题目大意：给定 A, B, 求 [A, B] 中与 N 互质的数的个数。
分解 N 的素因数 P[i]，考虑 [1, B] 中是 P[1] 倍数的数，是 P[2] 倍数的数...这些数的
交集是 [1, B] 中不与 N 互质的数（即与 N 有非 1 公约数的数）。
同理求 [1, A) 中不与 N 互质的数。前者减后者得到 t, 即 [A, B] 中不与 N 互质的数的数量。
答案是 B-A+1 - t.
1 <= A <= B <= 1015
1 <=N <= 109
注意下 getans() 函数里二进制枚举子集（紫书里提到过）进行容斥原理计算的代码。
1 #include <stdio.h> 2 3 typedef long long LL; 4 5 LL l, r, n, Pcnt; 6 LL P[2000000]; 7 8 void div() 9 { 10 Pcnt = 0; 11 LL v = n; 12 for (LL i = 2; i*i <= v; ++i) { 13 if (!(v % i)) P[++Pcnt] = i; 14 while (!(v % i)) v /= i; 15 } 16 if (v != 1) P[++Pcnt] = v; 17 return; 18 } 19 20 LL getans(LL k) 21 { 22 LL ans = 0; 23 for (LL i = 1; i < (1<<Pcnt); ++i) { 24 LL v = 1, tot = 0; 25 for (LL j = 1; j <= Pcnt; ++j) 26 if ((i>>j-1) & 1) v *= P[j], tot ^= 1; 27 ans += k / v * (tot ? 1 : -1); 28 } 29 return ans; 30 } 31 32 int main() 33 { 34 LL T, Ti; 35 scanf("%lld", &T); 36 for (Ti = 1; Ti <= T; ++Ti) { 37 scanf("%lld%lld%lld", &l, &r, &n); 38 div(); 39 printf("Case #%lld: %lld ", Ti, r-l+1 - (getans(r)-getans(l-1))); 40 } 41 return 0; 42 }
题目: http://acm.hdu.edu.cn/showproblem.php?pid=4135
Co-prime
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6311 Accepted Submission(s): 2538
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.
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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