Step by Step solution about How to resolve the algorithm Iterated digits squaring step by step in the Kotlin programming language

Explanation:

Function endsWith89:

• Takes an integer n as input.
• Initializes variables digit, sum, and nn to store the digit extracted from n, the sum of squared digits, and a copy of n.
• Enters an infinite loop (represented by while (true)) to iteratively calculate the sum of squared digits:
  • It extracts each digit from nn and adds its square to sum.
  • It divides nn by 10 to remove the last digit.
• If sum becomes 89, it returns true, indicating that n ends with 89.
• If sum becomes 1, it returns false, indicating that n does not end with 89.
• It updates nn to be sum and resets sum to 0.

Main Function:

• Initializes an array sums of size 8 * 81 + 1, where 8 * 81 represents numbers up to 100 million.
• Initializes sums[0] and sums[1] to 1 and 0, respectively, as the sums of squared digits for 0 and 1.
• Utilizes nested loops to calculate the sums for every number from 1 to 8 * 81:
  • The outer loop iterates through numbers from 1 to 8, representing the starting point for a possible chain of squared digit summing.
  • The middle loop iterates through numbers from the current starting point down to 1.
  • The inner loop iterates through digits from 1 to 9 and calculates the sum of squared digits for each possible digit combination.
• Initializes count89 to 0, which will track the count of numbers from 1 to 100 million that end with 89.
• Iterates through numbers from 1 to 8 * 81 and checks if they end with 89 using the endsWith89 function. If true, it increments count89 by the number of ways to reach that number by summing squared digits.
• Finally, prints the count of numbers from 1 to 100 million that end with 89.

// version 1.0.6

fun endsWith89(n: Int): Boolean {
    var digit: Int
    var sum = 0
    var nn = n
    while (true) {
        while (nn > 0) {
            digit = nn % 10
            sum += digit * digit
            nn /= 10
        }
        if (sum == 89) return true
        if (sum == 1) return false
        nn = sum
        sum  = 0
    }
}

fun main(args: Array<String>) {
    val sums = IntArray(8 * 81 + 1)
    sums[0] = 1
    sums[1] = 0
    var s: Int
    for (n in 1 .. 8)
        for (i in n * 81 downTo 1) 
            for (j in 1 .. 9) {
                s = j * j
                if (s > i) break
                sums[i] += sums[i - s]
            }
    var count89 = 0 
    for (i in 1 .. 8 * 81) 
        if (endsWith89(i)) count89 += sums[i]
    println("There are $count89 numbers from 1 to 100 million ending with 89")
}