Roman_numerals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Roman numerals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Roman numerals to decimals\n",
    "\n",
    "Write a function which receives a Roman numeral written out as a string, and returns an integer representing the decimal form of the input number. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mapping = {\"I\" : 1, \n",
    "           \"V\" : 5,\n",
    "           \"X\" : 10,\n",
    "           \"L\" : 50,\n",
    "           \"C\" : 100,\n",
    "           \"D\" : 500,\n",
    "           \"M\" : 1000}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def roman_to_decimal(rom):\n",
    "    \"\"\"Convert a Roman numeral to decimal.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    rom : str\n",
    "        A Roman numeral representing a positive integer.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    dec : int\n",
    "        The result of conversion of `rom` into a decimal system.\n",
    "    \"\"\"\n",
    "    last = False\n",
    "    result = 0\n",
    "    for char in reversed(rom):\n",
    "        if last and mapping[char]<last:\n",
    "            last = mapping[char]\n",
    "            result -= mapping[char]\n",
    "        else:\n",
    "            last = mapping[char]\n",
    "            result += mapping[char]\n",
    "            \n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some tests for you to test your code. Your code must pass all of them. You also need to come up with several more tests (your choice)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "test_pairs = [(\"IX\", 9), (\"XI\", 11), (\"MCCII\", 1202), (\"MMXVIII\", 2018), (\"XLIX\", 49)]\n",
    "\n",
    "for rom, dec in test_pairs:\n",
    "    converted = roman_to_decimal(rom)\n",
    "    print(converted == dec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Decimal numbers to roman numerals.\n",
    "\n",
    "The maximum grade for first task (Roman to decimal) is 7 on the 10-point HSE scale. For extra credit, complete the second task: *given a decimal number, convert it to the Roman form*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "REVERSE_MAPPING = [\n",
    "    (1000, \"M\"),\n",
    "    (900, \"CM\"),\n",
    "    (500, \"D\"),\n",
    "    (400, \"CD\"),\n",
    "    (100, \"C\"),\n",
    "    (90, \"XC\"),\n",
    "    (50, \"L\"),\n",
    "    (40, \"XL\"),\n",
    "    (10, \"X\"),\n",
    "    (9, \"IX\"),\n",
    "    (5, \"V\"),\n",
    "    (4, \"IV\"),\n",
    "    (1, \"I\"),\n",
    "]\n",
    "def decimal_to_roman(dec):\n",
    "    \"\"\"Convert a decimal to the Roman form.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    dec : int\n",
    "        A positive integer number\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    rom : str\n",
    "        A string representation of a Roman numeral form of `dec`.\n",
    "    \"\"\"\n",
    "    local_copy = int(dec) # maybe we have something nonprimitive\n",
    "    rom = \"\"\n",
    "    for rem, latin in REVERSE_MAPPING:\n",
    "        while rem<=local_copy:\n",
    "            rom += latin\n",
    "            local_copy -= rem\n",
    "    return rom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need to come up with test cases to show that your conversion works as expected. \n",
    "NB: the conversion is ambiguous in some cases. Any valid conversion is accepted. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True 9 IX IX\n",
      "True 11 XI XI\n",
      "True 1202 MCCII MCCII\n",
      "True 2018 MMXVIII MMXVIII\n",
      "True 49 XLIX XLIX\n"
     ]
    }
   ],
   "source": [
    "for rom, dec in test_pairs:\n",
    "    converted = decimal_to_roman(dec)\n",
    "    print(converted == rom, dec, rom, converted)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All OK!\n"
     ]
    }
   ],
   "source": [
    "failed = False\n",
    "for dec in range(100000):\n",
    "    if dec!=roman_to_decimal(decimal_to_roman(dec)):\n",
    "        failed = True\n",
    "        print(\"Failed on %d=%s\", dec, decimal_to_roman(dec))\n",
    "        \n",
    "if not failed:\n",
    "    print(\"All OK!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}