Factorial does not work for all values

Question

Hi everyone I edited my post because I have another problem with my code.I had a problem with the factorial function yesterday but I managed to solve it thanks to your answers , it was a ridiculous mistake. The problem now is that for some values that are higher than 15, the final results(not the factorials of individual numbers) are always 0 or -1 for the lesser values it works fine.Can someone tell me whats wrong with this code :

    #include <iostream>
    #include<time.h>

    using namespace std;



    int factorial(int a){
    if(a==1)
      return 1;
    else if(a==0)
      return 1;
    else 
      return factorial(a-1)*a;

    }

    int main(){
    std::cout.setf(std::ios_base::fixed, std::ios_base::floatfield);
    std::cout.precision(5);
    int n,k;
    int x,y,z,w,v; 


    cout<<"give n : ";
    cin>>n;


     cout<<"give k : ";
     cin>>k;

     clock_t t;

        t = clock();



      if(n>=k&&k>1){

       x=factorial(n-1);
       y=factorial(k-1);
       z=factorial(n-1-k);
       w=factorial(n-k);
       v=factorial(k);


         cout<<"Result is "<<(x/(v*z))+(x/(y*w))<<endl;
       }
       else if (n==0||n==k)
         cout<<"Result is  1"<<endl;
       else
         cout<<"Result is  0"<<endl;


       t = clock() - t;
       cout<<"It took "<<t<<" clicks  ("<<((float)t)/CLOCKS_PER_SEC<<" seconds )"<<endl;    



       return 0;
       }

Answer 1

Integer overflow.

If int is 32 bits on your system, the largest value it can represent is 2147483647. 13 factorial is 6227020800.

If you use a 64-bit integer type such a long long, you can go up to 20 factorial.

Floating-point will give you more range, but with a loss of precision.

If you really need to compute large factorials, you'll need to use some multi-precision library like GMP, or use a language that has built-in arbitrary-precision integer arithmetic (C doesn't).

Answer 2

The following might call factorial with a zero or negative argument:

z=factorial(n-1-k);
w=factorial(n-k);

You need to make sure that your factorial function can handle such arguments without crashing (I suspect it doesn't).