ACM-ICPC 2018 徐州赛区网络预赛 D 杜教筛 前缀和

链接 https://nanti.jisuanke.com/t/31456

参考题解  https://blog.csdn.net/ftx456789/article/details/82590044

 #include <bits/stdc++.h>
 #define pb push_back
 #define mp make_pair
 #define fi first
 #define se second
 #define all(a) (a).begin(), (a).end()
 #define fillchar(a, x) memset(a, x, sizeof(a))
 #define huan printf("\n");
 #define debug(a,b) cout<<a<<" "<<b<<" "<<endl;
 using namespace std;
 const int maxn=1e6+;
 typedef long long ll;
 map<ll,ll> ma,yin;
 int check[maxn],prime[maxn],mu[maxn];
 void Mobius(int N)//莫比乌斯函数线性筛
 {
     int pos=;mu[]=;
     for (int i =  ; i <= N ; i++)
     {
         if (!check[i])
             prime[pos++] = i,mu[i]=-;
         for (int j =  ; j < pos && i*prime[j] <= N ; j++)
         {
             check[i*prime[j]] = ;
             if (i % prime[j] == )
             {
                 mu[i*prime[j]]=;
                 break;
             }
             mu[i*prime[j]]=-mu[i];
         }
     }
     for(int i=;i<=N;i++)
         mu[i]+=mu[i-];
 }
 ll sum(ll a)
 {
     if(a<=1e6)
         return mu[a];
     if(ma.count(a))
         return ma[a];
     ll temp=;
     for(ll i=;i<=a;)
     {
         ll t=a/i;
         ll k=a/t;
         temp-=(k-i+)*sum(t);
         i=k+;
     }
     return ma[a]=temp;
 }
 void shai(ll n)//筛素因子
 {
     ll x=n;
     for(ll i=;i*i<=x;i++)
     {
         while(x%i==)
         {
             yin[i]++;
             x/=i;
         }
     }
     if(x>)yin[x]++;
 }
 ll solve(ll n,ll m)
 {
     if(m==)return ;//m等于0就是0喽
     if(n==)return sum(m);//n等于1 就是莫比乌斯函数 u 的前 m 项和
     for(auto it:yin)
     {
         if(n%it.fi==)
         {
             return solve(n,m/it.fi)-solve(n/it.fi,m);
         }
     }
 }
 int main()
 {
     Mobius(1e6);
     ll n,m;
     cin>>n>>m;
     shai(m);
     for(auto it:yin)
         if(it.se>)
         {
             cout<<<<endl;
             return ;
         }
     cout<<solve(m,n)<<endl;
     return ;
 }

ACM-ICPC 2018 徐州赛区网络预赛