hdu 1695 GCD (欧拉函数+容斥原理+线性筛法)
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题目:http://acm.hdu.edu.cn/showproblem.php?pid=1695
GCD
Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 7605 Accepted Submission(s): 2801
Problem Description
Given 5 integers: a, b, c, d, k, you're to find x in a...b, y in c...d that GCD(x, y) = k. GCD(x, y) means the greatest common divisor of x and y. Since the number of choices may be very large, you're only required to output the total number of different number pairs.
Please notice that, (x=5, y=7) and (x=7, y=5) are considered to be the same.
Yoiu can assume that a = c = 1 in all test cases.
Please notice that, (x=5, y=7) and (x=7, y=5) are considered to be the same.
Yoiu can assume that a = c = 1 in all test cases.
Input
The input consists of several test cases. The first line of the input is the number of the cases. There are no more than 3,000 cases.
Each case contains five integers: a, b, c, d, k, 0 < a <= b <= 100,000, 0 < c <= d <= 100,000, 0 <= k <= 100,000, as described above.
Each case contains five integers: a, b, c, d, k, 0 < a <= b <= 100,000, 0 < c <= d <= 100,000, 0 <= k <= 100,000, as described above.
Output
For each test case, print the number of choices. Use the format in the example.
Sample Input
21 3 1 5 11 11014 1 14409 9
Sample Output
Case 1: 9Case 2: 736427HintFor the first sample input, all the 9 pairs of numbers are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 5), (3, 4), (3, 5).
Source
2008 “Sunline Cup” National Invitational Contest
#include <iostream>#include <cstdio>#include <algorithm>using namespace std;const int maxn=1e6+10;typedef long long LL;LL prime[maxn],top;bool notprime[maxn];void getprime(){ top=0; for(LL i=2;i<maxn;i++){ if(!notprime[i])prime[top++]=i; for(LL j=0;j<top&&prime[j]*i<maxn;j++){ notprime[prime[j]*i]=1; if(i%prime[j]==0) break; } }}LL factor[1005],faccnt;void resolve(LL x){ faccnt=0; for(int i=0;prime[i]*prime[i]<=x;i++){ if(x%prime[i]==0){ factor[faccnt++]=prime[i]; while(x%prime[i]==0){ x/=prime[i]; } } } if(x>1)factor[faccnt++]=x;}int euler[100010];void getEuler(){ euler[1] = 1; for(int i = 2;i <= 100000;i++) if(!euler[i]) for(int j = i; j <= 100000;j += i) { if(!euler[j]) euler[j] = j; euler[j] = euler[j]/i*(i-1); }}int main(){ //freopen("cin.txt","r",stdin); getprime(); getEuler(); LL t,ca; LL a,b,c,d,k; LL kb,kd; cin>>t; for(ca=1;ca<=t;ca++){ scanf("%lld%lld%lld%lld%lld",&a,&b,&c,&d,&k); if(k==0||k>b||k>d) { //除以0会出现0x0000005c的错误 printf("Case %lld: 0\n",ca); continue; } if(b>d) swap(b,d); b=b/k; d=d/k; LL ans=0; for(int i=1;i<=b;i++){ ans+=euler[i]; } for(int i=b+1;i<=d;i++){ resolve(i); LL q1=0; for(int j=1;j<(1<<faccnt);j++){ LL temp=1,sum=0; for(int k=0;k<faccnt;k++){ if((1<<k)&j){ sum++; temp*=factor[k]; } } if(sum&1) q1=q1+b/temp; else q1=q1-b/temp; } ans=ans+b-q1; } printf("Case %lld: %lld\n",ca,ans); } return 0;}
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