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

The provided C code is designed to identify and count "Kaprekar numbers" within a particular range and then calculate the percentage savings achieved by using only the Kaprekar numbers. A Kaprekar number is defined as a positive number for which the square of the number, when represented in the same base, can be split into two parts that add up to the original number again.

Here's a breakdown of the code:

1. Header Files:

   • The code includes the standard input/output header <stdio.h> and the math header <math.h> to use functions like printf and pow.

2. Constants and Variables:

   • N: A constant representing the number of digits in the numbers being considered. In this case, it is set to 2, as the code checks numbers with 2 digits.
   • base: The base in which the numbers are represented. Here, it is set to 10, indicating a decimal base.
   • c1: A counter to keep track of the total number of numbers checked.
   • c2: A counter to keep track of the total number of Kaprekar numbers found.
   • k: The number being tested.

3. Loop for Checking Kaprekar Numbers:

   • The code uses a for loop to iterate through numbers starting from 1 up to base^N - 1, which is the highest N-digit number in the given base.
   • For each number k:
     • It increments c1 to count the number of numbers being checked.
     • It checks if k is a Kaprekar number by calculating k^2 and splitting it into two parts: the left part L and the right part R.
     • If k % (base - 1) == (k * k) % (base - 1), it means that splitting k^2 satisfies the Kaprekar number definition, and k is a Kaprekar number. In this case, it increments c2 and prints k.

4. Calculating Percentage Savings:

   • After the loop completes, the code calculates the percentage savings achieved by using only Kaprekar numbers. It does this by comparing the total number of numbers checked (c1) to the number of Kaprekar numbers found (c2) and then calculating the percentage difference.
   • The savings percentage is printed out.

This code aims to demonstrate the concept of Kaprekar numbers and the potential savings in terms of computational resources by using only these numbers in specific applications.

#include <stdio.h>
#include <math.h>

int main() {
    const int N = 2;
    int base = 10;
    int c1 = 0;
    int c2 = 0;
    int k;

    for (k = 1; k < pow(base, N); k++) {
        c1++;
        if (k % (base - 1) == (k * k) % (base - 1)) {
            c2++;
            printf("%d ", k);
        }
    }

    printf("\nTring %d numbers instead of %d numbers saves %f%%\n", c2, c1, 100.0 - 100.0 * c2 / c1);
    return 0;
}