# norvig/pytudes

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 import random import collections import itertools """ Game of Set (Peter Norvig 2010-2015) How often do sets appear when we deal an array of cards? How often in the course of playing out the game? Here are the data types we will use: card: A string, such as '3R=0', meaning "three red striped ovals". deck: A list of cards, initially of length 81. layout: A list of cards, initially of length 12. set: A tuple of 3 cards. Tallies: A dict: {12: {True: 33, False: 1}}} means a layout of size 12 tallied 33 sets and 1 non-set. """ #### Cards, dealing cards, and defining the notion of sets. CARDS = [number + color + shade + symbol for number in '123' for color in 'RGP' for shade in '@O=' for symbol in '0SD'] def deal(n, deck): "Deal n cards from the deck." return [deck.pop() for _ in range(n)] def is_set(cards): "Are these 3 cards a set? No if any feature has 2 values." for f in range(4): values = {card[f] for card in cards} if len(values) == 2: return False return True def find_set(layout): "Return a set found from this layout, if there is one." for cards in itertools.combinations(layout, 3): if is_set(cards): return cards return () #### Tallying set:no-set ratio def Tallies(): "A data structure to keep track, for each size, the number of sets and no-sets." return collections.defaultdict(lambda: {True: 0, False: 0}) def tally(tallies, layout): "Record that a set was found or not found in a layout of given size; return the set." s = find_set(layout) tallies[len(layout)][bool(s)] += 1 return s #### Three experiments def tally_initial_layout(N, sizes=(12, 15)): "Record tallies for N initial deals." tallies = Tallies() deck = list(CARDS) for deal in range(N): random.shuffle(deck) for size in sizes: tally(tallies, deck[:size]) return tallies def tally_initial_layout_no_prior_sets(N, sizes=(12, 15)): """Simulate N initial deals for each size, keeping tallies for Sets and NoSets, but only when there was no set with 3 fewer cards.""" tallies = Tallies() deck = list(CARDS) for deal in range(N): random.shuffle(deck) for size in sizes: if not find_set(deck[:size-3]): tally(tallies, deck[:size]) return tallies def tally_game_play(N): "Record tallies for the play of N complete games." tallies = Tallies() for game in range(N): deck = list(CARDS) random.shuffle(deck) layout = deal(12, deck) while deck: s = tally(tallies, layout) # Pick up the cards in the set, if any for card in s: layout.remove(card) # Deal new cards if len(layout) < 12 or not s: layout += deal(3, deck) return tallies def experiments(N): show({12: [1, 33], 15: [1, 2500]}, 'the instruction booklet') show(tally_initial_layout(N), 'initial layout') show(tally_game_play(N // 25), 'game play') show(tally_initial_layout_no_prior_sets(N), 'initial layout, but no sets before dealing last 3 cards') def show(tallies, label): "Print out the counts." print() print('Size | Sets | NoSets | Set:NoSet ratio for', label) print('-----+--------+--------+----------------') for size in sorted(tallies): y, n = tallies[size][True], tallies[size][False] ratio = ('inft' if n==0 else int(round(float(y)/n))) print('{:4d} |{:7,d} |{:7,d} | {:4}:1' .format(size, y, n, ratio)) def test(): assert len(CARDS) == 81 == len(set(CARDS)) assert is_set(('3R=O', '2R=S', '1R=D')) assert not is_set(('3R=0', '2R=S', '1R@D')) assert find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R=D']) == ('3R=0', '2R=S', '1R=D') assert not find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R@D']) photo = '2P=0 3P=D 2R=0 3GO0 2POD 3R@D 2RO0 2ROS 1P@S 2P@0 3ROS 2GOD 2P@D 1GOD 3GOS'.split() assert not find_set(photo) assert set(itertools.combinations([1, 2, 3, 4], 3)) == {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)} print('All tests pass.') test() experiments(100000)