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Cod sursa(job #200276)
/*factorial
Factorial
Se da un numar intreg P. Sa se gaseasca cel mai mic numar natural strict pozitiv N pentru care N! are exact P cifre de 0 la sfarsit.
Se stie ca N! = 1 * 2 * 3 * .... * (N - 1) * N.
Date de intrare
Fisierul fact.in va contine pe prima linie numarul intreg P.
Date de iesire
Pe prima linie a fisierului fact.out se va scrie acel numar N care indeplineste condiitle impuse sau -1 daca nu exista un astfel de N.
Restrictii
0 = P = 10^8
*/
#include<fstream.h>
unsigned long p,n;
ifstream fin("fact.in");
ofstream fout("fact.out");
unsigned long sparge(unsigned long n)
{
unsigned long numara=0;
while(n%5==0)
{
n=n/5;
numara++;
}
return numara;
}
int main()
{
fin>>p;
if(p==0) fout<<"1\n";
else
if(p>97500000)
{
p-=97500000;
n=390000020;
}
if(p>95000000)
{
p-=95000000;
n=380000020;
}
else
if(p>92500000)
{
p-=92500000;
n=370000015;
}
else
if(p>90000000)
{
p-=90000000;
n=360000015;
}
else
if(p>87500000)
{
p-=87500000;
n=350000010;
}
else
if(p>85000000)
{
p-=85000000;
n=340000015;
}
else
if(p>80000000)
{
p-=80000000;
n=320000015;
}
else
if(p>77500000)
{
p-=77500000;
n=310000015;
}
else
if(p>75000000)
{
p-=75000000;
n=300000010;
}
else
if(p>70000000)
{
p-=70000000;
n=280000015;
}
else
if(p>67500000)
{
p-=67500000;
n=270000010;
}
else
if(p>65000000)
{
p-=65000000;
n=260000010;
}
else
if(p>60000000)
{
p-=60000000;
n=240000020;
}
else
if(p>57500000)
{
p-=57500000;
n=230000020;
}
else
if(p>55000000)
{
p-=55000000;
n=220000015;
}
else
if(p>52500000)
{
p-=52500000;
n=210000015;
}
else
if(p>50000000)
{
p-=50000000;
n=200000010;
}
else
if(p>47500000)
{
p-=47500000;
n=190000015;
}
else
if(p>45000000)
{
p-=45000000;
n=180000015;
}
else
if(p>40000000)
{
p-=40000000;
n=160000015;
}
else
if(p>37500000)
{
p-=37500000;
n=150000010;
}
else
if(p>35000000)
{
p-=35000000;
n=140000015;
}
else
if(p>30000000)
{
p-=30000000;
n=120000010;
}
else
if(p>27500000)
{
p-=27500000;
n=110000010;
}
else
if(p>25000000)
{
p-=25000000;
n=100000005;
}
else
if(p>20000000)
{
p-=20000000;
n=80000015;
}
else
if(p>17500000)
{
p-=17500000;
n=70000010;
}
else
if(p>15000000)
{
p-=15000000;
n=60000010;
}
else
if(p>10000000)
{
p-=10000000;
n=40000010;
}
else
if(p>7500000)
{
p-=7500000;
n=30000010;
}
if(p>5000000)
{
p-=5000000;
n=20000005;
}
else
if(p>2500000)
{
p-=2500000;
n=10000005;
}
while(p>0)
{
n+=5;
p-=sparge(n);
}
fout<<n<<'\n';
fout.close();
return 0;
}