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