Step by Step solution about How to resolve the algorithm Smith numbers step by step in the Kotlin programming language

The provided Kotlin code is designed to find and print all Smith numbers below 10,000. A Smith number is a composite number whose sum of digits is the same as the sum of digits in its prime factors.

Here's a breakdown of the code:

1. The program begins with three helper functions:

   • getPrimeFactors(n): This function takes an integer n and returns a mutable list containing the prime factors of n. It uses a while loop to repeatedly divide n by prime numbers until n is equal to 1, and collects the prime factors along the way.

   • sumDigits(n): This function takes an integer n and returns the sum of its digits. If n is less than 10, it returns n directly. Otherwise, it repeatedly extracts the last digit of n and adds it to a running sum until n becomes 0.

   • isSmith(n): This function checks whether a given integer n is a Smith number. It first ensures that n is a composite number (i.e., n has more than one prime factor). Then, it calculates the sum of digits in n using sumDigits(n) and the sum of digits in its prime factors (using sumBy and sumDigits). If these two sums are equal, n is a Smith number.

2. The main function, which is the entry point of the program, does the following:

   • It iterates through all integers from 2 to 9,999 (exclusive).

   • For each integer i, it checks if it's a Smith number using the isSmith function.

   • If i is a Smith number, its value is printed on the console, and a count of Smith numbers found is incremented.

3. After processing all integers, the program prints the total count of Smith numbers found below 10,000.

In summary, this Kotlin program efficiently finds and displays all Smith numbers below 10,000 using its helper functions for calculating prime factors and summing digits.

// version 1.0.6

fun getPrimeFactors(n: Int): MutableList<Int> {
    val factors = mutableListOf<Int>()
    if (n < 2) return factors
    var factor = 2
    var nn = n
    while (true) {
        if (nn % factor == 0) {
            factors.add(factor)
            nn /= factor
            if (nn == 1) return factors
        }
        else if (factor >= 3) factor += 2
        else factor = 3
    }
}

fun sumDigits(n: Int): Int = when {
        n < 10 -> n
        else   -> {
            var sum = 0
            var nn = n
            while (nn > 0) {
                sum += (nn % 10)
                nn /= 10
            }
            sum
        }
    }

fun isSmith(n: Int): Boolean {
    if (n < 2) return false
    val factors = getPrimeFactors(n)
    if (factors.size == 1) return false
    val primeSum = factors.sumBy { sumDigits(it) }
    return sumDigits(n) == primeSum
}

fun main(args: Array<String>) {
    println("The Smith numbers below 10000 are:\n")
    var count = 0
    for (i in 2 until 10000) {
        if (isSmith(i)) {
            print("%5d".format(i))
            count++
        }
    }
    println("\n\n$count numbers found")
}