146 lines
3.4 KiB
Plaintext
146 lines
3.4 KiB
Plaintext
{
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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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"# Problem 14:\n",
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"\n",
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"[Euler Project #14](https://projecteuler.net/problem=14)\n",
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"\n",
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"\n",
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"\n",
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"> The following iterative sequence is defined for the set of positive integers:\n",
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"> \n",
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"> n → n/2 (n is even)\n",
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"> n → 3n + 1 (n is odd)\n",
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"> \n",
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"> Using the rule above and starting with 13, we generate the following sequence:\n",
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"> 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\n",
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"> \n",
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"> It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\n",
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"> \n",
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"> Which starting number, under one million, produces the longest chain?\n",
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"> \n",
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"> NOTE: Once the chain starts the terms are allowed to go above one million.\n",
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"\n",
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"\n",
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"---"
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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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"## Reserved Space For Imports\n",
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"---"
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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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"import os"
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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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"## Reserved Space For Method Definition\n",
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"---"
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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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"outputs": [],
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"source": [
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"def collatz_length(n: int):\n",
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" count=0\n",
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" while n != 1:\n",
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" if n%2 == 0:\n",
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" n=int(n/2)\n",
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" count+=1\n",
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" else:\n",
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" n=int(3*n+1)\n",
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" count+=1\n",
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" return int(count+1)"
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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 can't think of a way to simplify the problem, so brute force then???"
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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": 8,
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"metadata": {
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"tags": []
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},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": "The longest sequence was 525 members long, with a starting number of 837798\n"
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}
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],
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"source": [
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"# initialize a dictionary for storage\n",
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"solution_dict = {\n",
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" 'candidate': 1,\n",
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" 'length': 1\n",
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"}\n",
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"\n",
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"for i in range(1000000):\n",
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" length=collatz_length(i+1)\n",
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" if length > solution_dict['length']:\n",
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" solution_dict['candidate']=i\n",
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" solution_dict['length']=length\n",
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"\n",
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"print(\"The longest sequence was \",solution_dict['length'],\" members long, with a starting number of \",solution_dict['candidate']) "
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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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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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": "3.8.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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} |