Cod sursa(job #2061904)

Utilizator BogdanisarBurcea Bogdan Madalin Bogdanisar Data 9 noiembrie 2017 20:10:50
Problema Factorial Scor 100
Compilator cpp Status done
Runda Arhiva de probleme Marime 1.51 kb
#include <iostream>
#include <fstream>
#include <set>
#include <algorithm>

#if 1
#define pv(x) cout<<#x<<" = "<<x<<"; ";cout.flush()
#define pn cout<<endl
#else
#define pv(x)
#define pn
#endif

using namespace std;
ifstream in("fact.in");
ofstream out("fact.out");

using ll = long long;
using ull = unsigned long long;
using ui = unsigned int;
#define pb push_back
#define mp make_pair
const int NMax = 5e6 + 5;
const ll inf = 1e18 + 5;
const int mod = 100003;
using zint = int;

ll P;

ll nrZero(ll);

int main() {
    in>>P;

    if (P == 0) {
        out<<1;
        return 0;
    }


    const ll lim = 4e8 + 50;

    // se cauta binar cel mai mare numar care are P-1 zerouri la final;
    ll nr = 0,pw = 1;
    for (;pw <= lim;pw <<= 1) ;
    pw >>= 1;

    while (pw) {
        if (nrZero(nr+pw) < P) {
            nr += pw;
        }

        pw >>= 1;
    }

    out<<((nrZero(nr+1) == P) ? nr+1 : -1);

    in.close();out.close();
    return 0;
}

// functie care return-eaza cate zero-uri are la sfarsit numarul x!;
// un zero la sfarsit este determinat de un 2*5;
// din moment ce 2 va aparea de mult mai multe ori decat 5,
// trebuie sa numaram numarul de aparitii ale lui 5;
// fiecare putere de tipul 5^k ne va da k zerouri la sfarsit;
// x / pw = numarul de puteri de tipul pw (putere a lui 5) care se gasesc in x!;
ll nrZero(ll x) {
    ll ans = 0, pw = 5;

    while (x / pw != 0) {
        ans += x / pw;
        pw *= 5;
    }

    return ans;
}