1853: [Scoi2010]幸运数字[容斥原理]

/*
    一个非常显然的事实就是幸运号码不会太多。把表打出来，就会发现在10^10以内的幸运数只有2404个
　　这个时候一个非常显然的想法就是对这些数进行容斥，即加上每个数的倍数个数，减去两个数的lcm的倍数个数，加上三个的lcm的倍数个数，……以此类推。
　　这样的复杂度显然是不对的，理论上可达O(2^x)，其中xx为幸运数个数。但是由于多个数的倍数不能超过右边界，就可以剪枝，实际复杂度低了不知道多少。
　　但是这样时间不够。我们还可以对幸运数进行处理，将其中是另外的幸运数的倍数的数给去掉。这样可以将需要考虑的数的个数减掉一半左右。
　　最后还有一个小优化，那就是将最后需要处理的幸运数按从大到小排好序。这样可以让乘积尽早变得更大，可以减掉许多不必要的计算。
　　加了上述优化，就差不多可以AC了。
*/
#include<cstdio>
#include<iostream>
#include<algorithm>
#define set(x) freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);
using namespace std;
const int N=3000;
typedef long long ll;
ll l,r,now,ci,ans;
ll num,cnt,a[N],b[N];
void init(ll x){
    if(x>r) return ;
    a[num++]=x;
    init(x*10+6);
    init(x*10+8);
}
void dfs(ll x){
    if(x>cnt){
        if(!ci) return ;
        if(ci&1) ans+=r/now-(l-1)/now;
        else ans-=r/now-(l-1)/now;
        return ;
    }
    dfs(x+1);
    ll tx=now;
    now=now/__gcd(now,b[x]);ci++;
    if((double)now*b[x]<=r){
        now*=b[x];
        dfs(x+1);
    }
    ci--;now=tx;
}
int main(){
    set(luckynumber);
    cin>>l>>r;
    init(0);num--;
    sort(a+1,a+num+1);
    for(int i=1;i<=num;i++){
        b[++cnt]=a[i];
        for(int j=1;j<cnt;j++){
            if(!(a[i]%b[j])){
                cnt--;break;
            }
        }
    }
    reverse(b+1,b+cnt+1);
    now=1;
    dfs(1);
    cout<<ans;
    return 0;
}
/*30分hash 
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define set(x) freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);
using namespace std;
typedef long long ll;
ll a,b,n;
ll 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struct Thash{
    static const int N=2e6+5,MOD=1733333;
    ll tot,head[MOD+10],val[N],h[N],next[N];
    void clear(){tot=0;memset(head,0,sizeof head);}
    void insert(ll H,ll VAL){
        for(ll i=head[H%MOD];i;i=next[i]) if(h[i]==H){val[i]=VAL;return ;}
        h[++tot]=H;val[tot]=VAL;next[tot]=head[H%MOD];head[H%MOD]=tot;
    }
    ll get(ll H){
        for(ll i=head[H%MOD];i;i=next[i]) if(h[i]==H) return val[i];
        return 0;
    }
}M;
ll solve(ll lim){
    ll ans=0;
    M.clear();
    for(ll i=0;;i++){
        if(list[i]>lim) break;
        for(ll j=list[i];j<=lim;j+=list[i]){
            if(!M.get(j)){
                ans++;
                M.insert(j,1);
            }
        }
    }
    return ans;
}
int main(){
    set(luckynumber);
    cin>>a>>b;
    cout<<solve(b)-solve(a-1);
    return 0;
}*/