332 lines
9.5 KiB
Plaintext
332 lines
9.5 KiB
Plaintext
{
|
||
"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",
|
||
"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",
|
||
"> 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,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
},
|
||
{
|
||
"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,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>0</th>\n",
|
||
" <th>1</th>\n",
|
||
" <th>2</th>\n",
|
||
" <th>3</th>\n",
|
||
" <th>4</th>\n",
|
||
" <th>5</th>\n",
|
||
" <th>6</th>\n",
|
||
" <th>7</th>\n",
|
||
" <th>8</th>\n",
|
||
" <th>9</th>\n",
|
||
" <th>10</th>\n",
|
||
" <th>11</th>\n",
|
||
" <th>12</th>\n",
|
||
" <th>13</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>197</th>\n",
|
||
" <td>5.0</td>\n",
|
||
" <td>5.0</td>\n",
|
||
" <td>7.0</td>\n",
|
||
" <td>6.0</td>\n",
|
||
" <td>6.0</td>\n",
|
||
" <td>8.0</td>\n",
|
||
" <td>9.0</td>\n",
|
||
" <td>6.0</td>\n",
|
||
" <td>6.0</td>\n",
|
||
" <td>4.0</td>\n",
|
||
" <td>8.0</td>\n",
|
||
" <td>9.0</td>\n",
|
||
" <td>5.0</td>\n",
|
||
" <td>2.351462e+10</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" 0 1 2 3 4 5 6 7 8 9 10 11 12 \\\n",
|
||
"197 5.0 5.0 7.0 6.0 6.0 8.0 9.0 6.0 6.0 4.0 8.0 9.0 5.0 \n",
|
||
"\n",
|
||
" 13 \n",
|
||
"197 2.351462e+10 "
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"df.sort_values(by=series_len,ascending=False).head(1)"
|
||
]
|
||
},
|
||
{
|
||
"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": "3.8.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|