#OK to post homework

#Zidong Zhang, 31/1/2021, Assignment 2


with(combinat):

#SetToVec(S,n): that inputs a subset S of {1,...,n} and outputs the 0-1 vector of length n #such that v[i]=1 iff i belongs to S. Be sure to check that the input is legal (i.e. that S is #indeed a set, and that n is a non-neg. integer and that S is indeed a subset of {1,...,n}.

SetToVec := proc(S,n) local i,j,v:

if not (type(S,set)  and n>=0) then
	print(`illegal input!`):
	RETURN(FAIL):
fi:

if not  S subset {seq(i, i =1..n)}=true then
	print(`wrong input`):
	RETURN(FAIL):
fi:

v:=[]:

for j from 1 to n do 
	if j in S then
		v := [op(v),1]:
	else 
		v := [op(v),0]:
fi: 
od:
v:
end:


#VecToSet(v): that inputs a 0-1 vector v and outputs the subset of {1,...,n} (where n=nops#(v)) such that v[i]=1 iff i belongs to S.


VecToSet := proc(v) local i,s,j,n:

n:=nops(v):

for i from 1 to n do
	if  v[i]>1 then
		print(`entries of v should either 0 or 1`):
		RETURN(FAIL):
		
	fi:
od:

s :={}:

for j from 1 to nops(v) do 
	if v[j] = 1 then
		s := s union {j}:
	fi:
od:
s:

end:



#CheckBij(n): that checks that SetToVec(VecToSet(v),n)=v is always true for each member #of Box([1$n]) and VecToSet(SetToVec(S,n))=S for each member of MyPS({seq(i,i=1..n)}) .

CheckBij := proc(n) local v,i,j,S,k:

v := [seq(rand(0..1)(), i =1..n)]:


if SetToVec(VecToSet(v),n) = v then 
	print(`SetToVec(VecToSet(v),n) = v  is true.`):
	
else
	print(`SetToVec(VecToSet(v),n) = v is not true.`):
	
fi:

S := MyPS({seq(j,j=1..n)}):
for k from 1 to nops(S) do

if VecToSet(SetToVec(S[k],n))=S[k] then
	print(`VecToSet(SetToVec(S,n))=S is true for each member of MyPS({seq(i,i=1..n)})`):
	RETURN(TRUE):
else
	print(`VecToSet(SetToVec(S[k],n))=S[k] is false for each member of MyPS({seq(i,i=1..n)})`):
	RETURN(FALSE):
fi:
od:
end: