Light oj 1045 Digits of Factorial Solution

 problem link  : Light oj 1045

Explain: We know that 10 base number system digit of x number is  =

⌊log10x⌋+1

According to the same way  b base number system digit of x number is =  

⌊logbx⌋+1

Accoding to the logarithm law:

   We know    

                               

   is the answer 

///La ilaha illellahu muhammadur rasulullah

///******Bismillahir-Rahmanir-Rahim******///

///Abul Hasnat  Tonmoy

///Department of CSE,23rd batch

///Islamic University,Bangladesh

Solution in c++:

#include <bits/stdc++.h>

using namespace std;

double v[1000000];

int main()

{

    long long  int t,b,i,j,k,r,n;

    for(int i=1; i<=1000000; i++)

        v[i]=v[i-1] + log(i);

    cin>>t;

    for(k=1; k<=t; k++)

    {

        cin>>n>>b;

        r=v[n]/log(b);

        printf("Case %d: %lld\n", k,r+1);

    }

    return 0;

}