Max-3-cover (len(s)//3-1)

import json
from copy import deepcopy
import random

# integers only and list of lists only

s =  input("Input list of integers (no repeating elements) for S with commas (eg. 1,2,3,4...) : ").split(',')
c =  input('enter list for C (eg. [1,2,3],[4,5,6]): ')
c = json.loads(c)
s = [int(a) for a in s]
c_copy = deepcopy(c)

random.seed()
miss = []
delete = []
def input_validation():
    # checking for missing elements.
    for a in c:
        for b in a:
            miss.append(b)
    for d in s:
        if d not in miss:
            print('False', d)
    # Throw out unwanted orderings of sub-lists
    for a in range(0, len(c)):
        c[a] = sorted(c[a])
    # Lists are treated as sets, so lists
    # with repeating elements is thrown out
    for r in range(0, len(c)):
        if len(c[r]) != len(set(c[r])):
            c[r] = [['xx']]
    # Throw out lists that have elements that do
    # not exist in s.
    # Throw out lists with more than 3
    # Throw out lists less than 3
    for a in range(0, len(c)):
      for b in c[a]:
        if c[a].count(b) > 1:
          delete.append(c[a])
          break
        if len(c[a]) != 3:
          delete.append(c[a])
      for bb in c[a]:
        if bb not in s:
          delete.append(c[a])
    for b in delete:
      if b in c:
        del c[c.index(b)]

s_copy = deepcopy(s)
input_validation()

# remove repeating lists
c = [c[x] for x in range(len(c)) if not(c[x] in c[:x])]
def bijective_mapp():
    for a in range(0, len(s)):
        s[a] = a+1
    for b in range(0, len(c)):
        for bb in range(0, len(c[b])):
            c[b][bb] = s_copy.index(c[b][bb])+1
bijective_mapp()
c = [sorted(y) for y in c]
def shuff(c, n):
    for i in range(n-1,0,-1):
        j = random.randint(0,i)
        c[i],c[j] = c[j],c[i]
c.append(sorted(c[len(c)-1]))
n = len(s)
steps = n*(2**2)*((n*(2**2))-1)*((n*(2**2))-2)//6
reset = 0
c_elem = set()
set_cover = []
partial = []
for a in range(0, steps + 1):
    reset = reset + 1
    if reset > len(c):
        c_elem = set()
        reset = 0
        shuff(c, len(c))
        c = sorted(c, key=lambda parameter: parameter[0])
        set_cover = []
    c.append(c[0])
    del(c[0])
    for l in c:
        if not any(v in c_elem for v in l):
            set_cover.append(l)
            c_elem.update(l)
    # if exact solution not found,
    # then use partial solution
    if set_cover not in partial:
        partial.append(set_cover)
list_of_partials = [len(r) for r in partial]
k = partial[list_of_partials.index(max(list_of_partials))]
# Reversing the Bijective mapping
# to the original input.
for a in range(0, len(k)):
    for b in range(0, len(k[a])):
        l = s.index(k[a][b])
        k[a][b] = s_copy[l]
for a in range(0, len(k)):
  k[a] = sorted(k[a])
for a in c_copy:
  if sorted(a) in k:
    l = k.index(sorted(a))
    k[l] = a
print(k)