#OK to post homework
#Wanying Rao, 03/14/2021, Assignment 14

#1
BZ := proc(L,j) local t,n,L1:
t := nops(L):
n := sum(L[k],k=1..nops(L))+(3*j^2+j)/2:

if t+3*j >= L[1] then
 L1 := [t+3*j-1,op(L-[1$t])]:
 RETURN([L1,j-1]):
fi:

if t+3*j<L[1] then
 L1 := [op(L[2..t]+[1$(t-1)]), 1$(L[1]-3*j-t-1)]:
 RETURN([L1,j+1])
fi:

end:

#2
#ODD(n)->DIS(n)
Glashier := proc(L) local k,L1,i,j,m,b:
L1 := []:
for i in convert(L,set) do
 m := 0:
 for j from 1 to nops(L) do
  if L[j] = i then
   m := m+1:
  fi:
 od:
 b := convert(m,binary):
 for k from 1 to length(b) do
  if b mod 10^k = 10^(k-1) then
   b := b-10^(k-1):
   L1 := [op(L1),i*2^(k-1)]:
  fi: 
 od:
od:

RETURN(L1):
end:

#DIS(n)->ODD(n)
InvGlashier := proc(L) local L1,L2,i,j:
L1 := L:
L2 := []:
for i from 1 to nops(L) do
 j := 0:
 while L1[i] mod 2 = 0 do
  L1[i] := L1[i]/2:
  j := j+1:
 od:
 L2 := [op(L2),L1[i]$2^j]:
od:
 RETURN(L2):
end:

#3
#ODD(n)->DIS(n)
Sylverster := proc(L) local i,m,L1,L2:

if L=[] then
 RETURN([]):
fi:

if convert(L,set) = {1} then
 RETURN([nops(L)]):
fi:

m := 0:
for i from 1 to nops(L) do
 if L[i]=1 then
  m := m+1:
 fi:
od:

L1 := Sylverster(L[2..(nops(L)-m)]-[2$(nops(L)-m-1)]):
L2 := [(L[1]-1)/2 + nops(L), (L[1]-1)/2 + nops(L)-m - 1, op(L1)]:
end:

#DIS(n)->ODD(n)
InvSylverster := proc(L) local L1,L2,a1,m:

if L = [] then
 RETURN([]):
fi:

if nops(L) = 1 then
 RETURN([1$L[1]]):
fi:

L1 := InvSylverster(L[3..nops(L)]):
a1 := L[2]-nops(L1):
m := L[1]-L[2]-1:
L2 := [2*a1+1,op(L1+[2$nops(L1)]),1$m]:
RETURN(L2):
end: