Project Euler Q32 - LO Man Hei

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   "source": [
    "### Q32\n",
    "Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital."
   ]
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    "def pandigital_products(num_index=0,selected_digits=None,remaining_digits=None):\n",
    "    if remaining_digits is None:\n",
    "        remaining_digits = [1,2,3,4,5,6,7,8,9]\n",
    "        selected_digits = []\n",
    "    result = set()\n",
    "    if num_index == 2 and selected_digits[0]*selected_digits[1] > 10:\n",
    "        return set()\n",
    "    if num_index == 5:\n",
    "        prod_1 = (selected_digits[0]*100+selected_digits[2]*10+selected_digits[3]) * (selected_digits[1]*10+selected_digits[4])\n",
    "        prod_2 = (selected_digits[0]*1000+selected_digits[2]*100+selected_digits[3]*10+selected_digits[4]) * (selected_digits[1])\n",
    "        if sorted(str(prod_1)) == sorted([str(i) for i in remaining_digits]):\n",
    "            return {prod_1}\n",
    "        elif sorted(str(prod_2)) == sorted([str(i) for i in remaining_digits]):\n",
    "            return {prod_2}\n",
    "        else:\n",
    "            return set()\n",
    "    else:\n",
    "        for i,v in enumerate(remaining_digits):\n",
    "            temp = remaining_digits.copy()\n",
    "            result.update(pandigital_products(num_index+1,selected_digits+[temp.pop(i)],temp))\n",
    "        return result\n"
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     "name": "stdout",
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     "text": [
      "CPU times: user 13.3 ms, sys: 397 µs, total: 13.7 ms\n",
      "Wall time: 12.8 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "45228"
      ]
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     "execution_count": 2,
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   "source": [
    "%%time\n",
    "sum(pandigital_products())"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "id": "97e43e46-3bbf-464d-bdd6-182aed1710bb",
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   "source": [
    "def factorize(n):\n",
    "    result = []\n",
    "    for i in range(1,int((n)**(0.5))+1):\n",
    "        if (n%i==0):\n",
    "            result.append(i)\n",
    "            #result.append(int(n/i))\n",
    "        result.sort()\n",
    "    return result\n",
    "\n",
    "def get_multipy_num(n,factor):\n",
    "    quotient = int(n/factor)\n",
    "    num = []\n",
    "    expressionstr = str(factor)+str(quotient)+str(n)\n",
    "    for digit in expressionstr:\n",
    "        num.append(int(digit))\n",
    "    return sorted(num)\n",
    "\n",
    "def judge_pandigitial(num):\n",
    "    if num == list(range(1,10)):\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "    \n",
    "def pandigital_products_2():\n",
    "    res = []\n",
    "    for i in range(999,10000):\n",
    "        factors_list =factorize(i)\n",
    "        for factor in factors_list:\n",
    "            num = get_multipy_num(i,factor)\n",
    "            if judge_pandigitial(num):\n",
    "                res.append(i)\n",
    "                break\n",
    "    return set(res)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
   "id": "28985d34-5489-41ce-aed8-4f177d692c21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 13.8 ms, sys: 555 µs, total: 14.4 ms\n",
      "Wall time: 13.8 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "45228"
      ]
     },
     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "%%time \n",
    "sum(pandigital_products())"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "59e8ca52-58a2-4a3f-a66e-83022712d0c5",
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   "outputs": [],
   "source": []
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