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Shaun Setlock
2020-08-02 07:38:10 -04:00
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 8:\n",
"\n",
"[Euler Project #8](https://projecteuler.net/problem=8)\n",
"\n",
"\n",
"\n",
"> The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.\n",
"\n",
"> 73167176531330624919225119674426574742355349194934\n",
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"\n",
"> Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?\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\n",
"import pandas"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reserved Space For Method Definition\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Can we describe a few approaches to solving this problem?\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Let's discuss a few ways to work through this, then select one to implement.*\n",
"\n",
" 1. Create a 2D array in which we can place each candidate series of integers.\\\n",
" A column vector can also be created in which can store the product of each series.\\\n",
" If we zip these arrays together, sort on the product column, we can identify the\\\n",
" the maximum product and its associate string of integers.\n",
"<br/>\n",
"<br/>\n",
" 2. Create an array (of the specified length) to store a series of integers from the input\\\n",
" number. Allow this to be an array that we use to compute the a product. It will shift as we\\\n",
" slide along the input number. A second array of identical dimension, plus an additional place,\\\n",
" could store the largest product, and the associated list of integers. \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Let's try the first approach!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1. a) Take in problem statement information."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# problem statement input 1000 digit integer\n",
"input_list = [int(n) for n in \"\\\n",
"73167176531330624919225119674426574742355349194934\\\n",
"96983520312774506326239578318016984801869478851843\\\n",
"85861560789112949495459501737958331952853208805511\\\n",
"12540698747158523863050715693290963295227443043557\\\n",
"66896648950445244523161731856403098711121722383113\\\n",
"62229893423380308135336276614282806444486645238749\\\n",
"30358907296290491560440772390713810515859307960866\\\n",
"70172427121883998797908792274921901699720888093776\\\n",
"65727333001053367881220235421809751254540594752243\\\n",
"52584907711670556013604839586446706324415722155397\\\n",
"53697817977846174064955149290862569321978468622482\\\n",
"83972241375657056057490261407972968652414535100474\\\n",
"82166370484403199890008895243450658541227588666881\\\n",
"16427171479924442928230863465674813919123162824586\\\n",
"17866458359124566529476545682848912883142607690042\\\n",
"24219022671055626321111109370544217506941658960408\\\n",
"07198403850962455444362981230987879927244284909188\\\n",
"84580156166097919133875499200524063689912560717606\\\n",
"05886116467109405077541002256983155200055935729725\\\n",
"71636269561882670428252483600823257530420752963450\"]\n",
"\n",
"# problem statement request series length\n",
"series_len = 13"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1. b) Build out the candidate array. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# number of possible integer-series candidates\n",
"rows = len(input_list) - series_len\n",
"# length of the requested series, plus an additional column to store the product\n",
"columns = series_len + 1\n",
"\n",
"# construct the array with placeholder values\n",
"array = numpy.array(numpy.ones((rows,columns)))\n",
"\n",
"# loop for each candidate\n",
"for i in range(rows):\n",
" # loop to fill out each candidate and store its product in the last column\n",
" for j in range(series_len):\n",
" \n",
" array[i][j] = input_list[i+j]\n",
" array[i][-1] *= array[i][j]\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1. c) Cheat by using pandas to print out the maximum product and its associated series of integers. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"df = pandas.DataFrame(array)"
]
},
{
"cell_type": "code",
"execution_count": 5,
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