Project Euler in R Problem 9

December 13, 2012
By

[This article was first published on Frank Portman, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

In Problem 9 of Project Euler we are tasked with finding the product (abc) of the Pythagorean Triplet (a, b, c) such that a + b + c = 1000.

A Pythagorean triplet is a set of three natural numbers such that a2 + b2 = c2.

To solve this problem, we first see that c = (a2 + b2)1/2. Without loss of generality, we can only run the for loop for a and b, since c will be uniquely determined given a certain a and b.

The code I used:

1
2
3
4
5
6
7
8
9
10
11
for (a in 1:499) {
 for (b in 1:499) {
   if (a + b + sqrt(a^2 + b^2) == 1000) {
     print(a * b * sqrt(a^2 + b^2))
     break
   }
 }
 if (a + b + sqrt(a^2 + b^2) == 1000) {
   break
 }
}

I use nested for loops to test values of a and b between 1 and 499. a and b cannot take values greater than 499 because then a + b + sqrt(a2 + b2) would be greater than 1000.

The if statement in the nested loops checks to see whether a, b, and c add up to 1000. If they do, it prints their product and then breaks the loop. This is a short script which produces the correct answer in a few milliseconds. The trick here was expressing c in terms of a and b to reduce the amount of loops we need to run.

To leave a comment for the author, please follow the link and comment on their blog: Frank Portman.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Search R-bloggers

Sponsors

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)