多项式相乘

最新推荐文章于 2023-03-04 16:03:26 发布

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最新推荐文章于 2023-03-04 16:03:26 发布

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分类专栏：算法文章标签：算法

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问题

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
N
2

… 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≤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
结尾无空行
Sample Output:
3 3 3.6 2 6.0 1 1.6
结尾无空行

思路

利用map以key按大小顺序排序的特性存储第一个多项式。在第二个多项式的输入过程中与第一个多项式的每一项相乘，将结果保留在结果多项式（也是一个map），然后顺序输出就行。

代码

#include <bits/stdc++.h>
using namespace std;

map<int,float,greater<int>> mp;
map<int,float,greater<int>> res;
int n,m;


int main() {
    int iNum;
    float fNum;
    cin>>n;
    for (int i = 0; i < n; ++i) {
        getchar();
        scanf("%d %f",&iNum,&fNum);
        mp[iNum] = fNum;
    }
    cin>>m;
    int newiNum;
    float newfNum;
    for (int j = 0; j < m; ++j) {
        getchar();
        scanf("%d %f",&iNum,&fNum);

        for (map<int,float>::iterator it=mp.begin();it!=mp.end();++it) {
            newfNum = it->second*fNum;
            newiNum = it->first+iNum;
            if(res.count(newiNum)!=0){
                res[newiNum] = res[newiNum]+newfNum;
                if(res[newiNum] == 0){
                    res.erase(newiNum);
                }
            }
            else{
                res[newiNum] = newfNum;
                if(res[newiNum] == 0){
                    res.erase(newiNum);
                }
            }

        }
    }
    cout<<res.size();
    if(res.size()!=0)
        cout<<" ";
    int count = 0;
    for (map<int,float>::iterator it=res.begin();it!=res.end();++it) {
        count++;
        printf("%d %.1f",it->first,it->second);
        if(count!=res.size())
            cout<<" ";
    }
    cout<<endl;
    return 0;
}