【莫比乌斯反演+树状数组+分块求和】GCD Array

https://www.bnuoj.com/v3/contest_show.php?cid=9149#problem/I

【题意】

给定长度为l的一个数组，初始值为0；规定了两种操作：

【思路】

找到了一个讲解很清楚的博客http://www.cnblogs.com/flipped/p/HDU4947.html

【Accepted】

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <stack>
 #include <queue>
 #include <string>
 #include <vector>
 #include <set>
 #include <map>
 #include <cassert>
 using namespace std;

 #define CLR(a,b) memset(a,b,sizeof(a))
 typedef long long LL;
 const int N = +;
 bool check[N];
 int mu[N],prime[N];

 vector<int> fac[N];
 LL f[N];
 int l,q;

 void Mobius()
 {
     CLR(check, );
     mu[] = ;
     int tot = ;
     for(int i = ; i < N ; i++){
         if(!check[i]){
             prime[tot ++] = i;
             mu[i] = -;
         }
         for(int j =  ;j < tot; j ++){
             if(i * prime[j] >= N)break;
             check[i * prime[j]] = true;
             if(i % prime[j] == ){
                 mu[i * prime[j]] = ;
                 break;
             }else{
                 mu[i * prime[j]] = -mu[i];
             }
         }
     }
     for(int i =  ;i < N ; i++){
         for(int j = i ; j < N ; j += i){
             fac[j].push_back(i);
         }
     }
 }

 inline LL sum(int p){
     LL s = ;
     while(p > ){
         s += f[p];
         p -= p & (-p);
     }
     return s;
 }

 inline void add(int p,int v){
     while(p <= l){
         f[p] += v;
         p += (p) & (-p);
     }
 }

 void update(int n,int d,int v){
     if(n % d != )return;

     n = n/d;
     for(int i =  ;i < fac[n].size() ; i++){
         int q = fac[n][i];
         add(q * d, v * mu[q]);
     }
 }

 LL query(int p)
 {
     LL ans = ;
     for(int i = ,last = i ; i <= p ; i = last + ){
         last = p/(p/i);
         ans += (LL)(p/i) * (sum(last) - sum(i-)) ;
     }
     return ans;
 }

 int main()
 {
     Mobius();
     int cas = ;
     while(~scanf("%d%d",&l,&q)){
         if(l ==  && q == )break;
         CLR(f, );
         cas ++;
         printf("Case #%d:\n",cas);
         while(q--){
             int t;
             scanf("%d",&t);
             if(t == ){
                 int n,d,v;
                 scanf("%d%d%d",&n,&d,&v);
                 update(n, d, v);
             }else{
                 int x;
                 scanf("%d",&x);
                 printf("%I64d\n",query(x));
             }
         }
     }
     return ;
 }

 /*

  6 4
  1 4 1 2
  2 5
  1 3 3 3
  2 3
  0 0

 */