Step by Step solution about How to resolve the algorithm Seven-sided dice from five-sided dice step by step in the Kotlin programming language

This Kotlin program simulates rolling a 7-sided die and checks the distribution of the results. Here's a detailed explanation:

1. Importing Java Libraries:

   import java.util.Random

   Imports the Java Random class for generating random numbers.

2. Random Number Generation:

   val r = Random()

   Creates an instance of the Random class for generating random numbers.

3. dice5 Function:

   fun dice5() = 1 + r.nextInt(5)

   Simulates rolling a 5-sided die by generating a random number between 0 and 4 and adding 1 to it, resulting in values from 1 to 5.

4. dice7 Function:

   fun dice7(): Int {
      while (true) {
          val t = (dice5() - 1) * 5 + dice5() - 1
          if (t >= 21) continue
          return 1 + t / 3
      }
   }

   This function simulates rolling a 7-sided die. It does this by rolling two 5-sided dice and creating a number t between 0 and 20. If t is greater than or equal to 21, it continues rolling the dice. Otherwise, it returns 1 plus the integer division of t by 3, resulting in values from 1 to 7.

5. checkDist Function:

   fun checkDist(gen: () -> Int, nRepeats: Int, tolerance: Double = 0.5) {
      // ...
   }

   This function is used to check the distribution of the results generated by a given function gen (which takes no arguments and returns an integer). It takes three parameters:

   • gen: A function that generates random numbers.
   • nRepeats: The number of times to roll the dice.
   • tolerance: The acceptable percentage error for each number (default is 0.5%).

6. Distribution Checking: The checkDist function generates nRepeats random numbers using gen, counts the occurrences of each number, and compares the observed distribution to the expected distribution. It prints the results in a table, showing the integer value, number of occurrences, error, and whether the error is acceptable according to the specified tolerance.

7. Main Function:

   fun main(args: Array<String>) {
      checkDist(::dice7, 1_400_000)
   }

   In the main function, the checkDist function is called with the dice7 function and 1,400,000 repeats. This simulates rolling a 7-sided die 1,400,000 times and checks the distribution of the results against an expected uniform distribution, with a tolerance of 0.5%. The program prints the results, indicating whether the overall distribution is acceptable within the specified tolerance.

// version 1.1.3

import java.util.Random

val r = Random()

fun dice5() = 1 + r.nextInt(5)

fun dice7(): Int {
    while (true) {
       val t = (dice5() - 1) * 5 + dice5() - 1
       if (t >= 21) continue
       return 1 + t / 3
    }
}

fun checkDist(gen: () -> Int, nRepeats: Int, tolerance: Double = 0.5) {
    val occurs = mutableMapOf<Int, Int>()
    for (i in 1..nRepeats) {
        val d = gen()
        if (occurs.containsKey(d))
            occurs[d] = occurs[d]!! + 1
        else
            occurs.put(d, 1)
    }
    val expected = (nRepeats.toDouble()/ occurs.size).toInt()
    val maxError = (expected * tolerance / 100.0).toInt()
    println("Repetitions = $nRepeats, Expected = $expected")
    println("Tolerance = $tolerance%, Max Error = $maxError\n")
    println("Integer   Occurrences   Error  Acceptable")
    val f = "  %d        %5d      %5d     %s" 
    var allAcceptable = true
    for ((k,v) in occurs.toSortedMap()) {
        val error = Math.abs(v - expected)
        val acceptable = if (error <= maxError) "Yes" else "No"
        if (acceptable == "No") allAcceptable = false
        println(f.format(k, v, error, acceptable))
    }  
    println("\nAcceptable overall: ${if (allAcceptable) "Yes" else "No"}")
}

fun main(args: Array<String>) {
    checkDist(::dice7, 1_400_000)
}