//// Counting adjacencies in random shuffles of large decks

//Session file
SetLogFile("adjR.log": Overwrite := true);

//adjacency counter
numADJ := function(sd);
   s := 0;
   n := #sd;
   for  i := 1 to n-1 do
        if  Abs(sd[i]-sd[i+1]) eq 1 then s := s+1; end if;
        end for;
   return s;
   end function;

//define deck, set up "shuffle group", sample size
n := 15;
udeck := [1..n];
G := SymmetricGroup(n);
numsamp :=5000;

//average number of adjacencies
nadj := 0;
for i := 1 to numsamp do
    pi := Random(G);
    nadj := nadj+numADJ(udeck^(pi^(-1))); 
    end for;
avgADJ := nadj/numsamp;
print "avgADJ = ",avgADJ;

//probability of an adjacency
a := 0;
for i := 1 to numsamp do
    pi := Random(G);
    if numADJ(udeck^(pi^(-1))) gt 0 then a := a+1; end if; 
    end for;
probADJ := a/numsamp;
print "probADJ = ",probADJ;

//End Session
UnsetLogFile();