Mathematically some problems look hard. But with the help of the computer, some problems can be easily solvable.
In this problem, you will be given two integers a and b. You have to find the summation of the scores of the numbers from a to b (inclusive). The score of a number is defined as the following function.
score (x) = n2, where n is the number of relatively prime numbers with x, which are smaller than x
For example,
For 6, the relatively prime numbers with 6 are 1 and 5. So, score (6) = 22 = 4.
For 8, the relatively prime numbers with 8 are 1, 3, 5 and 7. So, score (8) = 42 = 16.
Now you have to solve this task.
Input starts with an integer T (≤ 105), denoting the number of test cases.
Each case will contain two integers a and b (2 ≤ a ≤ b ≤ 5 * 106).
For each case, print the case number and the summation of all the scores from a to b.
3
6 6
8 8
2 20
Case 1: 4
Case 2: 16
Case 3: 1237
Euler's totient function applied to a positive integer n is defined to be the number of positive integers
less than or equal to n that are relatively prime to n.
is read "phi of n."
Given the general prime factorization of , one can compute
using
the formula
题意:假设所有小于等于x的数中,与x互质的数的个数为n,则sorce(x)=n的平方。给你a和b,求从a到b所有的sorce(i)的和。
其实就是一道简单的欧拉函数的模板题,但是坑点实在太多。
坑点:
1、会爆long long导致wa,应该定义为unsigned long long。
2、不能开两个数组,不然会爆内存。求欧拉函数值的数组和前缀和的数组可以用一个数组表示。
3、不能用cout输出,不然会超时,应该用printf。
#include <bits/stdc++.h>
#define N 5000000+10
using namespace std;
typedef unsigned long long ll;
ll Euler[N];
void init()
{
Euler[1]=1;
for(int i=2; i<N; i++)
Euler[i]=i;
for(int i=2; i<N; i++)
if(Euler[i]==i)
for(int j=i; j<N; j+=i)
Euler[j]=Euler[j]/i*(i-1);
}
void solve()
{
for(int i=2; i<N; i++)
Euler[i]=Euler[i-1]+Euler[i]*Euler[i];
}
int main()
{
init();
solve();
int t,a,b;
cin>>t;
for(int cas=1; cas<=t; cas++)
{
scanf("%d%d",&a,&b);
printf("Case %d: %llu\n",cas,Euler[b]-Euler[a-1]);
}
return 0;
}