119 lines
2.7 KiB
Plaintext
119 lines
2.7 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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"metadata": {},
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"source": [
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"# Champernowne's constant (Euler Problem 40)\n",
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"\n",
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"<https://projecteuler.net/problem=40>\n",
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"\n",
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"An irrational decimal fraction is created by concatenating the positive integers:\n",
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"\n",
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" 0.123456789101112131415161718192021...\n",
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"\n",
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"It can be seen that the 12th digit of the fractional part is 1.\n",
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"\n",
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"If dn represents the nth digit of the fractional part, find the value of the following expression.\n",
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"\n",
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"$d_{1} × d_{10} × d_{100} × d_{1000} × d_{10000} × d_{100000} × d_{1000000}$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"I do not see why we cannot hold $8 bytes \\times 10^{6} = 8 MB$ in memory."
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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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"metadata": {},
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"outputs": [],
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"source": [
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"def get_irrational_fraction(digits_max):\n",
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" s = []\n",
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" n = 1\n",
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" digits = 0\n",
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" while digits < digits_max:\n",
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" s.append(str(n))\n",
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" digits += len(str(n))\n",
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" n += 1\n",
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" return \"\".join(s)\n",
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"\n",
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"assert(get_irrational_fraction(20)[12] == \"1\")\n",
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"\n",
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"f = get_irrational_fraction(1000001)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Okay, we got the fractional. No we get the digits at the different positions and calculate the product. For that purpose we reuse our poduct function from problem 8."
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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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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def product(xs):\n",
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" from operator import mul\n",
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" from functools import reduce\n",
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" return reduce(mul, xs, 1)"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"210\n"
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]
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}
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],
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"source": [
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"s = product(map(int, [f[10**i - 1] for i in range(7)]))\n",
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"print(s)\n",
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"assert(s == 210)"
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]
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}
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],
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"metadata": {
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"completion_date": "Sun, 20 May 2018, 00:40",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.5",
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"name": "python3"
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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": "3.5.5"
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},
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"tags": [
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"champernowne",
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"product",
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"fraction"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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