Error "Exception in thread "main" java.lang.Arithmeticexception: / by zero" in java

Question

I’m trying to solve an exercise, but it keeps going wrong. I wonder if someone could help me?

public class mod_IV_ex_1 {
static int fatorial(int numero){
    int fatorial = 0;
    if (numero == 0) {
        fatorial = 1;
        return fatorial;
    } else{
        for (int i = 2; i <= numero; i++) {
            fatorial *= i;
        }
        return fatorial;
    }
}
public static void main(String[] args) {
    System.out.println("EXERCICIO 1, MODULO IV");
    int j, i;
    
    double fracao = 0;
    double soma = 0;

    for (i = 100; i >= 80; i--) {
        for (j = 0; j <= 20; j++) {
            fracao = i / fatorial(j);
            soma += fracao;
            System.out.printf("%d / %d + ", i, fatorial(j));
        }

    }
    System.out.printf(" = %.2f\n", soma);
}

}

And the error that appears is this:

Answer 1

The problem is in the function that calculates the factorial.

Notice that fatorial starts with zero. If the number is, say, 2, he enters the else, and within the for you multiply fatorial for i. But how fatorial is zero, multiplying it by any number will result in zero. Then within the loop you are trying to make a division by zero, which gives error.

So actually the factorial should start at 1, not zero:

static double fatorial(int numero) {
    double fatorial = 1;
    for (int i = 2; i <= numero; i++) {
        fatorial *= i;
    }
    return fatorial;
}

Notice you don’t even need the if, because if the number is zero, it doesn’t enter the for (since the condition i <= numero will be false) and will be returned 1.

And changed the kind of int for double, because the factor of 17 bursts the maximum size of a int (which is 2147483647), and there occurs a overflow and the account goes wrong.

And the calculation is also wrong. By making a loop inside each other, actually you’re doing 100 / 0! + 100 / 1! + ... + 100 / 20! + 99 / 0! + 99 / 1! .... You only need to make one loop, and keep changing i and j at the same time:

double soma = 0;
for (int i = 100, j = 0; i >= 80; i--, j++) {
    soma += i / fatorial(j);
    System.out.printf("%d / %f + ", i, fatorial(j));
}

---

But in fact it does not need a method to calculate the factorial (unless it is requirement of exercise). For when you calculate, for example, 3!, you have already multiplied 2 and 3. In the next iteration, you will calculate 4! and you will have to multiply again 2 and 3, then multiply by 4.

In this case, it is better to keep the last calculated factorial and only multiply what is missing:

double soma = 0;
double denominador = 1;
for (int i = 100, j = 0; i >= 80; i--, j++) {
    soma += i / denominador;
    System.out.printf("%d / %f + ", i, denominador);
    if (j > 0)
        denominador *= (j + 1);
}