170 lines
3.8 KiB
Plaintext
170 lines
3.8 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 9:\n",
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"\n",
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"[Euler Project #9](https://projecteuler.net/problem=9)\n",
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"\n",
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"\n",
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"\n",
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">A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,\n",
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"a2 + b2 = c2\n",
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"\n",
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">For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.\n",
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"\n",
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">There exists exactly one Pythagorean triplet for which a + b + c = 1000.\n",
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"Find the product abc.\n",
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"\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\n",
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"import pprint\n",
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"import time # Typically imported for sleep function, to slow down execution in terminal.\n",
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"import typing\n",
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"import decorators # Typically imported to compute execution duration of functions.\n",
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"import numpy\n",
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"import pandas"
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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": 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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"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": "markdown",
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"metadata": {},
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"source": [
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"## Can we describe a few approaches to solving this problem?\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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"*Let's discuss a few ways to work through this, then select one to implement.*\n",
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"\n",
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" 1. Create a 2D array in which we can place each candidate series of integers.\\\n",
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" A column vector can also be created in which can store the product of each series.\\\n",
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" If we zip these arrays together, sort on the product column, we can identify the\\\n",
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" the maximum product and its associate string of integers.\n",
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"<br/>\n",
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"<br/>\n",
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" 2. Create an array (of the specified length) to store a series of integers from the input\\\n",
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" number. Allow this to be an array that we use to compute the a product. It will shift as we\\\n",
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" slide along the input number. A second array of identical dimension, plus an additional place,\\\n",
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" could store the largest product, and the associated list of integers. \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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"### Let's try the first approach!"
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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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"#### 1. a) Take in problem statement information."
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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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"#### 1. b) Build out the candidate array. "
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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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"#### 1. c) Cheat by using pandas to print out the maximum product and its associated series of integers. "
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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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}
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