【PAT甲级】1009 Product of Polynomials (25 分)

1009 Product of Polynomials

题目描述：

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_​N1 N​₂ a_​N​2 … N_K a_NK

​where K is the number of nonzero terms in the polynomial, N​_i and a_Ni(i=1,2,⋯,K) are the exponents and coefficients, respectively. It is given that 1≤K≤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

思路：

由于两个多项式最高次为1000，因此相乘以后最高次不超过2000，因此定义三个数组，分别存放A，B，AxB的系数，同时，还需要定义两个数组来存放A，B的索引，即多项式的指数。以及两个数字来记录多项式非零项个数

计算的时候，对A，B中所有项进行一个两层的循环，分别计算A中每一项乘以B中每一项的结果

poly[2][p[0][i]+p[1][j]]+=poly[0][p[0][i]]*poly[1][p[1][j]];

注意在上面poly[i]表示第i个多项式的信息，i=0是A，i=1是B，i=2是AxB
同时， p[0][i]表示第一个多项次的第i项的指数

代码：

#include<stdio.h>

#define MAXK 2001

int main()
{
    
    
    double poly[3][MAXK]={
    
    0};//pay attention to initialize the array
    int K[2];int *p[2];
    for(int i=0;i<2;i++)
    {
    
    
        scanf("%d",&K[i]);
        p[i]=new int[K[i]];
        for(int j=0;j<K[i];j++)
        {
    
    
            scanf("%d",&p[i][j]);
            scanf("%lf",&poly[i][p[i][j]]);
        }
    }
    for(int i=0;i<K[0];i++)
    {
    
    
        for(int j=0;j<K[1];j++)
        {
    
    
            poly[2][p[0][i]+p[1][j]]+=poly[0][p[0][i]]*poly[1][p[1][j]];
        }
    }
    int count=0;
    for(int i=0;i<MAXK;i++)
    {
    
    
        if(poly[2][i]!=0)
            count++;
    }
    printf("%d",count);
    for(int i=MAXK-1;i>=0;i--)
    {
    
    
        if(poly[2][i]!=0)
            printf(" %d %.1f",i,poly[2][i]);
    }
    printf("\n");
    return 0;
}

git仓库：Product of Polynomials