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-rwxr-xr-xcapset.py70
1 files changed, 0 insertions, 70 deletions
diff --git a/capset.py b/capset.py
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--- a/capset.py
+++ /dev/null
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-#!/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()
-