PAT1009 Product of Polynomials （25 分）

最新推荐文章于 2022-02-20 15:19:12 发布

原创最新推荐文章于 2022-02-20 15:19:12 发布 · 280 阅读

0 ·

CC 4.0 BY-SA版权

PAT-A 专栏收录该内容

81 篇文章

订阅专栏

本文详细解析了一道关于多项式相乘的问题，通过双重循环实现了两个多项式的相乘，并考虑了相乘后可能出现的零系数项及指数排序问题。文章提供了一个C语言的代码示例，展示了如何处理这些细节。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

1009 Product of Polynomials （25 分）

This time, you are supposed to find A×B where A and B are two polynomials.
Input Specification:
Each input file contains one test case. Each case occupies 2 lines, and each line contains the information of a polynomial:K $N_1\ a_{N_1}\ N_2\ a_{N2}\ ...\ N_K\ a_{N_K}$
where K is the number of nonzero terms in the polynomial, $N_i$ and $a_{N_i}$
(i=1,2,⋯,K) are the exponents and coefficients, respectively. It is given that $1 \leq K \leq 10$ , $0≤N_K<⋯<N_2<N_1≤1000$ .
Output Specification:
For each test case you should output the product of A and B in one line, with the same format as the input. Notice that there must be NO extra space at the end of each line. Please be accurate up to 1 decimal place.
Sample Input:

2 1 2.4 0 3.2
2 2 1.5 1 0.5

Sample Output:

3 3 3.6 2 6.0 1 1.6

解析

这题要注意的是：多项式相乘后：有的项的系数可能为0.注意筛选。
多项式相乘：用双重循环相乘后，生成的多项式：可能指数不是按从大到小排序的。
比如说：
polynomial1 $x^3+x^1$
polynomial2 $x^{100}+x^{1}$
polynomial $x^{103}+x^{4}+x^{101}+x^{2}$
无论用什么数据结构：都要注意这上面的两点哟。

Code:

#include <stdio.h>
double polynomial[2020];
double temp[1010];
int main()
{
    int k, exp;
    double coe;
    scanf("%d", &k);
    while ( k-- ){
        scanf("%d %lf", &exp, &coe);
        temp[exp] = coe;
    }
    scanf("%d", &k);
    while ( k-- ){
        scanf("%d %lf", &exp, &coe);
        for(int i=0; i<1010; i++)
            if(temp[i] != 0.0)
                polynomial[i+exp] += coe*temp[i];
    }
    int count = 0;
    for( int i=0; i<2020; i++)
        if ( polynomial[i] != 0.0)
            ++count;
    printf("%d", count);
    for( int i=2019; i>=0; i--)
        if ( polynomial[i] != 0.0)
            printf(" %d %.1f", i, polynomial[i]);
}