Project Euler 11: Largest product in a grid
Peter Prevos |
217 words | 2 minutes
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Project Euler 11 is a relatively straightforward application of vector arithmetics in R. Just like problem 8, it asks for the largest product.
Project Euler 11 Definition
In the 20×20 grid below, four numbers along a diagonal line have been marked in red. The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
Solution
The solution applies straightforward vector arithmetic to multiply the verticals, horizontals and diagonals. The product of all verticals is an array of the product of rows 1 to 4, rows 2 to 5 and so on. The code uses a similar logic for the horizontals and the diagonals.
## Project Euler 11: Largest product in a grid
square <- as.matrix(read.delim("data/p011_matrix.txt", header = FALSE, sep = " "))
prod.vert <- square[1:17, ] * square[2:18, ] * square[3:19, ] * square[4:20, ]
prod.hori <- square[ ,1:17] * square[ ,2:18] * square[ ,3:19] * square[ ,4:20]
prod.dia1 <- square[1:17, 1:17] * square[2:18, 2:18] * square[3:19, 3:19] * square[4:20, 4:20]
prod.dia2 <- square[4:20, 1:17] * square[3:19, 2:18] * square[2:18, 3:19] * square[1:17, 4:20]
answer <- max(prod.vert, prod.hori, prod.dia1, prod.dia2)
print(answer)Share this content
