project-euler/Sidef/009 Special Pythagorean triplet.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 10 October 2017
# https://github.com/trizen

# A Pythagorean triplet is a set of three natural numbers, a < b < c, for which: a^2 + b^2 = c^2

# For example:
#   3^2 + 4^2 = 9 + 16 = 25 = 5^2.

# There exists exactly one Pythagorean triplet for which a + b + c = 1000.
# Find the product abc.

# https://projecteuler.net/problem=9

# Runtime: 0.135s

func pythagorean_triplet(limit) {
    for n in (1..limit) {
        for m in (n+1 .. limit -> by(2)) {

            gcd(n, m) == 1 || next

            var x = (m**2 - n**2)
            var y = 2*n*m
            var z = (m**2 + n**2)

            for (var k = 1; true ; ++k) {
                var a = k*x
                var b = k*y
                var c = k*z

                break if (a+b+c > limit)

                if (a+b+c == limit) {
                    return a*b*c
                }
            }
        }
    }
}

say pythagorean_triplet(1000)