diff --git a/notebooks/problem0089.ipynb b/notebooks/problem0089.ipynb new file mode 100644 index 0000000..d91d73e --- /dev/null +++ b/notebooks/problem0089.ipynb @@ -0,0 +1,188 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "dbdd8508", + "metadata": {}, + "source": [ + "# [Roman Numerals](https://projecteuler.net/problem=89)\n", + "\n", + "First, we have to read in all the [Roman numerals](https://en.wikipedia.org/wiki/Roman_numerals) we're working with." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e2925aba", + "metadata": {}, + "outputs": [], + "source": [ + "with open(\"txt/0089_roman.txt\") as f:\n", + " numerals = [s.strip() for s in f.readlines()]" + ] + }, + { + "cell_type": "markdown", + "id": "b57710ca", + "metadata": {}, + "source": [ + "To assist us, we'll make a map from denominations to Roman numerals." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5b4b8abd", + "metadata": {}, + "outputs": [], + "source": [ + "denominations = {\n", + " 1: \"I\",\n", + " 2: \"II\",\n", + " 3: \"III\",\n", + " 4: \"IV\",\n", + " 5: \"V\",\n", + " 6: \"VI\",\n", + " 7: \"VII\",\n", + " 8: \"VIII\",\n", + " 9: \"IX\",\n", + " 10: \"X\",\n", + " 20: \"XX\",\n", + " 30: \"XXX\",\n", + " 40: \"XL\",\n", + " 50: \"L\",\n", + " 60: \"LX\",\n", + " 70: \"LXX\",\n", + " 80: \"LXXX\",\n", + " 90: \"XC\",\n", + " 100: \"C\",\n", + " 200: \"CC\",\n", + " 300: \"CCC\",\n", + " 400: \"CD\",\n", + " 500: \"D\",\n", + " 600: \"DC\",\n", + " 700: \"DCC\",\n", + " 800: \"DCCC\",\n", + " 900: \"CM\",\n", + " 1000: \"M\",\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "339bbd69", + "metadata": {}, + "source": [ + "We can make a simple greedy parser to convert the given Roman numerals to ints." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "01623002", + "metadata": {}, + "outputs": [], + "source": [ + "def to_int(s):\n", + " rev_denominations = {v: k for (k, v) in denominations.items()}\n", + " prefixes = sorted(rev_denominations.keys(), key=len, reverse=True)\n", + " \n", + " n = 0\n", + " while s != \"\":\n", + " for prefix in prefixes:\n", + " if s.startswith(prefix):\n", + " n += rev_denominations[prefix]\n", + " s = s.removeprefix(prefix)\n", + " break\n", + " \n", + " return n" + ] + }, + { + "cell_type": "markdown", + "id": "594d35b8", + "metadata": {}, + "source": [ + "It's arguably easier to convert an int to the minimal Roman numeral." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "fc3ce748", + "metadata": {}, + "outputs": [], + "source": [ + "def to_roman(n):\n", + " s = [\"\", \"\", \"\", \"\"]\n", + " \n", + " for i in range(1, 4):\n", + " d = n % 10^i\n", + " if d in denominations:\n", + " s[-i] = denominations[d]\n", + " \n", + " n -= d\n", + " \n", + " s[0] = \"M\" * (n // 1000)\n", + " \n", + " return \"\".join(s)" + ] + }, + { + "cell_type": "markdown", + "id": "e1f6d92d", + "metadata": {}, + "source": [ + "To solve, convert each Roman numeral to an int, then convert that int to the minimal Roman numeral, and count the characters saved." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b88ee547", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "743" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "total = 0\n", + "for numeral in numerals:\n", + " value = to_int(numeral)\n", + " minimal = to_roman(value)\n", + " total += len(numeral) - len(minimal)\n", + "\n", + "total" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 9.5", + "language": "sage", + "name": "sagemath" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git 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