Quick X Algorithm
The Quick X Algorithm is a groundbreaking and innovative approach to solving a wide range of complex computational problems in the digital world. This advanced algorithm, also known as 'QuickX,' is designed to foster a decentralized, trustless, and secure environment, primarily in the blockchain and cryptocurrency space. Its primary focus is to address issues such as transaction time, scalability, and cross-chain transfers of assets in a highly efficient and cost-effective manner. By leveraging state-of-the-art techniques, the Quick X Algorithm aims to revolutionize the way decentralized applications and platforms operate, providing a seamless user experience and overcoming limitations associated with traditional blockchain systems.
At the core of the Quick X Algorithm is the concept of off-chain transactions, which significantly reduces the load on the blockchain network, resulting in faster transaction processing and reduced fees. The algorithm achieves this by utilizing a network of off-chain liquidity providers, known as 'Multipliers,' which facilitate near-instantaneous transfers of assets between different blockchains. Additionally, the Quick X Algorithm incorporates advanced cryptographic techniques and consensus mechanisms, ensuring the highest level of security and reliability for all transactions. With its unparalleled speed, scalability, and interoperability, the Quick X Algorithm is poised to usher in a new era of blockchain technology, paving the way for mass adoption and widespread integration of cryptocurrencies and decentralized applications in various industries.
package org.gs.sort
import scala.annotation.tailrec
import scala.collection.mutable.ArrayBuffer
import scala.reflect.ClassTag
import scala.util.Random
/** Quicksort
*
* @constructor creates a new QuickX
* @tparam A elements are generic and ordered ClassTag preserves Array type at runtime
* @param ord implicitly provides ordering
* @see [[https://algs4.cs.princeton.edu/23quicksort/QuickX.java.html]]
* @author Scala translation by Gary Struthers from Java by Robert Sedgewick and Kevin Wayne.
*/
class QuickX[A: ClassTag](implicit ord: A => Ordered[A]) {
private def shuffleArrayBuffer[A: ClassTag](xs: Array[A]): Array[A] = {
val a = Random.shuffle(xs.toBuffer)
a.toArray
}
/** exchange i and j in array */
def exchange(i: Int, j: Int, xs: Array[A]) {
val iVal = xs(j)
val jVal = xs(i)
xs.update(i, iVal)
xs.update(j, jVal)
}
/** Insertion sort is faster when partition or array has fewer than 10 elements
* Exchange 2 elements when the one on the left is greater than the one on the right
*
* @param generic array to sort
*/
def insertionSort(xs: Array[A]): Unit = {
var i = 1
@tailrec
def loopI(): Unit = {
var j = i
@tailrec
def loopJ(): Unit = {
if (xs(j) >= xs(j - 1)) j = 0 else {
exchange(j, j - 1, xs)
j -= 1
}
if (j > 0) loopJ()
}
i += 1
loopJ()
if (i < xs.length) loopI()
}
loopI()
}
private def partition(lo: Int, hi: Int, xs: Array[A]): Int = {
def medianOf3(xs: Array[A]): Int = { //@TODO
val center = (lo + hi) / 2
if (xs(lo) > xs(center)) exchange(lo, center, xs)
if (xs(lo) > xs(hi)) exchange(lo, hi, xs)
if (xs(center) > xs(hi)) exchange(center, hi, xs)
exchange(center, hi - 1, xs)
hi - 1
}
/** Scan from left of array until finding element greater than partition
*
* stop incrementing when x >= lo
*
* @param i partition
* @param xs array
* @return new i index
*/
def scanLR(i: Int, xs: Array[A]): Int = {
def stopInc(x: A): Boolean = x >= xs(lo)
def from(): Int = if (lo < i) i else lo + 1
xs indexWhere (stopInc(_), from)
}
/** Scan from right of array until finding element greater than partition
*
* stop decrementing when x <= lo
*
* @param i partition
* @param xs array
* @return new j index
*/
def scanRL(j: Int, xs: Array[A]): Int = {
def stopDec(x: A) = (x <= xs(lo))
xs lastIndexWhere (stopDec(_), j)
}
@tailrec /** scan both partition, put i, j in order, loop */
def loop(i: Int, j: Int, xs: Array[A]): Int = {
val rl = scanRL(j, xs)
scanLR(i, xs) match {
case lr if(lr == rl) => rl
case lr if(lr > rl) => {
exchange(lo, rl, xs)
rl
}
case lr => {
exchange(lr, rl, xs)
loop(lr, rl, xs)
}
}
}
loop(lo + 1, hi, xs)
}
private def sort(low: Int, high: Int, xs: Array[A]): Unit = if (low < high) {
if ((low + 10) > high) insertionSort(xs) else {
val j = partition(low, high: Int, xs)
sort(low, j - 1, xs)
sort(j + 1, high, xs)
}
}
/** Quicksort recursively partition and sort partions
*
* @param a generic array
* @param shuffle optionally shuffle for performance
* @return sorted array
*/
def sort(a: Array[A], shuffle: Boolean = true): Array[A] = {
val myArray = if (shuffle) shuffleArrayBuffer(a) else a
sort(0, myArray.length - 1, myArray)
myArray
}
}
