ZOJ.2723 Semi-Prime【数论】 2015/09/16

Semi-Prime

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Prime Number Definition
An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For instance, 2, 11, 67, 89 are prime numbers but 8, 20, 27 are not.

Semi-Prime Number Definition
An integer greater than one is called a semi-prime number if it can be decompounded to TWO prime numbers. For example, 6 is a semi-prime number but 12 is not.

Your task is just to determinate whether a given number is a semi-prime number.

Input

There are several test cases in the input. Each case contains a single integer N (2 <= N <= 1,000,000)

Output

One line with a single integer for each case. If the number is a semi-prime number, then output "Yes", otherwise "No".

Sample Input

3
4
6
12

Sample Output

No
Yes
Yes
No

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Author: LIU, Yaoting

Source: Zhejiang University Local Contest 2006, Preliminary

题意：若一个数可表示为两个素因子的乘积，则该数就是一个Semi-Prime数。

先打表求出2~1000000内的素数，再从 2~sqrt(n)依次访问，对所有n可以整除的i中，找出是否存在一个i，使得i与n/i都为素数，若存在，则Yes，否则No

#include
#include
#include
#include

using namespace std;

bool p[1000005];
int a[500000],k;

void init(){
    int i,j;
    k=0;
    memset(p,false,sizeof(p));
    for( i = 2 ; i <= 1000000 ; ++i ){
        if( !p[i] ){
            a[k++] = i;
            for( j = i+i ; j <= 1000000 ; j+=i )
                p[j] = true;
        }
    }
}

int main(){
    int n;
    init();
    while( ~scanf("%d",&n) ){
        int ret = (int)sqrt(n);
        bool flag = false;
        for( int i = 2 ; i <= ret ; ++i ){
            if( n%i == 0 ){
                if( !p[i] && !p[n/i] ){
                    flag = true;
                    break;
                }
            }
        }
        if( flag ) printf("Yes\n");
        else printf("No\n");
    }
    return 0;
}