Project Euler Q40 - LO Man Hei

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    "### Q40\n",
    "If \\(d_n\\) represents the n-th digit of the fractional part, find the value of the following expression.\n",
    "\n",
    "\\[d_{1} \\times d_{10} \\times d_{100} \\times d_{1000} \\times d_{10000} \\times d_{100000} \\times d_{1000000} \\]"
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    "def prod(x_vector):\n",
    "    result = 1\n",
    "    for i in x_vector:\n",
    "        result *= i\n",
    "    return result\n",
    "\n",
    "def champernownes_constant(n_vector):\n",
    "    max_n = max(n_vector)\n",
    "    max_range = int(max_n*10/9+10) // (len(str(max_n))-1) if max_n > 9 else max_n\n",
    "    champernownes_str = \"\".join(str(i) for i in range(1,max_range))\n",
    "    return prod(int(champernownes_str[n-1]) for n in n_vector)"
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     "text": [
      "CPU times: user 26.1 ms, sys: 0 ns, total: 26.1 ms\n",
      "Wall time: 24.2 ms\n"
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       "210"
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   "source": [
    "%%time\n",
    "champernownes_constant([1,10,100,1000,10000,100000,1000000])"
   ]
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    "def n_champernownes(n):\n",
    "    num_digit = 0\n",
    "    n_len = 0\n",
    "    temp_sum = 0\n",
    "    while n > n_len:\n",
    "        temp_sum += n_len\n",
    "        num_digit += 1\n",
    "        n_len = num_digit*9*10**(num_digit-1)\n",
    "    n -= 1\n",
    "    return int(str((n-temp_sum)//num_digit+10**(num_digit-1))[(n-temp_sum)%num_digit])\n",
    "\n",
    "def champernownes_constant_2(n_vector):\n",
    "    return prod(n_champernownes(n) for n in n_vector)"
   ]
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     "text": [
      "CPU times: user 14 µs, sys: 6 µs, total: 20 µs\n",
      "Wall time: 21.7 µs\n"
     ]
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       "210"
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     "execution_count": 4,
     "metadata": {},
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   "source": [
    "%%time\n",
    "champernownes_constant_2([1,10,100,1000,10000,100000,1000000])"
   ]
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