Euler 026 - Reciprocal cycles.ipynb

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    "Euler Problem 26\n",
    "================\n",
    "\n",
    "A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\n",
    "\n",
    "    1/2  = \t0.5\n",
    "    1/3  = \t0.(3)\n",
    "    1/4  = \t0.25\n",
    "    1/5  = \t0.2\n",
    "    1/6  = \t0.1(6)\n",
    "    1/7  = \t0.(142857)\n",
    "    1/8  = \t0.125\n",
    "    1/9  = \t0.(1)\n",
    "    1/10 = \t0.1\n",
    "Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\n",
    "\n",
    "Find the value of $d < 1000$ for which $1/d$ contains the longest recurring cycle in its decimal fraction part."
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      "983\n"
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   "source": [
    "def decimal_period(n):\n",
    "    while n % 2 == 0:\n",
    "        n //= 2\n",
    "    while n % 5 == 0:\n",
    "        n //= 5\n",
    "    if n == 1:\n",
    "        return 0\n",
    "    k = 10 % n\n",
    "    p = 1\n",
    "    while k != 1:\n",
    "        k = (10*k) % n\n",
    "        p += 1\n",
    "    return p\n",
    "\n",
    "maxp = maxd = 0\n",
    "for d in range(1, 1000):\n",
    "    p = decimal_period(d)\n",
    "    if p > maxp:\n",
    "        (maxp, maxd) = (p, d)\n",
    "print(maxd)"
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