Co-prime
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
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}.
分析:求出n的素因子,然后容斥求解出不互质的个数,剩下的就是互质的个数;
代码:
#include <iostream> #include <cstdio> #include <cstdlib> #include <cmath> #include <algorithm> #include <climits> #include <cstring> #include <string> #include <set> #include <bitset> #include <map> #include <queue> #include <stack> #include <vector> #define rep(i,m,n) for(i=m;i<=n;i++) #define mod 1000000007 #define inf 0x3f3f3f3f #define vi vector<int> #define pb push_back #define mp make_pair #define fi first #define se second #define ll long long #define pi acos(-1.0) #define pii pair<int,int> #define sys system("pause") const int maxn=1e5+10; using namespace std; inline ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);} inline ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;} inline void umax(ll &p,ll q){if(p<q)p=q;} inline void umin(ll &p,ll q){if(p>q)p=q;} inline ll read() { ll x=0;int f=1;char ch=getchar(); while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();} while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();} return x*f; } int n,m,k,t,cnt,fac[maxn],cas; ll x,y; void init(int x) { cnt=0; if(x%2==0){ fac[++cnt]=2; while(x%2==0)x/=2; } for(int i=3;(ll)i*i<=x;i+=2) { if(x%i==0) { fac[++cnt]=i; while(x%i==0)x/=i; } } if(x>1)fac[++cnt]=x; } ll gao(ll x) { ll ret=0; for(int i=1;i<(1<<cnt);i++) { ll num=0,now=1; for(int j=0;j<cnt;j++) { if(i&(1<<j)) { ++num; now*=fac[j+1]; } } if(num&1)ret+=x/now; else ret-=x/now; } return x-ret; } int main() { int i,j; scanf("%d",&t); while(t--) { scanf("%lld%lld%d",&x,&y,&n); init(n); printf("Case #%d: %lld\n",++cas,gao(y)-gao(x-1)); } return 0; }