Project Euler Q30 - LO Man Hei

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    "### Q30\n",
    "Find the sum of all the numbers that can be written as the sum of fifth powers of their digits."
   ]
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    "def sum_of_n_powers_nums(n):\n",
    "    max_digit = 1\n",
    "    while len(str(max_digit*9**n)) > max_digit:\n",
    "        max_digit += 1\n",
    "    max_range = (int(str(max_digit*9**n)[0])-1)**n + (max_digit-1)*9**n\n",
    "    n_powers_nums_map = {str(i):i**n for i in range(10)}\n",
    "    sum_history = {}\n",
    "    result = 0\n",
    "    for i in range(10,max_range+1)[::-1]:\n",
    "        sorted_num_str = ''.join(sorted(str(i)))\n",
    "        if sorted_num_str in sum_history:\n",
    "            powers_sum = sum_history[sorted_num_str]\n",
    "        else:\n",
    "            powers_sum = sum(n_powers_nums_map[c] for c in str(i))\n",
    "            sum_history[sorted_num_str] = powers_sum\n",
    "        if i == powers_sum:\n",
    "            result += i\n",
    "    print(f\"history count: {len(sum_history)}\")\n",
    "    return result"
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     "text": [
      "history count: 6276\n",
      "CPU times: user 120 ms, sys: 0 ns, total: 120 ms\n",
      "Wall time: 118 ms\n"
     ]
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    {
     "data": {
      "text/plain": [
       "443839"
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     "execution_count": 2,
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   ],
   "source": [
    "%%time\n",
    "sum_of_n_powers_nums(5)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "b3d42f30-7cac-4ffe-bb6e-cfbf056c4b20",
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   "source": []
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