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

Kotlin Code Overview

This Kotlin code demonstrates the concept of Benford's law, which analyzes the distribution of the first digit in a set of numbers. It uses a NumberGenerator interface to generate a sequence of numbers and then applies Benford's analysis to the first digits of these numbers.

NumberGenerator Interface:

The NumberGenerator interface defines a single property numbers, which is an array of BigInteger numbers. This interface is used to abstract the number generation process from the Benford analysis logic.

Benford Class:

The Benford class implements the logic for Benford's analysis. It takes a NumberGenerator object as an argument and analyzes the first digits of the numbers generated by that generator.

• Initialization:

  • Initializes an integer array firstDigits to store the count of occurrences of each first digit.
  • Calculates the count as the total number of numbers generated by the NumberGenerator.
  • Builds the str string for displaying the analysis results.

• Analysis:

  • Iterates over each number in the numbers array generated by the NumberGenerator.
  • Increments the count for the first digit of each number in the firstDigits array.

FibonacciGenerator Object:

The FibonacciGenerator object implements the NumberGenerator interface and provides a lazy-initialized array of Fibonacci numbers as the numbers property.

Main Function:

• Creates a FibonacciGenerator object as the argument to the Benford constructor.
• Prints the string representation of the Benford object, which displays the distribution of the first digits according to Benford's law.

Output:

The output of the program is a table that shows:

• First digit: Values from 1 to 9
• Frequency: Frequency of occurrence of each first digit as a percentage of the total numbers
• Logarithm: Logarithmic value of the probability of each first digit occurring according to Benford's law

import java.math.BigInteger

interface NumberGenerator {
    val numbers: Array<BigInteger>
}

class Benford(ng: NumberGenerator) {
    override fun toString() = str

    private val firstDigits = IntArray(9)
    private val count = ng.numbers.size.toDouble()
    private val str: String

    init {
        for (n in ng.numbers) {
            firstDigits[n.toString().substring(0, 1).toInt() - 1]++
        }

        str = with(StringBuilder()) {
            for (i in firstDigits.indices) {
                append(i + 1).append('\t').append(firstDigits[i] / count)
                append('\t').append(Math.log10(1 + 1.0 / (i + 1))).append('\n')
            }

            toString()
        }
    }
}

object FibonacciGenerator : NumberGenerator {
    override val numbers: Array<BigInteger> by lazy {
        val fib = Array<BigInteger>(1000, { BigInteger.ONE })
        for (i in 2 until fib.size)
            fib[i] = fib[i - 2].add(fib[i - 1])
        fib
    }
}

fun main(a: Array<String>) = println(Benford(FibonacciGenerator))