PAT A1009 Product of Polynomials

PAT A1009 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​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

　　Sample Output:
　　3 3 3.6 2 6.0 1 1.6

参考代码：

参考1：

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 1 /****************************************************
 2 PAT A1009 Product of Polynomials
 3 ****************************************************/
 4 #include <iostream>
 5 #include <algorithm>
 6 #include <iomanip>
 7 #include <vector>
 8 #include <cmath>
 9 
10 using namespace std;
11 
12 struct Term {
13     int Exponent = 0;
14     double Coefficient = 0.0;
15 };
16 
17 bool cmp(Term A, Term B) {
18     return A.Exponent > B.Exponent;
19 }
20 
21 //整理得到的方程
22 void ArrangePoly(vector<Term>& poly) {
23     //合并指数相同项
24     for (vector<Term>::iterator itr = poly.begin() + 1; itr != poly.end(); ++itr) {
25         if (itr->Exponent == (itr - 1)->Exponent) {
26             (itr - 1)->Coefficient += itr->Coefficient;
27             itr = poly.erase(itr);
28             itr--;
29         }
30     }
31 
32     //移除系数绝对值小于0.1（包括0）项
33     for (vector<Term>::iterator itr = poly.begin(); itr != poly.end(); ++itr) {
34         if (itr->Coefficient == 0 || fabs(itr->Coefficient) < 0.1) {
35             itr = poly.erase(itr);
36             itr--;
37         }
38     }
39 }
40 
41 //计算两个方程相乘之后的新方程
42 vector<Term> GetPolynomial(const vector<Term> poly1, const vector<Term> poly2) {
43     Term temp;
44     vector<Term> poly3;
45 
46     for (int i = 0; i < poly1.size(); ++i) {
47         for (int j = 0; j < poly2.size(); ++j) {
48             temp.Exponent = poly1[i].Exponent + poly2[j].Exponent;
49             temp.Coefficient = poly1[i].Coefficient * poly2[j].Coefficient;
50 
51             poly3.push_back(temp);
52         }
53     }
54 
55     //结果按照指数从大到小的顺序排列，以便后续的处理
56     sort(poly3.begin(), poly3.end(), cmp);
57     ArrangePoly(poly3);
58 
59     return poly3;
60 }
61 
62 int main() {
63     int N1 = 0, N2 = 0;
64 
65     cin >> N1;
66     vector<Term> func1(N1);
67     for (int i = 0; i < N1; ++i)
68         cin >> func1[i].Exponent >> func1[i].Coefficient;
69 
70     cin >> N2;
71     vector<Term> func2(N2);
72     for (int i = 0; i < N2; ++i)
73         cin >> func2[i].Exponent >> func2[i].Coefficient;
74 
75     vector<Term> func3(GetPolynomial(func1, func2));
76 
77     func3.size() == 0 ? cout << '0' : cout << func3.size() << ' ';
78     for (int i = 0; i < func3.size(); ++i) {
79         cout << setiosflags(ios::fixed) << setprecision(0) << func3[i].Exponent << ' ';
80         cout << setiosflags(ios::fixed) << setprecision(1) << func3[i].Coefficient;
81         if (i != func3.size() - 1) cout << ' ';
82     }
83 
84     return 0;
85 }

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