Project Euler Q16 - LO Man Hei

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   "source": [
    "### Q16\n",
    "What is the sum of the digits of the number \\(2^{1000}\\)?"
   ]
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    "def dec_to_bin(dec):\n",
    "    return bin(dec).replace(\"0b\", \"\")\n",
    "\n",
    "def str_num_multiply(str_num_a, str_num_b):\n",
    "    len_a = len(str_num_a)\n",
    "    len_b = len(str_num_b)\n",
    "    result_str = [0]*(len_a+len_b)\n",
    "    carry = 0\n",
    "    for i in range(len_a)[::-1]:\n",
    "        for j in range(len_b)[::-1]:\n",
    "            temp_prod = result_str[j+i+1]+int(str_num_a[i])*int(str_num_b[j])+carry\n",
    "            result_str[j+i+1] = (temp_prod)%10\n",
    "            carry = temp_prod//10\n",
    "        if carry:\n",
    "            result_str[i+j] += carry\n",
    "            carry = 0\n",
    "    return \"\".join([str(i) for i in result_str]).lstrip(\"0\")\n",
    "\n",
    "def str_num_pow2n(str_num,n):\n",
    "    # str_num ** (2 ** n)\n",
    "    return str_num_pow2n(str_num_multiply(str_num,str_num),n-1) if n>=1 else str_num\n",
    "\n",
    "def str_num_pow(str_num,p):\n",
    "    exponent = dec_to_bin(p)[::-1]\n",
    "    result_str = \"1\"\n",
    "    for num in [str_num_pow2n(str_num,i) for i in range(len(exponent)) if exponent[i]==\"1\"]:\n",
    "        result_str = str_num_multiply(result_str,num)\n",
    "    return result_str"
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      "CPU times: user 12.9 ms, sys: 474 µs, total: 13.4 ms\n",
      "Wall time: 12 ms\n"
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       "1366"
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   "source": [
    "%%time\n",
    "sum([int(c) for c in str_num_pow(\"2\",1000)])"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "id": "a7259bcf-7b75-412f-9c48-e4621ca767fe",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 31 µs, sys: 0 ns, total: 31 µs\n",
      "Wall time: 33.1 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1366"
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "%%time\n",
    "sum([int(c) for c in str(2**1000)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61f65d34-9b29-4dc7-8365-508401a185d0",
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