CF1097F Alex and a TV Show

题目

CF1097F Alex and a TV Show

做法

奇偶性,考虑用(bitset)维护,(Set[i][j])为第(i)个集合中(j)作为因子出现的次数

预处理(yz[i])((i)中的因子)

(1):直接(Set[x]=yz[y])

(2):相加取奇偶相当于异或

(3):相乘取奇偶相当于且

(4)(F(n))(n)作为因子出现的次数,(f(n))(n)的出现次数

[egin{aligned} F(n)&=sumlimits_{n|d}f(d)\ f(n)&=sumlimits_{n|d}{mu(lfloorfrac{d}{n} floor)F(d)} end{aligned}]

My complete code

#include<cstdio>
#include<cstring>
#include<iostream>
#include<string>
#include<algorithm>
#include<bitset>
using namespace std;
typedef int LL;
inline LL Read(){
	LL x(0),f(1);char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9')x=(x<<3)+(x<<1)+c-'0',c=getchar();
	return x*f;
}
LL n,q;
bitset<7009> yz[7009],Mu[7009],Set[100009];
LL prime[7009],mu[7009];
bool visit[7009];
inline void First(LL N){
	mu[1]=1; LL tot(0);
	for(LL i=2;i<=N;++i){
		if(!visit[i]){
			mu[i]=-1;
			prime[++tot]=i;
		}
		for(LL j=1;j<=tot&&i*prime[j]<=N;++j){
			visit[prime[j]*i]=true;
			if((i%prime[j])==0)
				break;
			else
			    mu[i*prime[j]]=-mu[i];
		}
	}
}
int main(){
	First(7000);
	for(LL i=1;i<=7000;++i)
	    for(LL j=i;j<=7000;j+=i)
            yz[j][i]=1,Mu[i][j]=mu[j/i]!=0;
    n=Read(),q=Read();
    while(q--){
    	LL op(Read()),x(Read()),y(Read());
    	if(op==1){
    		Set[x]=yz[y];
		}else if(op==2){
			LL z(Read());
			Set[x]=Set[y]^Set[z];
		}else if(op==3){
			LL z(Read());
			Set[x]=Set[y]&Set[z];
		}else
		    printf("%d",(Set[x]&Mu[y]).count()&1);
	}
	return 0;
}
原文地址:https://www.cnblogs.com/y2823774827y/p/10332189.html