Step by Step solution about How to resolve the algorithm Knuth's algorithm S step by step in the Kotlin programming language

The provided Kotlin code demonstrates the implementation of a "Sample of N" (SOfN) algorithm, which is designed to maintain a sample of a fixed size (n) as new items are processed. When the sample size exceeds n, new items may randomly replace existing ones to maintain the sample size.

Here's a detailed explanation of the code:

Version 1.2.51

• The first version of the code defines a class called SOfN that takes a single parameter n, which represents the sample size.

• The class has three main properties:

  • sample: An ArrayList that stores the actual sample of items.
  • i: An integer that keeps track of the number of items processed so far.
  • process: A function that takes an item as input and returns the current sample. Here's how this function works:
    • If the number of items processed so far (i) is less than or equal to the sample size (n), the item is added to the sample.
    • Otherwise, a random index within the sample is generated. If that index is less than n, the item at that index is replaced with the new item.
    • In both cases, the updated sample is returned.

• The main function creates an integer array bin with a size of 10. It then iterates from 1 to 100,000, performing the following steps for each iteration:

  • It creates a new instance of SOfN with a sample size of 3.
  • For each integer from 0 to 8, it calls the process function of the SOfN instance, passing the integer as the input.
  • Finally, it calls process again with the number 9, and increments the corresponding element in the bin array for each element in the returned sample.

After all the iterations are complete, the main function prints the contents of the bin array, which shows the frequency of each number from 0 to 9 appearing in the sample.

Version 1.2.51

• This version of the code utilizes a slightly different approach using higher-order functions.
• It defines a function SOfNCreator that takes a sample size n as input and returns a function that takes an item of type T and returns a list of type T.
• The returned function, which is a closure, maintains an internal state (the sample) and behaves similarly to the process function in the previous version.
• The main function is essentially the same as in the previous version, except that it uses the SOfNCreator function to create a new sample of size 3 for each iteration.

// version 1.2.51

import java.util.Random

val rand = Random()

class SOfN<T>(val n: Int) {
    private val sample = ArrayList<T>(n)
    private var i = 0

    fun process(item: T): List<T> {
        if (++i <= n)
            sample.add(item)
        else if (rand.nextInt(i) < n)
            sample[rand.nextInt(n)] = item
        return sample
    }
}
 
fun main(args: Array<String>) {
    val bin = IntArray(10)
    (1..100_000).forEach {
        val sOfn = SOfN<Int>(3)
        for (d in 0..8) sOfn.process(d)
        for (s in sOfn.process(9)) bin[s]++
    }
    println(bin.contentToString())
}


// version 1.2.51

import java.util.Random

val rand = Random()

fun <T> SOfNCreator(n: Int): (T) -> List<T> {
    val sample = ArrayList<T>(n)
    var i = 0
    return {
        if (++i <= n)
            sample.add(it)
        else if (rand.nextInt(i) < n)
            sample[rand.nextInt(n)] = it
        sample
    }
}

fun main(args: Array<String>) {
    val bin = IntArray(10)
    (1..100_000).forEach {
        val sOfn = SOfNCreator<Int>(3)
        for (d in 0..8) sOfn(d)
        for (s in sOfn(9)) bin[s]++
    }
    println(bin.contentToString())
}