204 lines
5.0 KiB
Plaintext
204 lines
5.0 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Problem 5:\n",
|
|
"\n",
|
|
"[Euler Project #5](https://projecteuler.net/problem=5)\n",
|
|
"\n",
|
|
"> *2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.*\n",
|
|
"> *What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?*\n",
|
|
"\n",
|
|
"---"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Reserved Space For Imports\n",
|
|
"---"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import os\n",
|
|
"import pprint\n",
|
|
"import time # Typically imported for sleep function, to slow down execution in terminal.\n",
|
|
"import typing\n",
|
|
"import decorators # Typically imported to compute execution duration of functions.\n",
|
|
"import numpy"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Reserved Space For Method Definition\n",
|
|
"---"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def primes_gen(start_n: int,max_n: int):\n",
|
|
" \"\"\"\n",
|
|
" Returns a generator object, containing the \n",
|
|
" primes inside a specified range.\n",
|
|
" primes_gen(start_n,max_n)\n",
|
|
" param 'start_n': Previous prime.\n",
|
|
" param 'max_n': Maximum integer allowed to be returned. Quit if reached.\n",
|
|
" \"\"\"\n",
|
|
" start_n += 1\n",
|
|
" for candidate in range(start_n,max_n):\n",
|
|
" notPrime = False\n",
|
|
" \n",
|
|
" if candidate in [0,1,2,3]:\n",
|
|
" yield candidate\n",
|
|
" for dividend in range(2,candidate):\n",
|
|
" \n",
|
|
" if candidate%dividend == 0:\n",
|
|
" notPrime = True\n",
|
|
" \n",
|
|
" if not notPrime:\n",
|
|
" yield candidate"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def evenly_divisible(candidate: int,factors: list):\n",
|
|
" \"\"\"\n",
|
|
" Determines if the supplied integer candidate is \n",
|
|
" evenly divisble by the supplied list of factors.\n",
|
|
" \n",
|
|
" evenly_divisible(candidate: int, factors: list)\n",
|
|
"\n",
|
|
" param 'candidate': Integer to be tested.\n",
|
|
" param 'factors': List of factors for the modulus operator.\n",
|
|
" \n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" modulus_sum = 0\n",
|
|
"\n",
|
|
" for n in factors:\n",
|
|
" modulus_sum += candidate%n\n",
|
|
" \n",
|
|
" if modulus_sum == 0: \n",
|
|
" return True\n",
|
|
" else:\n",
|
|
" return False"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 1. Begin with testing the problem statement's example case.\n",
|
|
"---"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"*Mathematically, the trick is to recognize that this a LCM (Least Common Multiple) problem. The solution is list all the prime factors of each number in the factor list, then compute their collective product.*\n",
|
|
"\n",
|
|
" - [x] Create the list of factors, prescribed by the problem statement. Use a list.\n",
|
|
" - [ ] Generate a list of prime factors for each of the factors. Use a list of list.\n",
|
|
" - [ ] For each of the unique prime factors found in the previous list of lists, \n",
|
|
" find the factor for which the \n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Receive problem inputs...\n",
|
|
"smallest_factor = 1\n",
|
|
"largest_factor = 10\n",
|
|
"\n",
|
|
"# Compute intermediate inputs\n",
|
|
"factor_list = [int(i) for i in range(smallest_factor,largest_factor+1)]\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.8.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|