69 lines
1.4 KiB
Plaintext
69 lines
1.4 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "e71fcbbb",
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"metadata": {},
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"source": [
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"# [Largest Exponential](https://projecteuler.net/problem=99)\n",
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"\n",
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"Instead of trying to compare the powers $x^y$ directly, compare their logarithms $y\\log{x}$."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "0180569c",
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"metadata": {},
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"outputs": [],
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"source": [
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"with open(\"txt/0099_base_exp.txt\") as f:\n",
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" pairs = tuple(tuple(int(x) for x in line.split(\",\")) for line in f)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "a0c22c9e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(709, (895447, 504922))"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"logpows = {(x, y): y * log(x) for (x, y) in pairs}\n",
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"max(enumerate(logpows, start=1), key=lambda x: logpows[x[1]])"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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