188 lines
6.7 KiB
Plaintext
188 lines
6.7 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 11\n",
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"\n",
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"In the 20×20 grid below, four numbers along a diagonal line have been marked in red.\n",
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"\n",
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"~~~\n",
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"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n",
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"49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n",
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"81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n",
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"52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n",
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"22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n",
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"24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n",
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"32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n",
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"67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n",
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"24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n",
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"21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n",
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"78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n",
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"16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n",
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"86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n",
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"19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n",
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"04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n",
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"88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n",
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"04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n",
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"20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n",
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"20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n",
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"01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\n",
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"~~~\n",
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"\n",
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"The product of these numbers is $26 × 63 × 78 × 14 = 1788696$.\n",
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"\n",
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"What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?"
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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 start by parsing the array into three lists of lists (horizontal, diagonal, vertical).\n",
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"\n",
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"97, 17, 79, 11, 89, 44, 38, 94, 78, 0, 62, 54, 58, 4, 27, 53, 36, 1, 1, 1]"
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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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"scrolled": true
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},
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"outputs": [],
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"source": [
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"s = \"\"\"\n",
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"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n",
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"49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n",
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"81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n",
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"52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n",
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"22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n",
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"24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n",
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"32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n",
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"67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n",
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"24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n",
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"21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n",
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"78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n",
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"16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n",
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"86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n",
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"19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n",
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"04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n",
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"88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n",
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"04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n",
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"20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n",
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"20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n",
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"01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\n",
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"\"\"\"\n",
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"\n",
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"def get_index(xs, index, default):\n",
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" if index < 0:\n",
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" return default\n",
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" try:\n",
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" return xs[index]\n",
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" except IndexError:\n",
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" return default\n",
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"\n",
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"hss = [list(map(int, h.split())) for h in s.split('\\n') if h]\n",
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"vss = [list(vs) for vs in zip(*hss)]\n",
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"# diagonal from top left to bottom right\n",
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"dss = [[get_index(hs, -19 + i + j, 1) for j, hs in enumerate(hss)] for i in range(39)]\n"
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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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"I really love the way we retrieve the vertical list. (We need the ugly conversion to list because otherwise we cannot concatenate them.) It is at the limit of my mental capabilities to understand why this works. But actually it is quite straight forward. If we provide two lists, zip creates a two-tuple for each field in the lists. If we provide n lists, zip creates a n-tuple for each field in the lists. Easy.\n",
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"\n",
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"Now we create big list of lists and search each one for the greates four product and then get the maximum. Straight forward. We borrow the find product function from problem 8 because I like it."
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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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"source": [
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"xss = hss + vss + dss\n",
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"\n",
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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(xs, n):\n",
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" return max([product(xs[i:i + n]) for i in range(len(xs))])\n",
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"\n",
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"s = max([get_largest_product_of_n_digits(xs, 4) for xs in xss])\n",
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"assert(s != 70600674)"
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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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"Okay, I am actually really dumb. I forgot about the other diagonal. I think I have made the same mistake back when I solved this for the first time. So let's get the missing dss and get the solution."
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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": 3,
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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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"70600674\n"
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]
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}
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],
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"source": [
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"# diagonal from bottom left to top right\n",
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"hss.reverse()\n",
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"dss = [[get_index(hs, -19 + i + j, 1) for j, hs in enumerate(hss)] for i in range(39)]\n",
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"\n",
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"s = max([get_largest_product_of_n_digits(ds, 4) for ds in dss])\n",
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"assert(s == 70600674)\n",
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"print(s)"
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]
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}
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],
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"metadata": {
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"completion_date": "Sun, 31 Aug 2014, 07:39",
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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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"brute force",
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"product",
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"matrix",
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"tricky",
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"diagonal"
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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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