hdu4135---Co-prime(容斥原理)

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

The Third Lebanese Collegiate Programming Contest

Recommend

lcy | We have carefully selected several similar problems for you: 1796 1434 3460 1502 4136

先考虑区间[1, x]里和n不互质的数个数

考虑n的每个素因子

可以被某个素因子整除的数个数为(int)x / pi

但是不能这么单纯算,某些数会被多次统计

用容斥来搞

这个数的素因子不多

所以可以状压来搞出所有组合然后 奇加偶减

/*************************************************************************
    > File Name: hdu4135.cpp
    > Author: ALex
    > Mail: [email protected]
    > Created Time: 2015年05月26日 星期二 20时37分52秒
 ************************************************************************/

#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <map>
#include <bitset>
#include <set>
#include <vector>

using namespace std;

const double pi = acos(-1.0);
const int inf = 0x3f3f3f3f;
const double eps = 1e-15;
typedef long long LL;
typedef pair <int, int> PLL;

vector <int> fac;

LL calc(LL m) {
    int n = fac.size();
    LL ans = 0;
    for (int i = 1; i < (1 << n); ++i) {
        int cnt = 0;
        int getf = 1;
        for (int j = 0; j < n; ++j) {
            if (i & (1 << j)) {
                getf *= fac[j];
                ++cnt;
            }
        }
        if (cnt % 2) {
            ans += (m / getf);
        }
        else {
            ans -= (m / getf);
        }
    }
    return m - ans;
}

int main() {
    int t, icase = 1;
    scanf("%d", &t);
    while (t--) {
        LL l, r;
        int n;
        cin >> l >> r >> n;
        fac.clear();
        for (int i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                fac.push_back(i);
                while (n % i == 0) {
                    n /= i;
                }
            }
        }
        if (n > 1) {
            fac.push_back(n);
        }
        cout << "Case #" << icase++ << ": " << calc(r) - calc(l - 1) << endl;
    }
    return 0;
}