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

The provided Java program identifies Smith numbers in the range 1 to 10,000. Smith numbers are positive integers where the sum of their digits is equal to the sum of the digits in their prime factors.

Here's a breakdown of the code:

1. primeFactors method:

   • This method takes an integer n as input and returns a list of its prime factors.
   • It initializes an empty list result.
   • It enters a loop that divides n repeatedly by 2, adding 2 to the result list each time until n is no longer divisible by 2.
   • It then enters a loop that starts from 3 and iterates by 2 (to check odd numbers only). For each i, it repeatedly divides n by i and adds i to the result list until n is no longer divisible by i.
   • If n is still greater than 1 after both loops, it means n itself is a prime factor, so it is added to the result list.
   • Finally, the method returns the result list containing the prime factors of n.

2. sumDigits method:

   • This method takes an integer n as input and returns the sum of its digits.
   • It initializes a variable sum to 0.
   • It enters a loop that repeatedly calculates the last digit of n by taking n % 10, adds that digit to sum, and then removes the last digit from n by dividing it by 10.
   • The loop continues until n becomes 0.
   • Finally, the method returns the sum of the digits.

3. main method:

   • This is the entry point of the program.
   • It iterates over integers from 1 to 9,999 (exclusive).
   • For each n, it calls the primeFactors method to obtain the list of prime factors of n.
   • If n has more than one prime factor (i.e., the size of the prime factors list is greater than 1), it proceeds to check if it's a Smith number.
   • It calculates the sum of digits of n using the sumDigits method.
   • It then iterates over the prime factors of n and subtracts the sum of digits of each prime factor from the sum of digits of n.
   • If the result of this subtraction is 0, it indicates that n is a Smith number, and it is printed to the console.

import java.util.*;

public class SmithNumbers {

    public static void main(String[] args) {
        for (int n = 1; n < 10_000; n++) {
            List<Integer> factors = primeFactors(n);
            if (factors.size() > 1) {
                int sum = sumDigits(n);
                for (int f : factors)
                    sum -= sumDigits(f);
                if (sum == 0)
                    System.out.println(n);
            }
        }
    }

    static List<Integer> primeFactors(int n) {
        List<Integer> result = new ArrayList<>();

        for (int i = 2; n % i == 0; n /= i)
            result.add(i);

        for (int i = 3; i * i <= n; i += 2) {
            while (n % i == 0) {
                result.add(i);
                n /= i;
            }
        }

        if (n != 1)
            result.add(n);

        return result;
    }

    static int sumDigits(int n) {
        int sum = 0;
        while (n > 0) {
            sum += (n % 10);
            n /= 10;
        }
        return sum;
    }
}