OJ Board

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floor(log[n])+1.

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#include<iostream>
#include<cmath>
#include<vector>

using namespace std;

long double logNfactorial(unsigned long int n)
{
    //static to reuse past stored results 
    static vector<long double> logNf(2, 0);

    for(int i = logNf.size(); i <= n; i++)
        logNf.push_back(logNf[i-1] + log10(i));
    return logNf[n];
}

int main()
{
    unsigned long int n, k;
    while(cin >> n >> k)
        cout << (unsigned long int)
                ceil(logNfactorial(n)-logNfactorial(k)-logNfactorial(n-k))
             << endl;
    return 0;
}

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% ./a.out 
999999 999
3430
99999999 9999
Abort

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cutted after AC.. 
I just replaced data type from double to long double...  :-? 

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#include<iostream.h>
///using namespace std;
unsigned long int fact(int n);
int main()
{
	int result[10000],carry,n,index;

    while(cin>>n)
	{
	     cout<<"\n";
		if(n>1000)
		   continue;
	cout<<fact(n)<<"\n\n";
	}


	 return 0;

}

unsigned long int fact(int n)
{

	int result[10000],carry,index;
	unsigned long int sum=0;
		result[0]=1;
		index=carry=0;
		if(n>1)
		{
			for(int i=2;i<=n;i++)
			{
				for(int j=0;j<=index;j++)
				{
				carry+=result[j]*i;
				result[j]=carry%10;
				carry/=10;

				}
				if(carry!=0)
				{
				   do
				   {
					   result[++index]=carry%10;
					   carry/=10;
				   }while(carry!=0);
				}
			}
		}

		   //cout<<n<<"! \n";
		   for(int i=index;i>=0;i--)
		   {
			 //cout<<result[i];
			 sum+=result[i];
		   }

	   //cout<<"\n";
	    return sum;

}