#OK to post homework
#Joseph Koutsoutis, 03-09-2025, Assignment 12

read `C12.txt`:

#1

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


#AveLuckyVertexFriends(9,100) outputted 7.66