LOJ - 1197 - 《Help Hanzo》【区间素数】

最新推荐文章于 2021-09-12 22:14:26 发布

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最新推荐文章于 2021-09-12 22:14:26 发布

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分类专栏：数学 ACM 文章标签： ACM 数学

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在面对Amakusa的威胁时，Hanzo利用他的智慧和计划，通过计算哪些领土是安全的，从而节省体力。本文详细介绍了如何通过编程解决这个问题，包括输入测试案例的数量，每组测试案例的开始和结束领土编号，以及输出每个测试案例的安全领土数量。

1197 - Help Hanzo

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

Output for Sample Input

2 36

3 73

3 11

Case 1: 11

Case 2: 20

Case 3: 4

【实现代码】

#include<cstdio>
#include<cmath>
#define maxn 100005
bool IsPrime[maxn];
void SegmentPrime(int a,int b)
{
    int x=sqrt(b);
    int d=b-a+1;
    for(int i=0;i<d;i++)IsPrime[i]=(a+i)%2;
    for(int i=3;i<=x;i+=2)
    {
        if(i>=a&&!IsPrime[i-a])continue;
        int j=(a/i)*i;
        if(j<a)j+=i;
        if(j==i)j+=i;
        j=j-a;
        for(;j<d;j+=i)IsPrime[j]=0;
    }
    if(a==1)IsPrime[0]=0;
    if(a<=2)IsPrime[2-a]=1;
}
int main()
{
    int T;
    scanf("%d",&T);
    for(int t=1;t<=T;t++)
    {
        int a,b;
        scanf("%d%d",&a,&b);
        SegmentPrime(a,b);
        int sum=0;
        for(int i=0;i<=b-a;i++)if(IsPrime[i])sum++;
        printf("Case %d: %d\n",t,sum);
    }
    return 0;
}

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