Step by Step solution about How to resolve the algorithm Casting out nines step by step in the Kotlin programming language

The provided Kotlin code defines a function castOut that generates a list of integers within a specified range that satisfy a particular condition. Here's a detailed explanation of the code:

1. castOut Function:

   • It takes three integer parameters:
     • base: This is the number whose multiples are filtered out.
     • start: The starting point of the range.
     • end: The ending point of the range.
   • The function generates a list of integers within the range [start, end] that match a specific criterion.

2. Computation of b and ran:

   • The variable b is calculated as base - 1.
   • ran is a list of integers from 0 to b-1 (inclusive) that satisfy the following condition: it % b == (it * it) % b. This condition means that the square of each number in ran is congruent to the number itself when divided by b.

3. Initialization:

   • x is initialized to start / b.
   • result is initialized as an empty mutable list.

4. Loop:

   • The code enters an infinite loop that continues until it breaks out explicitly.
   • Inside the loop:
     • For each n in ran, the variable k is calculated as b * x + n.
     • If k is less than start, it is ignored and the loop continues to the next value of n.
     • If k is greater than end, it means the end of the range has been exceeded, so the function breaks out of the loop and returns the result list.
     • If k is within the range, it is added to the result list.
   • After iterating through all values of n in ran, x is incremented by 1, and the loop continues.

5. Return Value:

   • When the loop exits, the function returns the result list, which contains all the integers within the range [start, end] that satisfy the condition specified by the ran list.

6. Main Function:

   • The main function calls the castOut function three times with different parameters and prints the results to the console.

In summary, the castOut function filters out multiples of a given base (base) from a specified range ([start, end]) and generates a list of the remaining integers that satisfy a particular condition related to squaring modulo base. It accomplishes this by iteratively checking each integer in the range and only including those that meet the condition.

// version 1.1.3

fun castOut(base: Int, start: Int, end: Int): List<Int> {
    val b = base - 1
    val ran = (0 until b).filter { it % b == (it * it) % b }
    var x = start / b
    val result = mutableListOf<Int>()
    while (true) {
        for (n in ran) {
            val k = b * x + n
            if (k < start) continue
            if (k > end) return result
            result.add(k)
        }
        x++
    }
} 

fun main(args: Array<String>) {
    println(castOut(16, 1, 255))
    println()
    println(castOut(10, 1, 99))
    println()
    println(castOut(17, 1, 288))
}