Help Hanzo (素数筛+区间枚举)

Posted 2020-06-26 Shentr

 

Help Hanzo

题意：求a~b间素数个数(1 ≤ a ≤ b < 2³¹, b - a ≤ 100000).     (全题在文末)

 

题解：

a~b枚举必定TLE，普通打表MLE，真是头疼。。

b - a ≤ 100000 是关键。

类似素数筛的方法:

1.初始化vis[]=0 ;

2.素数的倍数vis[]=1;    

3.  b较小时,素数筛解决

　  b很大时,素数筛的vis[]会MLE，此时用vis2[i-a]保存vis[i]就不会MLE 了。。

 

 

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long LL;
const int N=1e5+5;

bool vis[N],visab[N];
int prime[N],cnt=0;
void is_prime()
{
    memset(vis,0,sizeof(vis));
    vis[1]=1;
    for(int i=2;i<N;i++)
    {
        if(!vis[i])
        {
            prime[cnt++]=i;
            for(int j=i+i;j<N;j+=i)
                vis[j]=1;
        }
    }
}


int main()
{
    int t;
    cin>>t;
    is_prime();
    for(int kase=1;kase<=t;kase++)
    {
        LL a,b;
        scanf("%lld%lld",&a,&b);
        int count=0;
        if(b<=N-1)
        {
            for(LL i=a;i<=b;i++)
            {
                if(!vis[i])
                    count++;
            }
        }
        else
        {
            memset(visab,0,sizeof(visab));
            for(int i=0;i<cnt&&prime[i]<=b;i++)
            {
                LL k=a/prime[i];
                if(k*prime[i]<a)
                    k++;
                for(LL j=k*prime[i];j<=b;j+=prime[i])
                {
                    visab[j-a]=1;
                }
            }
            for(LL i=a;i<=b;i++)
            {
                if(!visab[i-a])
                    count++;
            }
        }
        printf("Case %d: %d\n",kase,count);
    }
}

 

 

 

Help Hanzo

Time Limit:2000MS     Memory Limit:32768KB     64bit IO Format:%lld & %llu

Description

Amakusa, the evil spiritual leader has captured the beautiful princess Nakururu. The reason behind this is he had a little problem with Hanzo Hattori, the best ninja and the love of Nakururu. After hearing the news Hanzo got extremely angry. But he is clever and smart, so, he kept himself cool and made a plan to face Amakusa.

Before reaching Amakusa‘s castle, Hanzo has to pass some territories. The territories are numbered as a, a+1, a+2, a+3 ... b. But not all the territories are safe for Hanzo because there can be other fighters waiting for him. Actually he is not afraid of them, but as he is facing Amakusa, he has to save his stamina as much as possible.

He calculated that the territories which are primes are safe for him. Now given a and b he needs to know how many territories are safe for him. But he is busy with other plans, so he hired you to solve this small problem!

Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case contains a line containing two integers a and b (1 ≤ a ≤ b < 2³¹, b - a ≤ 100000).

Output

For each case, print the case number and the number of safe territories.

Sample Input

3

2 36

3 73

3 11

Sample Output

Case 1: 11

Case 2: 20

Case 3: 4