------------------------------==*
ELOOPN L R13,4(0,R13) epilog
LM R14,R12,12(R13) " restore
XR R15,R15 " rc=0
BR R14 exit
PINIT DC F'1',F'2',F'3',F'4',F'5',F'6',F'7',F'8',F'9',F'10'
CARDS DS 10F cards
P DS 10F p
COUNTM DS F countm
M DS F m
N DS F n
MD2 DS F m/2
PG DC CL20' ' buffer
XDEC DS CL12 temp
*------- ---- nextperm ----------{-----------------------------------
NEXTPERM L R9,N nn=n
SR R8,R8 jj=0
LR R7,R9 nn
BCTR R7,0 j=nn-1
LTR R7,R7 if j=0
BZ ELOOPJ1 then skip do loop
LOOPJ1 LR R1,R7 do j=nn-1 to 1 by -1; j ----+
SLA R1,2 . |
L R2,P-4(R1) p(j)
C R2,P(R1) if p(j)<p(j+1)
BNL PJGEPJP then
LR R8,R7 jj=j
B ELOOPJ1 leave j |
PJGEPJP BCT R7,LOOPJ1 j=j-1 ---------------------+
ELOOPJ1 LA R7,1(R8) j=jj+1
LOOPJ2 CR R7,R9 do j=jj+1 while j<nn ------+
BNL ELOOPJ2 . |
LR R2,R7 j
SLA R2,2 .
LR R3,R9 nn
SLA R3,2 .
L R0,P-4(R2) swap p(j),p(nn)
L R1,P-4(R3) "
ST R0,P-4(R3) "
ST R1,P-4(R2) "
BCTR R9,0 nn=nn-1
LA R7,1(R7) j=j+1 |
B LOOPJ2 ----------------------------+
ELOOPJ2 LTR R8,R8 if jj=0
BNZ JJNE0 then
LA R0,0 return(0)
BR R14 "
JJNE0 LA R7,1(R8) j=jj+1
LR R2,R7 j
SLA R2,2 r@p(j)
LR R3,R8 jj
SLA R3,2 r@p(jj)
LOOPJ3 L R0,P-4(R2) p(j) ----------------------+
C R0,P-4(R3) do j=jj+1 while p(j)<p(jj) |
BNL ELOOPJ3
LA R2,4(R2) r@p(j)=r@p(j)+4
LA R7,1(R7) j=j+1 |
B LOOPJ3 ----------------------------+
ELOOPJ3 L R1,P-4(R3) swap p(j),p(jj)
ST R0,P-4(R3) "
ST R1,P-4(R2) "
LA R0,1 return(1)
BR R14 ---------------}-----------------------------------
YREGS
END TOPSWOPS

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Task/Topswops/Elixir/topswops.elixir Normal file
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defmodule Topswops do
def get_1_first( [1 | _t] ), do: 0
def get_1_first( list ), do: 1 + get_1_first( swap(list) )
defp swap( [n | _t]=list ) do
{swaps, remains} = Enum.split( list, n )
Enum.reverse( swaps, remains )
end
def task do
IO.puts "N\ttopswaps"
Enum.map(1..10, fn n -> {n, permute(Enum.to_list(1..n))} end)
|> Enum.map(fn {n, n_permutations} -> {n, get_1_first_many(n_permutations)} end)
|> Enum.map(fn {n, n_swops} -> {n, Enum.max(n_swops)} end)
|> Enum.each(fn {n, max} -> IO.puts "#{n}\t#{max}" end)
end
def get_1_first_many( n_permutations ), do: (for x <- n_permutations, do: get_1_first(x))
defp permute([]), do: [[]]
defp permute(list), do: for x <- list, y <- permute(list -- [x]), do: [x|y]
end
Topswops.task

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Task/Topswops/Lua/topswops.lua Normal file
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-- Return an iterator to produce every permutation of list
function permute (list)
local function perm (list, n)
if n == 0 then coroutine.yield(list) end
for i = 1, n do
list[i], list[n] = list[n], list[i]
perm(list, n - 1)
list[i], list[n] = list[n], list[i]
end
end
return coroutine.wrap(function() perm(list, #list) end)
end
-- Perform one topswop round on table t
function swap (t)
local new, limit = {}, t[1]
for i = 1, #t do
if i <= limit then
new[i] = t[limit - i + 1]
else
new[i] = t[i]
end
end
return new
end
-- Find the most swaps needed for any starting permutation of n cards
function topswops (n)
local numTab, highest, count = {}, 0
for i = 1, n do numTab[i] = i end
for numList in permute(numTab) do
count = 0
while numList[1] ~= 1 do
numList = swap(numList)
count = count + 1
end
if count > highest then highest = count end
end
return highest
end
-- Main procedure
for i = 1, 10 do print(i, topswops(i)) end

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Task/Topswops/PARI-GP/topswops.pari Normal file
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flip(v:vec)={
my(t=v[1]+1);
if (t==2, return(0));
for(i=1,t\2, [v[t-i],v[i]]=[v[i],v[t-i]]);
1+flip(v)
}
topswops(n)={
my(mx);
for(i=0,n!-1,
mx=max(flip(Vecsmall(numtoperm(n,i))),mx)
);
mx;
}
vector(10,n,topswops(n))

11
Task/Topswops/Perl-6/topswops.pl6
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sub postfix:<!>(@a) {
@a == 1
?? [@a]
!! do for @a -> $a {
[ $a, @$_ ] for @a.grep(* != $a)!
}
}
sub swops(@a is copy) {
my $count = 0;
until @a[0] == 1 {
@ -14,6 +6,7 @@ sub swops(@a is copy) {
}
return $count;
}
sub topswops($n) { [max] map &swops, (1 .. $n)! }
sub topswops($n) { (sort map &swops, (1..$n).permutations)[*-1] }
say "$_ {topswops $_}" for 1 .. 10;

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Task/Topswops/PicoLisp/topswops.l Normal file
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(de fannkuch (N)
(let (Lst (range 1 N) L Lst Max)
(recur (L) # Permute
(if (cdr L)
(do (length L)
(recurse (cdr L))
(rot L) )
(zero N) # For each permutation
(for (P (copy Lst) (> (car P) 1) (flip P (car P)))
(inc 'N) )
(setq Max (max N Max)) ) )
Max ) )
(for I 10
(println I (fannkuch I)) )