project-euler/Sidef/075 Singular integer right triangles -- v2.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 21 March 2023
# https://github.com/trizen

# https://projecteuler.net/problem=75

# Runtime: 55.256s

func count_singular_integer_right_triangles(limit) {

    var triangle = Hash()

    var upto = limit.isqrt

    for n in (1 .. upto) {
        for m in (range(n+1, upto, 2)) {

            n.is_coprime(m) || next

            for (var k = 1; true; ++k) {

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

                var p = x+y+z
                break if (p > limit)
                triangle{p} := 0 ++
            }
        }
    }

    triangle.values.count_by { .is_one }
}

assert_eq(count_singular_integer_right_triangles(48), 6)
assert_eq(count_singular_integer_right_triangles(120), 13)
assert_eq(count_singular_integer_right_triangles(1200), 129)

say count_singular_integer_right_triangles(1_500_000)