牛客寒假多校训练赛第三场 G 大水题 容斥原理

版权声明：布呗之路的守望者 https://blog.csdn.net/hypHuangYanPing/article/details/82228941

/**
链接:https://www.nowcoder.com/acm/contest/75/G
题意:给出一个数n，求1到n中，有多少个数不是2 5 11 13的倍数;
容斥原理;可分为一类题的模板;

*/
#include<bits/stdc++.h>
#define ll long long
using namespace std;

/**********************************************Head-----Template****************************************/
bool Finish_read;
template<class T>inline void read(T &x){Finish_read=0;x=0;int f=1;char ch=getchar();while(!isdigit(ch)){if(ch=='-')f=-1;if(ch==EOF)return;ch=getchar();}while(isdigit(ch))x=x*10+ch-'0',ch=getchar();x*=f;Finish_read=1;}
template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
ll gcd(ll a,ll b){return b==0?a:gcd(b,a%b);}
ll lcm(ll a,ll b){ll gg=gcd(a,b);a/=gg;if(a<=LLONG_MAX/b) return a*b;return LLONG_MAX;}
/********************************Head----Temlate**********************************************/

int a[5];
ll ans,n;
void dfs(ll x,ll tmp,int flag){
	if(x==4){
		ans+=flag*n/tmp;
		return ;
	}
	dfs(x+1,tmp,flag);
	if(lcm(tmp,a[x])<=n) dfs(x+1,lcm(tmp,a[x]),-flag);
}

int main (){
	a[0]=2,a[1]=5,a[2]=11,a[3]=13;
	while(~scanf("%lld",&n)){
		ans=0;
		dfs(0,1,1);
		cout<<ans<<endl;
	}
	return 0;
}