《ACM程序设计》书中题目 R - 18 半素数
2017-03-16 17:14
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Description
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
这道题的基本题意为输入一个数,判断这个数是否为半素数(可以分解成两个素数相乘的数称为半素数)。
基本思路为先判断可以被这个数整除的数是否为素数,然后再判断商是否为素数,如果都为素数,则这个数为半素数。
源代码如下:
#include<bits/stdc++.h>
using namespace std;
int main()
{
int n,i,j,m,h;
while(cin>>n)
{ if(n==2||n==3)h=0;
else { h=0;
for(i=2;i<=n/2;++i)
{
if(n%i==0)
{m=n/i;
h=1;
for(j=2;i>2&&j<i;++j)
if(i%j==0)h=0;
for(j=2;m>2&&j<m;++j)
if(m%j==0)h=0;
}
}
}
if(h)cout<<"Yes"<<endl;
else cout<<"No"<<endl;
}
}
需要特别考虑n=2跟n=3的情况,还有找除数的循环用i<=n/2即可,没有必要循环到n。
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
这道题的基本题意为输入一个数,判断这个数是否为半素数(可以分解成两个素数相乘的数称为半素数)。
基本思路为先判断可以被这个数整除的数是否为素数,然后再判断商是否为素数,如果都为素数,则这个数为半素数。
源代码如下:
#include<bits/stdc++.h>
using namespace std;
int main()
{
int n,i,j,m,h;
while(cin>>n)
{ if(n==2||n==3)h=0;
else { h=0;
for(i=2;i<=n/2;++i)
{
if(n%i==0)
{m=n/i;
h=1;
for(j=2;i>2&&j<i;++j)
if(i%j==0)h=0;
for(j=2;m>2&&j<m;++j)
if(m%j==0)h=0;
}
}
}
if(h)cout<<"Yes"<<endl;
else cout<<"No"<<endl;
}
}
需要特别考虑n=2跟n=3的情况,还有找除数的循环用i<=n/2即可,没有必要循环到n。
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