Data commit

Task/Arithmetic-Rational/Kotlin/arithmetic-rational.kotlin

@@ -0,0 +1,127 @@
+// version 1.1.2
+
+fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)
+
+infix fun Long.ldiv(denom: Long) = Frac(this, denom)
+
+infix fun Int.idiv(denom: Int) = Frac(this.toLong(), denom.toLong())
+
+fun Long.toFrac() = Frac(this, 1)
+
+fun Int.toFrac() = Frac(this.toLong(), 1)
+
+class Frac : Comparable<Frac> {
+    val num: Long
+    val denom: Long
+
+    companion object {
+        val ZERO = Frac(0, 1)
+        val ONE  = Frac(1, 1)
+    }
+
+    constructor(n: Long, d: Long) {
+        require(d != 0L)
+        var nn = n
+        var dd = d
+        if (nn == 0L) {
+            dd = 1
+        }
+        else if (dd < 0) {
+            nn = -nn
+            dd = -dd
+        }
+        val g = Math.abs(gcd(nn, dd))
+        if (g > 1) {
+            nn /= g
+            dd /= g
+        }
+        num = nn
+        denom = dd
+    }
+
+    constructor(n: Int, d: Int) : this(n.toLong(), d.toLong())
+
+    operator fun plus(other: Frac) =
+        Frac(num * other.denom + denom * other.num, other.denom * denom)
+
+    operator fun unaryPlus() = this
+
+    operator fun unaryMinus() = Frac(-num, denom)
+
+    operator fun minus(other: Frac) = this + (-other)
+
+    operator fun times(other: Frac) = Frac(this.num * other.num, this.denom * other.denom)
+
+    operator fun rem(other: Frac) = this - Frac((this / other).toLong(), 1) * other
+
+    operator fun inc() = this + ONE
+    operator fun dec() = this - ONE
+
+    fun inverse(): Frac {
+        require(num != 0L)
+        return Frac(denom, num)
+    }
+
+    operator fun div(other: Frac) = this * other.inverse()
+
+    fun abs() = if (num >= 0) this else -this
+
+    override fun compareTo(other: Frac): Int {
+        val diff = this.toDouble() - other.toDouble()
+        return when {
+            diff < 0.0  -> -1
+            diff > 0.0  -> +1
+            else        ->  0
+        }
+    }
+
+    override fun equals(other: Any?): Boolean {
+       if (other == null || other !is Frac) return false
+       return this.compareTo(other) == 0
+    }
+
+    override fun hashCode() = num.hashCode() xor denom.hashCode()
+
+    override fun toString() = if (denom == 1L) "$num" else "$num/$denom"
+
+    fun toDouble() = num.toDouble() / denom
+
+    fun toLong() = num / denom
+}
+
+fun isPerfect(n: Long): Boolean {
+    var sum = Frac(1, n)
+    val limit = Math.sqrt(n.toDouble()).toLong()
+    for (i in 2L..limit) {
+        if (n % i == 0L) sum += Frac(1, i) + Frac(1, n / i)
+    }
+    return sum == Frac.ONE
+}
+
+fun main(args: Array<String>) {
+    var frac1 = Frac(12, 3)
+    println ("frac1 = $frac1")
+    var frac2 = 15 idiv 2
+    println("frac2 = $frac2")
+    println("frac1 <= frac2 is ${frac1 <= frac2}")
+    println("frac1 >= frac2 is ${frac1 >= frac2}")
+    println("frac1 == frac2 is ${frac1 == frac2}")
+    println("frac1 != frac2 is ${frac1 != frac2}")
+    println("frac1 + frac2 = ${frac1 + frac2}")
+    println("frac1 - frac2 = ${frac1 - frac2}")
+    println("frac1 * frac2 = ${frac1 * frac2}")
+    println("frac1 / frac2 = ${frac1 / frac2}")
+    println("frac1 % frac2 = ${frac1 % frac2}")
+    println("inv(frac1)    = ${frac1.inverse()}")
+    println("abs(-frac1)   = ${-frac1.abs()}")
+    println("inc(frac2)    = ${++frac2}")
+    println("dec(frac2)    = ${--frac2}")
+    println("dbl(frac2)    = ${frac2.toDouble()}")
+    println("lng(frac2)    = ${frac2.toLong()}")
+    println("\nThe Perfect numbers less than 2^19 are:")
+    // We can skip odd numbers as no known perfect numbers are odd
+    for (i in 2 until (1 shl 19) step 2) {
+        if (isPerfect(i.toLong())) print("  $i")
+    }
+    println()
+}