1009 Product of Polynomials（模拟）

淡淡的烟草味﹌ 2024-04-08 08:49 37阅读 0赞

## 1009 Product of Polynomials ##

### 0、题目 ###

This time, you are supposed to find  A × B A×B A×B where  A A A and  B B 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 N 2 . . . N K a N K K N\_1 a\_\{N\_1\} N\_2 a\_\{N\_2\} ... N\_K a\_\{N\_K\} KN1aN1N2aN2...NKaNK

where  K K K is the number of nonzero terms in the polynomial,  N i N\_i Ni and  a N i a\_\{N\_i\} aNi ( i = 1 , 2 , ⋯ , K i=1,2,⋯,K i=1,2,⋯,K) are the exponents and coefficients, respectively. It is given that  1 ≤ K ≤ 10 1≤K≤10 1≤K≤10,  0 ≤ N K < ⋯ < N 2 < N 1 ≤ 1000 0≤NK<⋯<N2<N1≤1000 0≤NK<⋯<N2<N1≤1000.

#### Output Specification: ####

For each test case you should output the product of  A A A and  B B 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

### 1、大致题目 ###

多项式相乘，求项数和系数

### 2、解题思路 ###

多项式相乘，可能因为学过计组，感觉也就这么回事，特别是之前有一道 [1002 A+B for Polynomials][1002 A_B for Polynomials] ，导致基本看不出啥难点。

### 3、AC代码 ###

#include<iostream>
    #include<map>
    #include<cmath>
    #include<iomanip>
    using namespace std;
    int K;
    map<int,double,greater<int> >ma1,ma2,ma;
    int a;
    double b;
    
    int main() {
        
    	ma.clear();
    	ma1.clear();
    	ma2.clear();
    	cin>>K;
    	for(int i=0; i<K; i++) {
        
    		cin>>a>>b;
    		if(ma1.count(a)==0&&b!=0) {
        
    			ma1[a]=b;
    		} else {
        
    			ma1[a]+=b;
    		}
    	}
    	cin>>K;
    	for(int i=0; i<K; i++) {
        
    		cin>>a>>b;
    		if(ma2.count(a)==0&&b!=0) {
        
    			ma2[a]=b;
    		} else {
        
    			ma2[a]+=b;
    		}
    	}
    	for(map<int,double>::iterator it1=ma1.begin(); (it1)!=ma1.end(); it1++) {
        
    		for(map<int,double>::iterator it2=ma2.begin(); (it2)!=ma2.end(); it2++) {
        
    			a=it1->first+it2->first;
    			b=it1->second*it2->second;
    			if(ma.count(a)==0&&b!=0) {
        
    				ma[a]=b;
    			} else {
        
    				ma[a]+=b;
    			}
    		}
    	}
    	for(map<int,double>::iterator it=ma.begin(); (it)!=ma.end();) {
        
    		if(it->second==0) {
        
    			ma.erase(it++);
    		} else {
        
    			++it;
    		}
    	}
    	if(ma.empty()) {
        
    		cout<<0<<endl;
    	} else {
        
    		cout<<ma.size();
    		for(map<int,double>::iterator it=ma.begin(); (it)!=ma.end(); it++) {
        
    			cout<<" "<<it->first<<" "<<setiosflags(ios::fixed)<<setprecision(1)<<it->second;
    		}
    		cout<<endl;
    	}
    	return 0;
    }

[1002 A_B for Polynomials]: https://blog.csdn.net/qq_46371399/article/details/126273141