求阶乘--二分答案+0结尾与5有关

1.二分答案求最小

2.结尾为0就是分解质因数5的个数,有多少5的倍数其阶乘末尾就有多少个0
求n阶乘中5因子的个数的公式就是n/5+n/25+n/125+...+n/5^i;

代码如下，记得判断-1的情况

#include<bits/stdc++.h>
using namespace std;
#define N 100011
typedef long long ll;
typedef pair<ll,int> PII;
ll k;
ll an;
bool check(ll x)
{
	ll c=0;
	ll s=5;
	while(x/s)
	{
		c+=x/s;
		if(c>=k) return true;
		s*=5;
    }
    return false;
}
ll c1(ll x)
{
	ll c=0;
	ll s=5;
	while(x/s)
	{
		c+=x/s;
		s*=5;
    }
    if(c==k) return true;
    return false;
}
int main()
{ 
cin>>k;
 ll l=0,r=0x3f3f3f3f3f3f3f3fLL;
 while(l<=r)
 {
 	ll m=(l+r)>>1;
 	if(check(m))
 	{
 		an=m;
 		r=m-1;
	}else l=m+1;
 }
 if(c1(an))cout<<an;
 else cout<<"-1";
return 0;
}
///10000 200;