Reduction

from copy import deepcopy
import math

# (No overlap) Decide if a subset of lists can be
# multiplied together that will equal N.


# Take any Exact-3-Cover Instance
# for the Reduction
s = [11,12,13,14,15,16]
c = [[11,12,13],[14,15,16]]

s_copy = deepcopy(s)
c_copy = deepcopy(c)

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()

# Take the total product of s
# Which is factorial(len(s))

N = math.factorial(len(s))

# We are going to need to convert N into
# a Universe. To show that both N & S
# can be reduced into each other
# efficently

n = 0
m = 1
u = []
while m < N:
    n = n + 1
    m = m * n
    u.append(n)

if u == s:
    print('Both u & s are equal')

print('input for N: ',N)
print('input for c: ',c)

print('original inputs')
print('s: ',s_copy)
print('c: ',c_copy)