#OK to post homework
#Salman Manzoor 03-09-2025, Assignment 12

with(combinat):
read `C12.txt`:

AveLuckyVertexFriends:=proc(n,K) local sum,A,H,v,i,j,frnds:
sum:=0:
A:=An(n):
for i from 1 to K do
	H:=combinat[randcomb](2^n,2^(n-1)+1):
	v:=LuckyVertex(n,H):
	frnds:=add(seq(abs(A[v][j]),j in H)):
	if evalb(frnds<evalf(sqrt(n))) then RETURN(FAIL): fi:
	sum:=sum+frnds:
od:
evalf(sum/K):
end:

#AveLuckyVertexFriends(9, 100) gave me 7.710000000