#!/bin/env python3
# A capset is a collection of cards that contains no sets.
# The supposed maximal cardinality of a capset in Set is 20.
# I wish to find such a collection with this program.

from random import shuffle
from itertools import combinations

def is_set(cards):
    if len(cards) != 3:
        raise Exception("Not the right number of cards.")
    for i in range(4):
        if cards[0][i] == cards[1][i] == cards[2][i]: continue
        if cards[0][i] != cards[1][i] != cards[2][i] != cards[0][i]: continue
        return False
    return True

def int2card(num):
    if num != int(num):
        raise Exception("Number must be an integer.")
    if num < 0:
        raise Exception("Number must be nonnegative.")
    if num > 80:
        raise Exception("Number must be less than 81.")
    strlist = []
    for i in range(4):
        strlist.append(str(num%3))
        num //= 3
    return ''.join(strlist[::-1])

def increment_tableau(tableau, deck, pop=False):
    index = deck.index(tableau[-1]) + 1
    if index != len(deck):
        if pop: tableau.pop()
        tableau.append(deck[index])
        return
    tableau.pop()
    index = deck.index(tableau.pop()) + 1
    if len(tableau) == 1:
        print("incrementing second card to index", index)
        if index + 18 > len(deck): quit()
    tableau.append(deck[index])

def check_tableau(tableau):
    if len(tableau) == 2: return True
    for comb in combinations(tableau, 3):
        if is_set(comb): return False
    return True

def main():
    outfile = open("./capset.out", mode="w")
    tableau = ["2222"]
    deck = reversed(range(80)) # all cards other than 2222
    deck = list(map(int2card, deck))
    #shuffle(deck)
    tableau.append(deck[0])
    maxim = 20
    while True:
        if check_tableau(tableau):
            if len(tableau) >= maxim:
                print(tableau)
                print(tableau, file=outfile, flush=True)
                maxim = len(tableau)
            increment_tableau(tableau, deck)
        else:
            increment_tableau(tableau, deck, pop=True)
    outfile.close()

if __name__ == "__main__": main()