PAT甲级 - 1009 Product of Polynomials （25 分）

朱雀 2022-03-18 04:48 173阅读 0赞

题目链接：[PAT甲级 - 1009 Product of Polynomials （25 分）][PAT_ - 1009 Product of Polynomials _25]

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 aN1 N2 aN2 ... NK aNK

where K is the number of nonzero terms in the polynomial, Ni and aNi (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

题解：一开始，测试点3,4总是通不过，原因在于多项式结果数组开小了。以指数作为数组下标，多项式相乘，同底数的指数相加，所以结果数组需要开到2\*maxn.

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3Mjc1Njgw_size_16_color_FFFFFF_t_70][]

#include <iostream>
    #include <cstdio>
    #include <cmath>
    #include <cstring>
    using namespace std;
    const int maxn=2010;
    double a[maxn],b[maxn],c[maxn];
    
    int main(){
    	int t,k1,k2;
    	while(~scanf("%d",&k1)){
    	 	memset(a,0,sizeof(a));
    	 	memset(b,0,sizeof(b));
    	 	memset(c,0,sizeof(c));
    	 	int mx1=-1,mx2=-1;
    	  	for(int i=0;i<k1;i++){
      			scanf("%d",&t);
      			mx1=max(mx1,t);
      			scanf("%lf",&a[t]);
      		}
    	  	scanf("%d",&k2);
    	  	for(int i=0;i<k2;i++){
    	  		scanf("%d",&t);
    	  		mx2=max(mx2,t);
      			scanf("%lf",&b[t]);
    	  	}
    	  	for(int i=0;i<=mx1;i++){
    	  		for(int j=0;j<=mx2;j++){
    	  			c[i+j]+=a[i]*b[j];
    			}
    		}
    		int cnt=0;
    		for(int i=0;i<=mx1+mx2;i++){
    			if(c[i]) cnt++;
    		}
    		printf("%d",cnt);
      		for(int i=mx1+mx2;i>=0;i--){
      			if(c[i])
      				printf(" %d %.1f",i,c[i]);
      		}
      		printf("\n");
    	}
    	
    	return 0;
    }

[PAT_ - 1009 Product of Polynomials _25]: https://pintia.cn/problem-sets/994805342720868352/problems/994805509540921344
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3Mjc1Njgw_size_16_color_FFFFFF_t_70]: /images/20220318/5114c1e77afa416cb64beeb2ce41c5f0.png