104 lines
3.5 KiB
Plaintext
104 lines
3.5 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "124fe12d",
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"metadata": {},
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"source": [
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"# [Largest Product in a Grid](https://projecteuler.net/problem=11)\n",
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"\n",
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"Here's that whole grid in a NumPy array."
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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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"id": "7d93e5b9",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"grid = np.array([[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]])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d4924c1d",
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"metadata": {},
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"source": [
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"Now we'll just iterate through every 4x4 subgrid of this grid, and for each subgrid, compute the product of the rows, columns, and diagonals, and record the largest product we see."
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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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"id": "7ac0e53c",
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"metadata": {},
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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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"maximum = 0\n",
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"for i in range(0, 16):\n",
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" for j in range(0, 16):\n",
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" subgrid = grid[i:i+4, j:j+4]\n",
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" \n",
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" cols = subgrid.prod(axis=0)\n",
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" rows = subgrid.prod(axis=1)\n",
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" diag = np.diag(subgrid).prod()\n",
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" anti_diag = np.diag(np.fliplr(subgrid)).prod()\n",
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" \n",
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" maximum = max(maximum, *cols, *rows, diag, anti_diag)\n",
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"\n",
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"print(maximum)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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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": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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