ScalaでProject Euler（60）

Problem 33

10進で(ab)₁₀と(bc)₁₀という二つの自然数があり、それがbを消しても分数の値が同じなら、a < cならa / c、a > cならc / aを出力するだけです。

class Fraction(num :BigInt, den :BigInt) {
    val (numerator, denominator) = init(num, den)
    
    def init(num :BigInt, den :BigInt) = {
        val d = gcd(num, den).abs
        if(den > 0)
            (num / d, den / d)
        else
            (-num / d, -den / d)
    }
    
    def *(f :Fraction) =
        new Fraction(numerator * f.numerator, denominator * f.denominator)
    
    def *(n :BigInt) =
        new Fraction(numerator * n, denominator)
    
    def +(f :Fraction) =
        new Fraction(numerator * f.denominator + denominator * f.numerator,
                                                denominator * f.denominator)
    
    override def toString() =
        if(denominator != 1)
            numerator.toString + "/" + denominator.toString
        else
            numerator.toString
    
    def gcd(m :BigInt, n :BigInt) :BigInt =
        if(n == 0) m else gcd(n, m % n)
}

val it = for(a <- 1 to 9; b <- 1 to 9; c <- 1 to 9
                if (10 * a + b) * c == (10 * b + c) * a && a != c)
            yield if(a < c) new Fraction(a, c) else new Fraction(c, a)

println (it.reduceLeft(_ * _).denominator)