Project Euler Q57 - LO Man Hei

Download notebook

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a469358e-2f57-4bd6-9c8d-c59f3d77920b",
   "metadata": {},
   "source": [
    "### Q57\n",
    "In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bd7ddc2f-5964-49c3-a927-774399b0b0a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def longer_numerator_than_denominator_in_range_n(n):\n",
    "    numerator, denominator = 1, 1\n",
    "    result = 0\n",
    "    for _ in range(n):\n",
    "        numerator,denominator = numerator+2*denominator, numerator+denominator\n",
    "        if len(str(numerator)) > len(str(denominator)):\n",
    "            result += 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3e78fa42-856e-4722-a279-245d9b8516a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.12 ms, sys: 321 µs, total: 1.45 ms\n",
      "Wall time: 1.45 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "153"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "longer_numerator_than_denominator_in_range_n(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b869eac9-8c59-4a32-a226-a1308dec4e4c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

Loading