add problem 99

notebooks/problem0099.ipynb

@@ -0,0 +1,68 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "e71fcbbb",
+   "metadata": {},
+   "source": [
+    "# [Largest Exponential](https://projecteuler.net/problem=99)\n",
+    "\n",
+    "Instead of trying to compare the powers $x^y$ directly, compare their logarithms $y\\log{x}$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "0180569c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open(\"txt/0099_base_exp.txt\") as f:\n",
+    "    pairs = tuple(tuple(int(x) for x in line.split(\",\")) for line in f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "a0c22c9e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(709, (895447, 504922))"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "logpows = {(x, y): y * log(x) for (x, y) in pairs}\n",
+    "max(enumerate(logpows, start=1), key=lambda x: logpows[x[1]])"
+   ]
+  }
+ ],
+ "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
+}