2021中国大学生程序设计竞赛（CCPC）- 网络选拔赛（重赛）1004

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2019中国大学生程序设计竞赛（CCPC）- 网络选拔赛（部分题解） 1001：^ & ^ 对第i位，如果A和B的第i位都是1，那么C的这一位需要为1，否则取0.C必须为正数，所以C可以取0的时候，要看A和B最小的一个为1一个为0的位出现的位置last，让C为1<<last（这样才能保证(A ^ C)&( B ^ C)最小）。如果没有这样的位置，就让C为1. #include<bits/stdc++.h> #define ll... 阅读详情

Primality Test

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 5305 Accepted Submission(s): 2464

Problem Description

A positive integer is called a prime if it is greater than 1 and cannot be written as the product of two smaller positive integers. A primality test is an algorithm for determining whether an input number is a prime. For example, the Miller-Rabin primality test is a probabilistic primality test. This problem is precisely the one about the primality test.

Let's define the function f(x) as the smallest prime which is strictly larger than x. For example, f(1)=2, f(2)=3, and f(3)=f(4)=5. And we use ⌊x⌋ to indicate the largest integer that does not exceed x.

Now given x, please determine whether g(x) is a prime.

g(x)=⌊f(x)+f(f(x))2⌋

Input

The first line of the input contains an integer T (1≤T≤105), indicating the number of test cases.

Each test case contains an integer x (1≤x≤1018) in a single line.

Output

For each test case, if g(x) is a prime, output 𝚈𝙴𝚂 in a single line. Otherwise, output 𝙽𝙾 in a single line.

Sample Input

2 1 2

Sample Output

YES NO

Hint

When x=1, f(x)=2, f(f(x))=f(2)=3, then g(x)=⌊2+32⌋=2, which is a prime. So the output is 𝚈𝙴𝚂.

When x=2, f(x)=3, f(f(x))=f(3)=5, then g(x)=⌊3+52⌋=4, which is not a prime. So the output is 𝙽𝙾.

#include <iostream>
#include <cstdio>
using namespace std;

int main()
{
    int T;
    cin >> T;
    while (T --)
    {
        long long x;
      scanf("%lld", &x);
        if (x == 1){
            puts("YES");
        } else {
            puts("NO");
        }
    }
    return 0;
}

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