#OK to post homework
#Joseph Koutsoutis, 04-28-2024, Assignment 27

read `C27.txt`:

#1 done

#2

MetaZKP3 := proc(n,E,C,K) local i,ra:
 ra := rand(1..2):
 for i from 1 to K do:
  if not ZKP3(n,E,C,ra()) then return(false): fi:
 od:

 true:
end:



#TestChangeColor(n,K,T) creates T graphs of size n using RGC3 and
#changes the color of C[1] before seeing if MetaZKP3(n,E,C,20) still returns true.
#This outputs (# times MetaZKP3 returned false) / (T).
TestChangeColoring := proc(n,K,T) local c,n1,E,C,i,ra,k:
 ra := rand(1..3):
 c := 0:
 for i from 1 to T do:
  n1,E,C := RGC3(n):
  k := ra():
  while k = C[1] do k := ra(): od:
  C[1] := k:
  if not MetaZKP3(n1,E,C,K) then c++: fi:
 od:

 c/T:
end:

#TestChangeColoring(20,20,10) outputted 1, so this means that MetaZKP3 detected
#the improper colorings.

#3 I didn't attempt this challenge.