Talk:Fairshare between two and more

Perl 6 count of how many turns each person gets

Whilst important to some degree, the sequence minimises any advantage that going first/going earlier might give. I've blogged twice, here, and here about it and the sequence appears many times in science and maths. (Try this paper (PDF), for example. --Paddy3118 (talk) 23:54, 1 February 2020 (UTC)

I have to say, I kind of missed the point of the task initially so was not really sure what it was demonstrating. The actual algorithm was simple, the reason for it escaped me. After reading your links, the lightbulb lit. I removed the "number of times each person goes" which was kind-of pointless, and added a "fairness correlation" calculation showing the relative fairness to the Perl 6 entry. --Thundergnat (talk) 13:43, 2 February 2020 (UTC)

Great :-)
--Paddy3118 (talk) 18:26, 2 February 2020 (UTC)

I tried to clearify things to me, like Paddy3118 described in his links.Without different values, it makes no sense.
The first will get the highest value of a bucket, the second the maximum of left over and so on.I use a bucket of size Peoplecnt and the values are PeopleCnt downto 1.The choosen people grabs one value from Top.After all people are finished the game starts again ( MOD peoplecnt). <lang pascal>program Fair;

{$IFDEF FPC}

 {$MODE DELPHI}
 {$OPTIMIZATION ON,ALL}
 {$CodeAlign proc=8}

{$ELSE}

 {$APPTYPE CONSOLE}

{$ENDIF}

const

  cntbasedigits = 21;

type

 tSumDigit = record
               sdSumDig  : NativeUint;
               sdBase    : NativeUint;
               sdNumber  : NativeUint;
               sdDigits  : array[0..cntbasedigits-1] of NativeUint;
             end;

var

 SumWealth : array of NativeUint;
 Values : array of NativeUint;

function InitSumDigit(n,base : NativeUint):tSumDigit; var

 sd : tSumDigit;
 qt : NativeUint;
 i  : integer;

begin

 with sd do
 begin
   sdNumber:= n;
   sdBase := base;
   fillchar(sdDigits,SizeOf(sdDigits),#0);
   sdSumDig :=0;
   i := 0;
   // calculate Digits und sum them up
   while n > 0 do
   begin
     qt := n div sdbase;
     {n mod base}
     sdDigits[i] := n-qt*sdbase;
     inc(sdSumDig,sdDigits[i]);
     n:= qt;
     inc(i);
   end;
 end;
 InitSumDigit:=sd;

end;

procedure IncSumDigit(var sd:tSumDigit); var

  i,d: integer;

begin

 i := 0;
 with sd do
 begin
   inc(sdNumber);
   repeat
     d := sdDigits[i];
     inc(d);
     inc(sdSumDig);
     //base-1 times the repeat is left here
     if d < sdbase then
     begin
       sdDigits[i] := d;
       BREAK;
     end
     else
     begin
       sdDigits[i] := 0;
       dec(sdSumDig,sdbase);
       inc(i);
     end;
   until i > high( sdDigits);
 end;

end;

procedure First25(base:NativeUint); var

 MySumDig : tSumDigit;
 cnt: NativeUint;

begin

 write(' [',base:5,'] -> ');
 MySumDig:=InitSumDigit(0,base);
 cnt := 0;
 repeat
   with MySumDig do
     write(sdSumDig MOD sdbase,'-');
   inc(cnt);
   IncSumDigit(MySumDig);
 until cnt >= 25;
 writeln('....');

end;

procedure CheckRoundsOfPeople(turns,peopleCnt:NativeUint); var

 MySumDig : tSumDigit;
 i,
 wholeWealth,
 minWealth,
 maxWealth  : NativeUint;

Begin

 setlength(SumWealth,peopleCnt);
 setlength(Values,peopleCnt);
 //Values[0] =  peopleCnt ...Values[peopleCnt-1] = 1
 For i := 0 to peopleCnt-1 do
   Values[i] := peopleCnt-i;

 MySumDig:=InitSumDigit(0,peopleCnt);
 i := 0;
 while i<turns do
 begin
   inc(SumWealth[MySumDig.sdSumDig MOD peopleCnt],Values[i MOD peopleCnt]);
   IncSumDigit(MySumDig);
   inc(i);
 end;
 setlength(Values,0);
 MinWealth := High(MinWealth);
 MaxWealth := Low(MaxWealth);
 For i := 0 to peopleCnt-1 do
 Begin
   wholeWealth := SumWealth[i];
   IF MaxWealth<wholeWealth then
     MaxWealth:=wholeWealth;
   IF MinWealth>wholeWealth then
     MinWealth := wholeWealth;
 end;
 writeln(peopleCnt:6,turns:11,MinWealth:10,MaxWealth:10, MinWealth/MaxWealth:10:7);
 setlength(SumWealth,0);

end;

procedure CheckRoundsOfPeopleOneByOne(turns,peopleCnt:NativeUint); var

 i,
 wholeWealth,
 minWealth,
 maxWealth  : NativeUint;

Begin

 setlength(SumWealth,peopleCnt);
 setlength(Values,peopleCnt);
 //Values[0] =  peopleCnt ...Values[peopleCnt-1] = 1
 For i := 0 to peopleCnt-1 do
   Values[i] := peopleCnt-i;

 i := 0;
 while i<turns do
 begin
   //first gets always the max value  0,1,2,3,4..,n
   inc(SumWealth[i MOD peopleCnt],Values[i MOD peopleCnt]);
   inc(i);
 end;
 setlength(Values,0);
 MinWealth := High(MinWealth);
 MaxWealth := Low(MaxWealth);
 For i := 0 to peopleCnt-1 do
 Begin
   wholeWealth := SumWealth[i];
   IF MaxWealth<wholeWealth then
     MaxWealth:=wholeWealth;
   IF MinWealth>wholeWealth then
     MinWealth := wholeWealth;
 end;
 writeln(peopleCnt:6,turns:11,MinWealth:10,MaxWealth:10, MinWealth/MaxWealth:10:7);
 setlength(SumWealth,0);

end;

const

 cTURNS = 500;

begin

 First25(2);First25(3);First25(5); First25(11);
 writeln;
 writeln('Fair share');
 writeln(' people     turns MinWealth MaxWealth ratio MinWealth/MaxWealth');
 CheckRoundsOfPeople(11*11,11);
 CheckRoundsOfPeople(1377 *1377,1377);
 CheckRoundsOfPeople(cTURNS*11,11);
 CheckRoundsOfPeople(cTURNS*1377,1377);

 writeln;
 writeln('First gets max value , last gets 1');
 writeln(' people     turns MinWealth MaxWealth ratio MinWealth/MaxWealth');
 CheckRoundsOfPeopleOneByOne(11*11,11);
 CheckRoundsOfPeopleOneByOne(1377 *1377,1377);
 CheckRoundsOfPeopleOneByOne(cTURNS*11,11);
 CheckRoundsOfPeopleOneByOne(cTURNS*1377,1377);

end.</lang>

Output:

 [    2] -> 0-1-1-0-1-0-0-1-1-0-0-1-0-1-1-0-1-0-0-1-0-1-1-0-0-....
 [    3] -> 0-1-2-1-2-0-2-0-1-1-2-0-2-0-1-0-1-2-2-0-1-0-1-2-1-....
 [    5] -> 0-1-2-3-4-1-2-3-4-0-2-3-4-0-1-3-4-0-1-2-4-0-1-2-3-....
 [   11] -> 0-1-2-3-4-5-6-7-8-9-10-1-2-3-4-5-6-7-8-9-10-0-2-3-4-....

Fair share
 people     turns MinWealth MaxWealth ratio MinWealth/MaxWealth
    11        121        66        66 1.0000000
  1377    1896129    948753    948753 1.0000000
    11       5500      2985      3015 0.9900498
  1377     688500    125250    563750 0.2221729

First gets max value , last gets 1
//[   11] -> 0-1-2-3-4-5-6-7-8-9-10-0-1-2-3-4-5-6-7-8-9-10-0-1-2-3-....
 people     turns MinWealth MaxWealth ratio MinWealth/MaxWealth
    11        121        11       121 0.0909091
  1377    1896129      1377   1896129 0.0007262
    11       5500       500      5500 0.0909091
  1377     688500       500    688500 0.0007262

This shows the fairness.But a cyclic value of people A to C is sufficient.
The easier sequence ABC_BCA_CAB will get the same results. A,B,C are in every possible position, so square( peopleCnt) is fair too. Horst.h14:16, 25 June 2020 (UTC)