#Shaurya Baranwal, Homework 27 due on April 28, 2024


# ----------------------------
# Part 2 - MetaZKP3(n,E,C,K) |
# ----------------------------

MetaZKP3 := proc(n, E, C, K) local ra, i:

  ra := rand(1..2):
  for i from 1 to K do
    if ZKP3(n, E, C, ra()) = false then
      return false:
    fi:
  od:

true:

end:

# Testing with proper colorings
n := 0: E := 0: C := 0: success := true:

for i from 1 to 20 do
  n, E, C := RGC3(i):
  if MetaZKP3(n, E, C, 20) = false then
    success := false;
    break;
  fi:
od:

print(success); # true was the output

# Testing with improper colorings
n := 0: E := 0: C := 0: ra := rand(1..3): success := true:

for i from 1 to 20 do
  n, E, C := RGC3(i):
  C := [seq(ra(), j = 1..i)]:
  if MetaZKP3(n, E, C, 20) = false then
    success := false;
    break;
  fi:
od:

print(success); # false was the output