Probabilistic Polynomial Solution for Exact Three Cover

from itertools import groupby
import random
from itertools import combinations
from itertools import permutations

s = 1,2,3,4,5,6,7,8,9
c = [[1,2,3],[4,5,7],[4,5,6],[1,2,8],[7,8,9],[1,2,4],[1,2,5],[1,2,7],[1,4,5]]

# I am creating a value
# so that I can break in
# an upcoming while loop

xx = s * 2
combinations_count = 0
for i in combinations(xx, 3):
    combinations_count = combinations_count + 1


if len(s) % 3 != 0:
    print('invalid input')
    quit()

ss = s

# Sort list to remove
# sets like (1,2,3) and (1,3,2)
# but leave (1,2,3)

delete = []
for a in range(0, len(c)):
    for i in permutations(c[a], 3):
        if list(i) in c[a:]:
            if list(i) != c[a]:
                delete.append(list(i))

for a in range(0, len(delete)):
    if delete[a] in c:
        del c[c.index(delete[a])]


# remove sets
# that have
# repeating
# elements

remove = []
for rem in range(0, len(c)):
    if len(c[rem]) != len(set(c[rem])):
        remove.append(c[rem])

for rem_two in range(0, len(remove)):
    if remove[rem_two] in c:
        del c[c.index(remove[rem_two])]

# remove sets
# that have
# elements
# that don't
# exist in S.

remove=[]
for j in range(0, len(c)):
   for jj in range(0, len(c[j])):
        if any(elem not in s for elem in c[j]):
            remove.append(c[j])

for rem_two in range(0, len(remove)):
    if remove[rem_two] in c:
        del c[c.index(remove[rem_two])]


# Remove repeating sets

solutions =[c[x] for x in range(len(c)) if not(c[x] in c[:x])]


c = solutions


length = len(solutions)
ss = s

# while loop to see
# if we can find
# an Exact Three Cover
# in poly-time.

stop = 0
w = 0
new = []

# Shuffle these
# annoying
# counter-examples
# that might ruin
# my day


print('Initalizing', combinations_count,'shuffles')
for a in range(0, combinations_count):
    random.shuffle(c)


stop = 0

while True:

    # Shuffling c randomly
    # to reduce chance of
    # error.

    random.shuffle(c)


    if len(new) == len(ss) // 3:
        # break if Exact
        # three cover is
        # found.
        #print(new)
        w = w + 1
        print(new, 'yes')
        print('took',stop,'steps in while loop')
        break



    # Keep c[0]
    # and append to
    # end of list
    # del c[0]
    # to push >>
    # in list.

    c.append(c[0])
    del [c[0]]
    new = []
    s = set()
    stop = stop + 1
    for l in c:
        if not any(v in s for v in l):
            new.append(l)
            s.update(l)


    if len(new) != len(ss)//3:
        if stop == length:
          # Reverse list just
          # to reduce false -/+
          # answer.
         for cc in range(0, len(c)):
              c = list(reversed(c))
              random.shuffle(c)
    if stop >= combinations_count:
        print('no')
        break