Prime Distence 大数据区间筛素数

题意：给定两个数1<=l< r<=2,147,483,647，求区间内距离最小和距离最大的两个素数

难点：数据太大，肯定不能正常打表，但是r-l<=1e6

思路：先打一部分表，大概N=1e5就够了，然后从所给区间[l,r],l<=i<=r打表，最多有1e6个数据

（接下来的话和题解无关：很郁闷一点就是因为不同的下标计算方法RE,现在还是没理解原理

for(int i=0;i<=r-l;++i)
if(pis[i]) bns[++cnt]=i+l;改成
for(int i=l;i<=r;++i)
if(pis[i-l]) bns[++cnt]=i;就RE,很无语啊。


）

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e5+10;
const int M=1e6+10;
int tot=0,cnt,ans[N],bns[M];
bool vis[N+5],pis[M];

void pri()
{
memset(vis,true,sizeof(vis));
for(int i=2;i<=N;++i)
{
if(vis[i]) ans[++tot]=i;
for(int j=1;(j<=tot)&&(i*ans[j]<=N);++j)
{
vis[i*ans[j]]=false;
if(i%ans[j]==0) break;
}
}
}

void primer(int l,int r)
{
cnt=0;
memset(bns,0,sizeof(bns));
memset(pis,true,sizeof(pis));
for(int i=1;(i<=tot)&&((ll)ans[i]*(ll)ans[i]<=r);++i)
{
ll k=l/ans[i]+(l%ans[i]>0);
if(k==1) k=2;
for(ll j=k*ans[i];j<=r;j+=ans[i])
pis[j-l]=false;
}
for(int i=0;i<=r-l;++i)
if(pis[i]) bns[++cnt]=i+l;
}

int main()
{
pri();
int l,r;
while(~scanf("%d%d",&l,&r))
{
if(l<2) l=2;
primer(l,r);
int mi1=0,mi2=1e7,ma1=0,ma2=0;
for(int i=2;i<=cnt;++i)
{
if(bns[i]-bns[i-1]<mi2-mi1){
mi1=bns[i-1];mi2=bns[i];
}
if(bns[i]-bns[i-1]>ma2-ma1){
ma1=bns[i-1];ma2=bns[i];
}
}
if(mi2==1e7) {printf("There are no adjacent primes.\n");continue;}
printf("%d,%d are closest, %d,%d are most distant.\n",mi1,mi2,ma1,ma2);
}
return 0;
}




 
 


  
  

   
   The branch of mathematics called number theory is about properties of numbers. One of the areas that has captured the interest of number theoreticians for thousands of years is the question of primality. A prime number is a number
 that is has no proper factors (it is only evenly divisible by 1 and itself). The first prime numbers are 2,3,5,7 but they quickly become less frequent. One of the interesting questions is how dense they are in various ranges. Adjacent primes are two numbers
 that are both primes, but there are no other prime numbers between the adjacent primes. For example, 2,3 are the only adjacent primes that are also adjacent numbers. 
   
   

Your program is given 2 numbers: L and U (1<=L< U<=2,147,483,647), and you are to find the two adjacent primes C1 and C2 (L<=C1< C2<=U) that are closest (i.e. C2-C1 is the minimum). If there are other pairs that are the same distance apart, use the first pair.
 You are also to find the two adjacent primes D1 and D2 (L<=D1< D2<=U) where D1 and D2 are as distant from each other as possible (again choosing the first pair if there is a tie).
  
  

 
 
 
 
  
  
Input
 
 
 
 


  
  

   
   Each line of input will contain two positive integers, L and U, with L < U. The difference between L and U will not exceed 1,000,000.
  
  

 
 
 
 
  
  
Output
 
 
 
 


  
  

   
   For each L and U, the output will either be the statement that there are no adjacent primes (because there are less than two primes between the two given numbers) or a line giving the two pairs of adjacent primes.
  
  

 
 
 
 
  
  
Sample Input
 
 
 
 


  
  
2 17
14 17


 
 
 
 
  
  
Sample Output
 
 
 
 


  
  
2,3 are closest, 7,11 are most distant.
There are no adjacent primes.