HUST 1214 Cubic-free numbers II

Cubic-free numbers II

Time Limit: 10000ms

Memory Limit: 131072KB

This problem will be judged on HUST. Original ID: 1214
64-bit integer IO format: %lld      Java class name: Main

 

A positive integer n is called cubic-free, if it can't be written in this form n = x*x*x*k, while x is a positive integer larger than 1. Now give you two Integers L and R, you should tell me how many cubic-free numbers are there in the range [L, R). Range [L, R) means all the integers x that L <= x < R.

 

Input

The first line is an integer T (T <= 100) means the number of the test cases. The following T lines are the test cases, for each line there are two integers L and R (L <= R <= ).

 

Output

For each test case, output one single integer on one line, the number of the cubic-free numbers in the range [L, R).

 

Sample Input

3
1 10
3 16
20 100

Sample Output

8
12
67

解题：容斥

 #include <bits/stdc++.h>
 using namespace std;
 const int maxn = ;
 typedef long long LL;
 LL cnt[maxn],L,R;
 LL calc(LL x) {
     if(x <= ) return ;
     memset(cnt,,sizeof cnt);
     LL i = ;
     for(i = ; i*i*i <= x; ++i)
         cnt[i] = x/(i*i*i);
     for(LL j = i - ; j >= ; --j) {
         for(LL k = j + j; k < i; k += j)
             cnt[j] -= cnt[k];
     }
     LL ret = ;
     for(LL j = ; j < i; ++j)
         ret += cnt[j];
     return ret;
 }
 int main() {
     int kase;
     scanf("%d",&kase);
     while(kase--) {
         scanf("%lld%lld",&L,&R);
         printf("%lld\n",R - L - calc(R - ) + calc(L - ));
     }
     return ;
 }