Factoring a Polynomial

Factoring a Polynomial

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 2561		Accepted: 1321

Description

Recently Georgie has learned about polynomials. A polynomial in one variable can be viewed as a formal sum a_nxⁿ + a_n-1x^n-1 + . . . + a1x + a0 , where x is the formal variable and a i are the coefficients of the polynomial. The greatest i such that ai != 0 is called the degree of the polynomial. If ai = 0 for all i, the degree of the polynomial is considered to be -∞. If the degree of the polynomial is zero or -∞, it is called trivial, otherwise it is called non-trivial. 
What really impressed Georgie while studying polynomials was the fact that in some cases one can apply different algorithms and techniques developed for integer numbers to polynomials. For example, given two polynomials, one may sum them up, multiply them, or even divide one of them by the other. 
The most interesting property of polynomials, at Georgie's point of view, was the fact that a polynomial, just like an integer number, can be factorized. We say that the polynomial is irreducible if it cannot be represented as the product of two or more non-trivial polynomials with real coefficients. Otherwise the polynomial is called reducible. For example, the polynomial x² - 2x + 1 is reducible because it can be represented as (x - 1)(x - 1), while the polynomial x² + 1 is not. It is well known that any polynomial can be represented as the product of one or more irreducible polynomials. 
Given a polynomial with integer coefficients, Georgie would like to know whether it is irreducible. Of course, he would also like to know its factorization, but such problem seems to be too difficult for him now, so he just wants to know about reducibility. 

Input

The first line of the input contains n --- the degree of the polynomial (0 <= n <= 20). Next line contains n + 1 integer numbers, a_n , a_n-1 , . . . , a1 , a0 --- polynomial coefficients (-1000 <= ai <= 1000, an != 0).

Output

Output YES if the polynomial given in the input file is irreducible and NO in the other case.

Sample Input

2 
1 -2 1 

Sample Output

NO

Source

Northeastern Europe 2003, Northern Subregion

 

#include <stdio.h>
int main()
{
    int n,a[25];
    scanf("%d",&n);
       for(int i=0;i<=n;i++)
       {
           scanf("%d",&a[i]);
       }
       if(n>2)
        printf("NO\n");
       if(n==2)
       {
           if(a[1]*a[1]>=4*a[0]*a[2])
            printf("NO\n");
           else
            printf("YES\n");
       }
       if(n>=0&&n<2)
       {
           printf("YES\n");
       }
    return 0;
}

这里有一个定理：

在实数范围内，任何多项式都可以分解为一次式与二次式的乘积（即三次以上的多项式都是可约的），只是系数未必是有理数，有时候很难计算准确值，常常借助于数值方法计算近似值。
所以可以直接判断大于2项式的可以被分解
2项式若有实数解也可直接判断为可以分解
这里也要注意数组的大小