Largest Product in a Grid — Project Euler (Problem 11)

I started solving Project Euler problems this month. Check out the Project Euler tab of this blog for a list of the problems I’ve solved (with solutions) till date. Here’s a problem you might find interesting:

Here’s my solution using Python (I basically search through the entire matrix which is of O(n²) complexity):

I first copy the maxtrix into a text file euler11.txt so that it can be later read into Python

	08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
	49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
	81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
	52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
	22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
	24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
	32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
	67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
	24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
	21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
	78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
	16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
	86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
	19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
	04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
	88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
	04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
	20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
	20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
	01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

view raw euler11.txt hosted with ❤ by GitHub

I then execute the following code from the same working directory as euler11.txt

	# import numpy module for matrix operations
	from numpy import *

	# read the file with the matrix of numbers
	filename = 'euler11.txt'

	# store each line of the file into an array
	with open(filename, "r") as ins:
	array = []
	for line in ins:
	array.append(line)
	print array

	# create a new array that converts the number strings into number integers
	newArray = []
	for i in array:
	j = i.split(' ')
	k = [int(n) for n in j]
	newArray.append(k)
	print newArray

	# convert the array of integers into a matrix of integers

	problemMatrix = matrix(newArray)
	print problemMatrix

	# set initial maximum product to be a dummy number, say 1
	maxProd = 1

	# search all combinations for maximum product

	for i in range(16):
	for j in range(16):
	prod1 = problemMatrix[i,j]problemMatrix[i+1,j]problemMatrix[i+2,j]*problemMatrix[i+3,j]
	if prod1 > maxProd:
	maxProd = prod1
	prod2 = problemMatrix[i,j]problemMatrix[i,j+1]problemMatrix[i,j+2]*problemMatrix[i,j+3]
	if prod2 > maxProd:
	maxProd = prod2
	prod3 = problemMatrix[i,j]problemMatrix[i+1,j+1]problemMatrix[i+2,j+2]*problemMatrix[i+3,j+3]
	if prod3 > maxProd:
	maxProd = prod3
	prod4 = problemMatrix[19-i,j]problemMatrix[18-i,j+1]problemMatrix[17-i,j+2]*problemMatrix[16-i,j+3]
	if prod4 > maxProd:
	maxProd = prod4
	print maxProd

view raw euler11.py hosted with ❤ by GitHub

Answer: 70600674

One thought on “Largest Product in a Grid — Project Euler (Problem 11)”

This is a little bit late, but I just found this and think the loop sequence is very clean, but I was wondering why you wouldn’t substitute all your top lines for this:
problemMatrix = np.loadtxt(“euler11.txt”)

Is there some benefit to your method?
Really like the blog btw

LikeLiked by 1 person

Denzel Farmer says:

December 27, 2017 at 3:51 am

This is a little bit late, but I just found this and think the loop sequence is very clean, but I was wondering why you wouldn’t substitute all your top lines for this:
problemMatrix = np.loadtxt(“euler11.txt”)

Is there some benefit to your method?
Really like the blog btw

LikeLiked by 1 person