Drafted solution for 53 and 54. I will have to validate.
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3eca2e83c2
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4acfe89f92
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@ -30,6 +30,58 @@
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"How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import math\n",
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"\n",
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"def combinations_naiv(n, r):\n",
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" return math.factorial(n) // (math.factorial(r) * math.factorial(n - r))\n",
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"\n",
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"assert(combinations_naiv(5, 3) == 10)\n",
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"assert(combinations_naiv(23, 10) == 1144066)\n",
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"assert(combinations_naiv(20, 20) == 1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"count = 0\n",
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"\n",
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"for n in range (1, 101):\n",
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" for r in range(1, n + 1):\n",
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" if combinations_naiv(n, r) > 10**6:\n",
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" count += 1\n",
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"\n",
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"s = count"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"4075\n"
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]
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}
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],
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"source": [
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"print(s)\n",
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"assert(s == 4075)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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@ -50,6 +50,207 @@
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"How many hands does Player 1 win?\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's start with some helper functions."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [],
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"source": [
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"def suit_to_value(suit):\n",
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" return {\n",
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" \"2\": 2,\n",
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" \"3\": 3,\n",
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" \"4\": 4,\n",
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" \"5\": 5,\n",
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" \"6\": 6,\n",
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" \"7\": 7,\n",
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" \"8\": 8,\n",
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" \"9\": 9,\n",
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" \"T\": 10,\n",
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" \"J\": 11,\n",
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" \"Q\": 12,\n",
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" \"K\": 13,\n",
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" \"A\": 14,\n",
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" }[suit]\n",
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"\n",
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"assert(suit_to_value('K') == 13)\n",
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"\n",
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"\n",
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"def is_flush(colors):\n",
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" first_color = colors[0]\n",
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" for color in colors:\n",
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" if color != first_color:\n",
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" return False\n",
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" return True\n",
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"\n",
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"\n",
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"assert(is_flush([\"H\", \"H\", \"H\", \"H\", \"H\"]))\n",
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"assert(is_flush([\"H\", \"H\", \"D\", \"H\", \"H\"]) == False)\n",
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"\n",
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"def is_straight(suits):\n",
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" suits = sorted(suits)\n",
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" first_suit = suits[0]\n",
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" for suit in suits[1:]:\n",
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" if first_suit + 1 != suit:\n",
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" return False\n",
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" first_suit = suit\n",
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" return True\n",
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"\n",
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"assert(is_straight([6,3,4,5,7]))\n",
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"assert(is_straight([6,3,4,5,8]) == False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_numbered_groups(ns):\n",
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" \"\"\" Takes [0, 3, 0, 3, 1] and returns\n",
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" [(2, 3), (2, 0), (1, 1)]\n",
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" \"\"\"\n",
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" rs = []\n",
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" current_group = []\n",
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" for n in sorted(ns, reverse=True):\n",
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" if not current_group or n in current_group:\n",
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" current_group.append(n)\n",
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" else:\n",
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" rs.append(current_group)\n",
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" current_group = [n]\n",
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" rs.append(current_group)\n",
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" rs = sorted([(len(r), r[0]) for r in rs], reverse=True)\n",
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" return rs\n",
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"\n",
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"assert(get_numbered_groups([0, 3, 0, 3, 1]) == [(2, 3), (2, 0), (1, 1)])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's put that stuff together."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"metadata": {},
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"outputs": [],
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"source": [
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"def rank(hand):\n",
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" \"\"\" A hand must be provided as a list of two letter strings.\n",
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" The first letter is the suit and the second the suit of a card.\n",
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" \n",
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" The function returns a tuple. The first value represents the hand as an integer\n",
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" where 0 means high card and 9 means Straight Flush. The second value is a list of integers\n",
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" ranking the value of the respective rank. For example, a Royal Flush would be (9, [14, 13, 12, 11, 10]),\n",
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" while 22aqj would be (1, [2, 2, 14, 12, 11]). By doing this we can simply compare to hands\n",
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" by first comparing the rank itself and then the list of integers.\n",
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" \n",
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" We get something like [\"5H\", \"6S\", \"7S\", \"5C\", \"KD\"].\n",
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" \"\"\"\n",
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" \n",
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" suits, colors = zip(*(map(lambda s: (s[0], s[1]), hand)))\n",
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" suits = sorted(map(suit_to_value, suits))\n",
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"\n",
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" flush = is_flush(colors)\n",
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" straight = is_straight(suits)\n",
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" numbered_suits = get_numbered_groups(suits)\n",
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" if flush and straight:\n",
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" return [8, numbered_suits]\n",
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" if flush:\n",
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" return [5, numbered_suits]\n",
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" if straight:\n",
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" return [4, numbered_suits]\n",
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" if numbered_suits[0][0] == 4:\n",
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" return [7, numbered_suits]\n",
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" if numbered_suits[0][0] == 3 and numbered_suits[1][0] == 2:\n",
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" return [6, numbered_suits]\n",
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" if numbered_suits[0][0] == 3:\n",
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" return [3, numbered_suits]\n",
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" if numbered_suits[0][0] == 2 and numbered_suits[1][0] == 2:\n",
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" return [2, numbered_suits]\n",
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" if numbered_suits[0][0] == 2:\n",
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" return [1, numbered_suits]\n",
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" return [0, numbered_suits]\n",
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" \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 55,
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"metadata": {},
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"outputs": [],
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"source": [
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"assert(rank([\"5H\", \"5C\", \"6S\", \"7S\", \"KD\"]) == [1, [(2, 5), (1, 13), (1, 7), (1, 6)]]) # Pair of Fives\n",
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"assert(rank([\"5D\", \"8C\", \"9S\", \"JS\", \"AC\"]) == [0, [(1, 14), (1, 11), (1, 9), (1, 8), (1, 5)]]) # Highest card Ace\n",
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"assert(rank([\"2D\", \"9C\", \"AS\", \"AH\", \"AC\"]) == [3, [(3, 14), (1, 9), (1, 2)]]) # Three Aces\n",
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"assert(rank([\"4D\", \"6S\", \"9H\", \"QH\", \"QC\"]) == [1, [(2, 12), (1, 9), (1, 6), (1, 4)]]) # Pair of Queens Highest card Nine\n",
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"assert(rank([\"2H\", \"2D\", \"4C\", \"4D\", \"4S\"]) == [6, [(3, 4), (2, 2)]]) # Full House With Three Fours\n",
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"assert(rank([\"2C\", \"3S\", \"8S\", \"8D\", \"TD\"]) == [1, [(2, 8), (1, 10), (1, 3), (1, 2)]]) # Pair of Eights \n",
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"assert(rank([\"2C\", \"5C\", \"7D\", \"8S\", \"QH\"]) == [0, [(1, 12), (1, 8), (1, 7), (1, 5), (1, 2)]]) # Highest card Queen \n",
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"assert(rank([\"3D\", \"6D\", \"7D\", \"TD\", \"QD\"]) == [5, [(1, 12), (1, 10), (1, 7), (1, 6), (1, 3)]]) # Flush with Diamonds \n",
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"assert(rank([\"3D\", \"6D\", \"7H\", \"QD\", \"QS\"]) == [1, [(2, 12), (1, 7), (1, 6), (1, 3)]]) # Pair of Queens Highest card Seven \n",
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"assert(rank([\"3C\", \"3D\", \"3S\", \"9S\", \"9D\"]) == [6, [(3, 3), (2, 9)]]) # Full House with Three Threes \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 67,
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"metadata": {},
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"outputs": [],
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"source": [
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"def read_hands():\n",
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" \"\"\" Reads a list of tuples where each field\n",
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" in the tuple represents a hand.\n",
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" \"\"\"\n",
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" hands = []\n",
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" with open(\"EulerProblem054.txt\", \"r\") as f:\n",
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" for line in f.readlines():\n",
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" cards = line.strip().split(\" \")\n",
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" hands.append((cards[:5], cards[5:]))\n",
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" return hands\n",
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"\n",
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"p1_wins = 0\n",
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"\n",
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"for p1_hand, p2_hand in read_hands():\n",
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" if rank(p1_hand) > rank(p2_hand):\n",
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" p1_wins += 1\n",
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" msg = \"P1 hand {} wins over P2 hand {}.\"\n",
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" #print(msg.format(p1_hand, p2_hand))\n",
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" else:\n",
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" msg = \"P1 hand {} loses versus P2 hand {}.\"\n",
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" #print(msg.format(p1_hand, p2_hand))\n",
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" \n",
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"s = p1_wins "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 70,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"376\n"
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]
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}
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],
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"source": [
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"print(s)\n",
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"assert(s == 376)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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