Step by Step solution about How to resolve the algorithm Van der Corput sequence step by step in the C programming language

The provided C code demonstrates how to convert an integer (in the range 0 to 9) from decimal to any arbitrary base between 2 and 5. It uses a simple algorithm to calculate the numerator and denominator of the fraction representing the value in the new base. Here's a detailed breakdown of the code:

1. Header File Inclusion:

   • The code includes the <stdio.h> header file for input/output operations like printf.

2. Function vc:

   • This function takes four arguments:

     • n: The integer to be converted from decimal to the new base.
     • base: The new base to convert to.
     • *num: A pointer to an integer where the numerator of the fraction representing the converted value will be stored.
     • *denom: A pointer to an integer where the denominator of the fraction representing the converted value will be stored.

   • Inside the function, the algorithm to convert n to base base is implemented as follows:

     • Initialize p to 0 and q to 1.
     • While n is not 0:
       • Multiply p by base and add n % base to it.
       • Multiply q by base.
       • Divide n by base.
     • Store the calculated p in *num and q in *denom.
     • Perform a GCD (Greatest Common Divisor) calculation on p and q to simplify the fraction.
     • Divide *num and *denom by the GCD to get the reduced fraction.

3. Function main:

   • This is the entry point of the program.
   • It iterates through base values from 2 to 5 using a for loop.
   • For each base, it prints the header "base [base]:" and then iterates through decimal values from 0 to 9 using another for loop.
   • For each decimal value, it calls the vc function to convert it to the specified base and print the result in the form of a fraction (n/d) or "0" if the decimal value is 0.

4. Output:

   • The program prints the converted values in the specified bases for decimal values from 0 to 9. For example, for base 2, it prints:

   base 2:  0  0/1  1/1  1/2
   

   • This shows that decimal 0 remains 0 in base 2, decimal 1 becomes 1/1 (same as in decimal), decimal 2 becomes 1/2 in base 2, and so on.

#include <stdio.h>

void vc(int n, int base, int *num, int *denom)
{
        int p = 0, q = 1;

        while (n) {
                p = p * base + (n % base);
                q *= base;
                n /= base;
        }

        *num = p;  
        *denom = q;

        while (p) { n = p; p = q % p; q = n; }
        *num /= q;
        *denom /= q;
}

int main()
{
        int d, n, i, b;
        for (b = 2; b < 6; b++) {
                printf("base %d:", b);
                for (i = 0; i < 10; i++) {
                        vc(i, b, &n, &d);
                        if (n) printf("  %d/%d", n, d);
                        else   printf("  0");
                }
                printf("\n");
        }

        return 0;
}