Step by Step solution about How to resolve the algorithm Digital root/Multiplicative digital root step by step in the C programming language

==> Notes for the code and the AI responses...

• The first response of the AI assistant was ok and its explanation was not completely wrong but it missed few details.
• The second response of the AI assistant was ok and its explanation was not completely wrong but it missed few details.

Here I will explain the code myself.

The C program is designed to find the MDR (multiplication of digits) and MP (multiplication of prime digits) of a given number. It starts with predefined values, builds a table of MDR values, and then prints the table.

• MDR (Multiplication of Digits): The MDR of a number is the product of all its digits. For example, the MDR of 1234 is 1 * 2 * 3 * 4 = 24.

• MP (Multiplication of Prime Digits): The MP of a number is the product of all its prime digits. For example, the MP of 1234 is 2 * 3 = 6, since 2 and 3 are the only prime digits in 1234.

--> The Code Structure:

• Import the stdio.h header for input and output operations.

• Define a constant twidth to specify the width or number of columns in the MDR table.

• Define a macro mdr to calculate the MDR and MP of a number. It takes three parameters:

  • rmdr: A pointer to store the MDR.
  • rmp: A pointer to store the MP.
  • n: The input number.

• Implement the internal function _mdr to recursively calculate the MDR and MP. It adjusts for the 0 case and calculates the result.

• In the main function:

  • Initialize variables for loop counters, MDR, and MP.

  • Set up an array values with predefined test values.

  • Print the initial test results.

  • Calculate and store MDR values in a 2D table table and count how many values have been filled for each MDR value in an array tfill.

  • Print the calculated MDR table.

--> The Execution Flow:

1. The program starts by displaying the MDR and MP for the provided test values.
2. It then calculates the MDR values for each number from 0 to 99 and fills up the MDR table.
3. Finally, it prints the MDR table, showing the MDR values for each MDR from 0 to 9, along with the numbers that produce those MDR values. This table can be useful for quickly finding MDR values for different numbers or for understanding the distribution of MDR values.

#include <stdio.h>

#define twidth 5
#define mdr(rmdr, rmp, n)\
    do { *rmp = 0; _mdr(rmdr, rmp, n); } while (0)

void _mdr(int *rmdr, int *rmp, long long n)
{
    /* Adjust r if 0 case, so we don't return 1 */
    int r = n ? 1 : 0;
    while (n) { 
        r *= (n % 10);
        n /= 10; 
    }

    (*rmp)++;
    if (r >= 10)
        _mdr(rmdr, rmp, r);
    else
        *rmdr = r;
}

int main(void)
{
    int i, j, vmdr, vmp;
    const int values[] = { 123321, 7739, 893, 899998 };
    const int vsize    = sizeof(values) / sizeof(values[0]);

    /* Initial test values */
    printf("Number    MDR    MP\n");
    for (i = 0; i < vsize; ++i) {
        mdr(&vmdr, &vmp, values[i]);
        printf("%6d   %3d   %3d\n", values[i], vmdr, vmp);
    }

    /* Determine table values */
    int table[10][twidth] = { 0 };
    int tfill[10]         = { 0 };
    int total             = 0;
    for (i = 0; total < 10 * twidth; ++i) {
        mdr(&vmdr, &vmp, i);
        if (tfill[vmdr] < twidth) {
            table[vmdr][tfill[vmdr]++] = i;
            total++;
        }
    }

    /* Print calculated table values */
    printf("\nMDR: [n0..n4]\n");
    for (i = 0; i < 10; ++i) {
        printf("%3d: [", i);
        for (j = 0; j < twidth; ++j)
            printf("%d%s", table[i][j], j != twidth - 1 ? ", " : ""); 
        printf("]\n");
    }

    return 0;
}