HDU4135 Co-prime
? 解题记录 ? ? 容斥 ? ? HDU ?    2018-08-21 11:19:44    597    0    0
Problem Description
Given a number N, you are asked to count the number of integers between A and B inclusive which are relatively prime to N.
Two integers are said to be co-prime or relatively prime if they have no common positive divisors other than 1 or, equivalently, if their greatest common divisor is 1. The number 1 is relatively prime to every integer.
 


Input
The first line on input contains T (0 < T <= 100) the number of test cases, each of the next T lines contains three integers A, B, N where (1 <= A <= B <= 1015) and (1 <=N <= 109).
 


Output
For each test case, print the number of integers between A and B inclusive which are relatively prime to N. Follow the output format below.
 


Sample Input
2
1 10 2
3 15 5
 


Sample Output
Case #1: 5
Case #2: 10
 

Hint

In the first test case, the five integers in range [1,10] which are relatively prime to 2 are {1,3,5,7,9}.

Source
 


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简单容斥,考虑枚举n的质因数,容斥出不能被其中任何一个质因数整除的数。分析复杂度:2*3*5*7*11*13*17*19*23*29刚好超过2e9,这时候只有10个数,一次的复杂度也就是O(1000),显然是轻松可过的。

#include<cstdio>
#include<cstring>
#include<cmath>
#define LL long long
using namespace std;
LL a[12], ans;
LL gcd(LL a, LL b) {
	return b ? gcd(b, a % b) : a;
}
void GetAns(int step, LL cnt, LL m, int rw) {
	if(cnt > m) return;
	if(step == (*a) + 1) {
		ans += (m / cnt) * rw;
		return ;
	}
	GetAns(step + 1, cnt * a[step] / gcd(a[step], cnt), m, rw * (-1));
	GetAns(step + 1, cnt, m, rw);
}

LL solve(LL n, LL m) {
	*a = 0, ans = 0;
	LL sqt = (LL)sqrt(n);
	for(register int i = 2; i <= n && i <= sqt; ++i) {
		if(n % i == 0) a[++(*a)] = i;
		while(n % i == 0) n /= i;
	}
	if(n != 1) a[++(*a)] = n;
	GetAns(1, 1, m, 1);
	return ans;
}

LL u, l, r, t;
int main() {
	scanf("%d", &t);
	for(register int cs = 1; cs <= t; ++cs) {
		scanf("%lld%lld%lld", &l, &r, &u);
		printf("Case #%d: %lld\n", cs, solve(u, r) - solve(u, l - 1));
	} 
	return 0;
}

 

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