PAT-A 1009. Product of Polynomials (25)

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本文介绍了一种计算两个多项式相乘的算法，并通过一个具体的C++代码示例展示了如何实现这一算法。输入包括两个多项式的非零项及其指数和系数，输出为相乘后的多项式表达式。

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1009. Product of Polynomials (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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 N1 a_N1 N2 a_N2 ... NK a_NK, where K is the number of nonzero terms in the polynomial, Ni and a_Ni (i=1, 2, ..., K) are the exponents and coefficients, respectively. It is given that 1 <= K <= 10, 0 <= NK < ... < N2 < N1 <=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

#include <cstdio>
struct Poly{
    int exp;//指数
    double cof;//系数
}poly[1001];

double ans[2001];//存放结果

int main(){
    int n, m, number = 0;
    scanf("%d", &n);//第一个多项式中非零系数的项数
    for(int i = 0; i < n; i++){
        scanf("%d %lf",&poly[i].exp,&poly[i].cof);//第一个多项式的指数和系数
    }
    scanf("%d", &m);//第二个多项式中非零系数的项数
    for(int i = 0; i < m; i++){
        int exp;
        double cof;
        scanf("%d %lf",&exp,&cof);//第二个多项式的指数和系数
        for(int j = 0; j < n; j++){//与第一个多项式中的每一项相乘
            ans[exp + poly[j].exp] += (cof * poly[j].cof);
        }
    }
    for(int i = 0; i <= 2000; i++){
        if(ans[i] != 0.0) number++;//累计非零系数的项数
    }
    printf("%d",number);
    for(int i = 2000; i >= 0; i--){//输出
        if(ans[i] != 0.0){
            printf(" %d %.1f", i, ans[i]);
        }
    }
    return 0;
}