Generating pentatopes as the frequencies of sum of digits of numbers in base n, excluding numbers with the digit 0

gistfile1.txt

#include <stdio.h>
#include <stdlib.h>

#define BASE 5
#define LENGTH 5
#define MAX_SUM (BASE * LENGTH - 1)

// Define a structure to hold index, number, and sum of digits
struct NumberInfo {
    int index;
    int number[LENGTH];
    int sum;
};

// Comparison function for qsort to sort NumberInfo array by sum
int compare(const void *a, const void *b) {
    const struct NumberInfo *num1 = (const struct NumberInfo *)a;
    const struct NumberInfo *num2 = (const struct NumberInfo *)b;
    return num1->sum - num2->sum;
}

void generateNumbers(struct NumberInfo numbers[], int n, int length, int frequency[]) {
    int number[length];
    int i, j;
    int count = 0;

    // Initialize all digits to 1
    for (i = 0; i < length; i++) {
        number[i] = 1;
    }

    // Generate numbers and store those without the digit 0
    while (1) {
        // Check if the number contains 0
        int hasZero = 0;
        int sum = 0;
        for (i = 0; i < length; i++) {
            if (number[i] == 0) {
                hasZero = 1;
                break;
            }
            sum += number[i];
        }
        if (!hasZero) {
            // Store the number, its index, and sum of digits in the struct array
            numbers[count].index = count + 1;
            numbers[count].sum = sum;
            for (i = 0; i < length; i++) {
                numbers[count].number[i] = number[i];
            }
            frequency[sum]++; // Update frequency array
            count++;
        }

        // Find the next number
        for (i = length - 1; i >= 0; i--) {
            if (number[i] < n - 1) {
                number[i]++;
                break;
            } else {
                number[i] = 1;
            }
        }
        if (i < 0) {
            break;  // All numbers generated
        }
    }
}

int main() {
    int numbersCount = 1; // Since 00000 will not be included
    for (int i = 1; i <= LENGTH; i++) {
        numbersCount *= BASE - 1; // There are BASE - 1 possibilities for each digit
    }

    // Define an array of structures to hold number info
    struct NumberInfo numbers[numbersCount];
    int frequency[MAX_SUM + 1] = {0}; // Initialize frequency array with zeros
    generateNumbers(numbers, BASE, LENGTH, frequency);

    // Sort the numbers array by sum of digits using qsort
    qsort(numbers, numbersCount, sizeof(struct NumberInfo), compare);

    // Printing the sorted numbers with index and sum of digits
    printf("Index\tNumber\tSum of Digits\n");
    for (int i = 0; i < numbersCount; i++) {
        printf("%d\t", numbers[i].index);
        for (int j = 0; j < LENGTH; j++) {
            printf("%d", numbers[i].number[j]);
        }
        printf("\t%d\n", numbers[i].sum);
    }

    // Printing the frequencies of each possible sum
    printf("\nFrequencies of each possible sum:\n");
    for (int i = 1; i <= MAX_SUM; i++) {
        printf("Sum %d: %d\n", i, frequency[i]);
    }

    return 0;
}