145 lines
4.6 KiB
Plaintext
145 lines
4.6 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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"# Euler Problem 8\n",
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"\n",
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"The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.\n",
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"\n",
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"~~~\n",
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"73167176531330624919225119674426574742355349194934\n",
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"96983520312774506326239578318016984801869478851843\n",
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"85861560789112949495459501737958331952853208805511\n",
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"12540698747158523863050715693290963295227443043557\n",
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"66896648950445244523161731856403098711121722383113\n",
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"62229893423380308135336276614282806444486645238749\n",
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"30358907296290491560440772390713810515859307960866\n",
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"70172427121883998797908792274921901699720888093776\n",
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"65727333001053367881220235421809751254540594752243\n",
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"52584907711670556013604839586446706324415722155397\n",
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"53697817977846174064955149290862569321978468622482\n",
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"83972241375657056057490261407972968652414535100474\n",
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"82166370484403199890008895243450658541227588666881\n",
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"16427171479924442928230863465674813919123162824586\n",
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"17866458359124566529476545682848912883142607690042\n",
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"24219022671055626321111109370544217506941658960408\n",
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"07198403850962455444362981230987879927244284909188\n",
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"84580156166097919133875499200524063689912560717606\n",
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"05886116467109405077541002256983155200055935729725\n",
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"71636269561882670428252483600823257530420752963450\n",
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"~~~\n",
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"\n",
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"Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?"
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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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"We need the number as a list of integers first."
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def remove_newlines(s):\n",
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" import re\n",
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" return re.sub(r'\\n', '', s)\n",
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"\n",
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"digits_string = \"\"\"73167176531330624919225119674426574742355349194934\n",
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"96983520312774506326239578318016984801869478851843\n",
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"85861560789112949495459501737958331952853208805511\n",
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"12540698747158523863050715693290963295227443043557\n",
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"66896648950445244523161731856403098711121722383113\n",
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"62229893423380308135336276614282806444486645238749\n",
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"30358907296290491560440772390713810515859307960866\n",
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"70172427121883998797908792274921901699720888093776\n",
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"65727333001053367881220235421809751254540594752243\n",
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"52584907711670556013604839586446706324415722155397\n",
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"53697817977846174064955149290862569321978468622482\n",
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"83972241375657056057490261407972968652414535100474\n",
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"82166370484403199890008895243450658541227588666881\n",
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"16427171479924442928230863465674813919123162824586\n",
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"17866458359124566529476545682848912883142607690042\n",
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"24219022671055626321111109370544217506941658960408\n",
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"07198403850962455444362981230987879927244284909188\n",
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"84580156166097919133875499200524063689912560717606\n",
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"05886116467109405077541002256983155200055935729725\n",
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"71636269561882670428252483600823257530420752963450\"\"\"\n",
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"\n",
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"digits = [int(d) for d in remove_newlines(digits_string)]"
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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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" Then we can use slicing to do a brute force."
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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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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"23514624000\n"
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]
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}
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],
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"source": [
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"def product(xs):\n",
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" from operator import mul\n",
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" from functools import reduce\n",
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" return reduce(mul, xs, 1)\n",
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"\n",
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"def get_largest_product_of_n_digits(digits, n):\n",
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" return max((product(digits[i:i + n]) for i in range(len(digits))))\n",
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"\n",
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"assert(get_largest_product_of_n_digits(digits, 4) == 5832)\n",
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"assert(get_largest_product_of_n_digits(digits, 13) == 23514624000)\n",
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"print(get_largest_product_of_n_digits(digits, 13))"
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]
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}
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],
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"metadata": {
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"completion_date": "Wed, 20 Aug 2014, 16:03",
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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": "3.5.4"
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},
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"tags": [
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"product",
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"reduce",
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"slice"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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