Blog Entry Monday, June 24, 2024 (c) James Pate Williams, Jr. Computing Binomial Coefficients and Pascal’s Triangle in the C Language

// BinomialCoefficient.c (c) Monday, June 24, 2024
// by James Pate Williams, Jr. BA, BS, MSwE, PhD

#include <stdio.h>
#include <stdlib.h>
typedef long long ll;

ll** Binomial(ll n)
{
    ll** C = (ll**)calloc(n + 1, sizeof(ll*));

    if (C == NULL)
        exit(-1);

    for (int i = 0; i < n + 1; i++)
    {
        C[i] = (ll*)calloc(n + 1, sizeof(ll));

        if (C[i] == NULL)
            exit(-1);
    }

    if (n >= 0)
    {
        C[0][0] = 1;
    }

    if (n >= 1)
    {
        C[1][0] = 1;
        C[1][1] = 1;
    }

    if (n >= 2)
    {
        for (int i = 2; i <= n; i++)
        {
            for (int j = 2; j <= n; j++)
            {
                C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }
    }

    return C;
}

ll Factorial(ll n)
{
    ll fact = 1;

    if (n > 1)
    {
        for (int i = 2; i <= n; i++)
            fact = i * fact;
    }

    return fact;
}

ll BC(ll n, ll k)
{
    return Factorial(n) / (Factorial(n - k) * Factorial(k));
}

int main()
{
    int i = 0, j = 0;
    ll** C = Binomial(20);

    while (1)
    {
        char buffer[256] = { '\0' };
        
        printf_s("Enter n (<= 18) below:\n");
        scanf_s("%s", buffer, sizeof(buffer));
        printf_s("\n");

        ll n = atoll(buffer);

        if (n == 0)
            break;

        printf_s("Enter k (<= 18) below:\n");
        scanf_s("%s", buffer, sizeof(buffer));
        printf_s("\n");

        ll k = atoll(buffer);
                
        printf_s("%lld\t%lld\n\n", C[n + 2][k + 2], BC(n, k));
    }

    printf_s("Pascal's Triangle:\n\n");

    for (i = 2; i <= 20; i++)
    {
        for (j = 2; j <= 20; j++)
            if (C[i][j] != 0)
                printf_s("%5lld ", C[i][j]);

        printf_s("\n");
    }

    for (i = 0; i <= 20; i++)
        free(C[i]);

    free(C);
}