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

The provided Kotlin code is designed to identify and print Munchausen numbers within a specified range of integers. Munchausen numbers are positive integers whose sum of digits raised to their respective powers equals the number itself. For example, 343 is a Munchausen number because 3^3 + 4^3 + 3^3 = 343.

1. Initialization:

• An integer array named powers is initialized with 10 elements to cache the values of n ^ n for n in the range 0 to 9. This step is crucial for improving the efficiency of the program.

2. isMunchausen Function:

• The isMunchausen function takes an integer n as input and returns true if n is a Munchausen number, and false otherwise.
• Inside the function:
  • It checks if n is negative, as Munchausen numbers are defined for positive integers. If n is negative, it returns false.
  • It initializes a long integer variable sum to 0 and a copy of n named nn.
  • It enters a loop that continues until nn becomes 0.
  • Inside the loop, it calculates the sum of the digits of n raised to their respective powers and adds it to sum.
  • If sum becomes greater than n, it means n is not a Munchausen number, and it returns false.
  • It divides nn by 10 to move to the next digit.
  • After the loop, it checks if sum is equal to n. If they are equal, it means n is a Munchausen number, and it returns true. Otherwise, it returns false.

3. Main Function:

• The main function is the entry point of the program.
• Inside main:
  • It populates the powers array with cached values of n ^ n for n in the range 0 to 9.
  • It then checks numbers from 0 to 500 million to find Munchausen numbers.
  • For each number i, it calls the isMunchausen function to determine if it's a Munchausen number.
  • If i is a Munchausen number, it prints it to the console.

4. Output:

• The program prints all the Munchausen numbers found within the range 0 to 500 million separated by spaces.

// version 1.0.6

val powers = IntArray(10)

fun isMunchausen(n: Int): Boolean {
    if (n < 0) return false
    var sum = 0L
    var nn = n
    while (nn > 0) {
        sum += powers[nn % 10]
        if (sum > n.toLong()) return false
        nn /= 10
    }
    return sum == n.toLong()  
}

fun main(args: Array<String>) {
   // cache n ^ n for n in 0..9, defining 0 ^ 0 = 0 for this purpose
   for (i in 1..9) powers[i] = Math.pow(i.toDouble(), i.toDouble()).toInt()

   // check numbers 0 to 500 million
   println("The Munchausen numbers between 0 and 500 million are:")
   for (i in 0..500000000) if (isMunchausen(i))print ("$i ")
   println()
}