# Homework 12 - Pablo Blanco
# OK to post

read(`C12.txt`):

# AveLuckyVertexFriends(9,100);
# 197/25

AveLuckyVertexFriends:=proc(n,K) local S,TotFriends,v,FriendsOfLucky,i,j,A:
 TotFriends:=0:
 A:=AM(Ck(n)):
 for i from 1 to K do: 
  S:=combinat[randcomb](2^n,2^(n-1)+1):
  v:=LuckyVertex(n,S):
  FriendsOfLucky:= add(A[j][v] ,j in S):
  if FriendsOfLucky < evalf(sqrt(n)) then
   error "Violates sensitivity lemma!":
  fi:
  TotFriends+=FriendsOfLucky:
 od:

 TotFriends/K:
end: