A program that calculate the factorial of big number

Question

It's a test in a website, here is the code

#include <stdio.h>

void Print_Factorial ( const int N );

int main()
{
    int N;
    scanf("%d",&N);
    Print_Factorial(N--);

    return 0;
}

/* your code will be put in here*/ 

#include <math.h>

int getFactLength(int N){
    double length = 0;
    while(N){
        length += log10(N--);
    }
    return (int)length+1;
}

void printFact(int fact[], int length){
    while(length--){
        printf("%d",*fact++);
    }
}

void initialNums(int nums[], int length, int num){
    while(length--){
        *nums++ = num;
    }
}

void Print_Factorial( const int N ){
    if(N < 0){
        printf("Invalid input");
        return ;
    }
        int NT = N;
    if(NT>=0 && NT<15){
        int fact = 1;
        while(NT){
            fact *= NT--;
        }
        printf("%d",fact);
        return ;
    }

    int length = getFactLength(N);
    int fact[length];
    initialNums(fact, length, 0);
    fact[length-1] = 1;
    int lastNoneZeroIndex = length-1;
    while(NT > 1){
        int lengthT = length;
        int carry = 0;
        while(lengthT-- > lastNoneZeroIndex){
            int result = NT*fact[lengthT] + carry;
            fact[lengthT] = result % 10;
            carry = result / 10;
        }
        while(carry){
            fact[--lastNoneZeroIndex] = carry % 10;
            carry /= 10;
        }
        NT--;
    }

    printFact(fact, length);
}

I use values from 0 to 20 to test it, all of them are right. But when I submit it in that website, a test case always do not pass. I don't know what that case is. But, there are 5 cases, all test cases are between 0 and 1000, and two of them are no more than 15, one of them is negative, one of them use most time to pass, so I think the case that didnt pass is a number that smaller than 1000. That's all I know, I can't imagine that 1000 was passed, but the number smaller than 1000 didn't pass. I don't know what is wrong with my lovely code. I hope you can watch my code, and find some bugs.

Answer 1

There create a overflow in the fact variable, here you use int type for fact variable. For input 13,14, it gives wrong answer.

Solution:

long long int fact = 1;

or,

change the condition- if(NT>=0 && NT<13)