#!/usr/bin/env python3

N=4
nr_tables=4

def gen_rainbow_reductors(k):
    def R1(x):
        return  x / 10 * 10 + x % 3

    def R2(x):
        return  x / 10 * 10 % 3 + 3

    def R3(x):
        return  x / 10 * 10 % 3 + 6

    def R4(x):
        return  x / 10 * 10 + 9

    Rint = [R1, R2, R3, R4]
    Rstr = []
    for rint in Rint:
        Rstr.append(lambda s : str(int(rint(int(s, 10))) ^ k).zfill(N))
    return Rstr


def hashfn(s):
    return s[2:] + s[0:2]


def chain_end(s, R):
    for r in R:
        s = r(hashfn(s))
    return s


def generate_table(f, R):
    v = []
    for l in f:
        v.append([l, chain_end(l, R)])
    return v


def matches(k, v, needle, entry, R):
    start_string = entry[0]
    end_string   = entry[1]
    s = start_string
    for i in range(0, k):
        s = R[i](hashfn(s))
    return hashfn(s) == needle


def gen_chain_from(needle, k, R):
    for i in range(k, len(R) - 1):
        needle = hashfn(R[i](needle))
    return R[len(R)-1](needle)