Factorial Function giving negative no

Question

So I have written a program in c++ which was suppose to print factorials of number from 1 endlessly. It printed the first some number as expected with correct factorial value but after that it is just end up getting negative value and Program got terminated due to condition mentioned. But I am not sure how a good working factorial program end up getting negative value.

#include<iostream>
using namespace std;
int main(){
    int a = 1;
    int c = 1;
    while(a>0){
        cout<<(a*c)<<endl;
       
        a = a*c;
        c = c+1;
    }
    return 0;
}

I have Expected Endless result of factorial from 1 to forever.

Result I got-

1
2
6
24
120
720
5040
40320
362880
3628800
39916800
479001600
1932053504
1278945280
2004310016
2004189184 //Number Decreased Instead of Increasing
-288522240 //Now It is negative

Answer 1

int is a signed type. Your factorials gets big enough to overflow that (exceed the largest value an int can store. When they do, you start to see answers that don't seem to make sense.

This can be readily seen with a simple demo program:

$ cat test.cpp
#include <iostream>
#include <iomanip>
#include <limits.h>

int factorial(int n) {
    int result = 1;
    for (; n > 1; n--) result *= n;
    return result;
}

int main() {
    for (int i = 1; i < 20; i++) {
        std::cout << std::setw(10) << std::right
                  << factorial(i) << std::endl
                  << INT_MAX << " <- max " << std::endl;
    }
}
$ g++ test.cpp
$ ./a.out
         1
2147483647 <- max
         2
2147483647 <- max
         6
2147483647 <- max
        24
2147483647 <- max
       120
2147483647 <- max
       720
2147483647 <- max
      5040
2147483647 <- max
     40320
2147483647 <- max
    362880
2147483647 <- max
   3628800
2147483647 <- max
  39916800
2147483647 <- max
 479001600
2147483647 <- max
1932053504
2147483647 <- max
1278945280
2147483647 <- max
2004310016
2147483647 <- max
2004189184
2147483647 <- max
-288522240
2147483647 <- max
-898433024
2147483647 <- max
 109641728
2147483647 <- max

If you want to see larger factorial results, you need to use a larger integer type, and likely a larger unsigned integer type.

If we do this, we buy ourselves some additional space to generate larger factorials.

$ cat test.cpp
#include <iostream>
#include <iomanip>

unsigned long long int factorial(int n) {
    unsigned long long int result = 1;
    for (; n > 1; n--) result *= n;
    return result;
}

int main() {
    for (int i = 1; i < 20; i++) {
        std::cout << std::setw(19) << std::right
                  << factorial(i) << std::endl
                  << ULONG_LONG_MAX << " <- max " << std::endl;
    }
}
$ g++ test.cpp
$ ./a.out
                  1
9223372036854775807 <- max
                  2
9223372036854775807 <- max
                  6
9223372036854775807 <- max
                 24
9223372036854775807 <- max
                120
9223372036854775807 <- max
                720
9223372036854775807 <- max
               5040
9223372036854775807 <- max
              40320
9223372036854775807 <- max
             362880
9223372036854775807 <- max
            3628800
9223372036854775807 <- max
           39916800
9223372036854775807 <- max
          479001600
9223372036854775807 <- max
         6227020800
9223372036854775807 <- max
        87178291200
9223372036854775807 <- max
      1307674368000
9223372036854775807 <- max
     20922789888000
9223372036854775807 <- max
    355687428096000
9223372036854775807 <- max
   6402373705728000
9223372036854775807 <- max
 121645100408832000
9223372036854775807 <- max