PAT 1009 Product of Polynomials

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最新推荐文章于 2022-11-13 18:02:45 发布

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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 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

#include <iostream>
#include <map>
#include <vector>
#include <algorithm>
using namespace std;
class  Polynomials {
public:
	int exponent;
	double coefficient;
};
Polynomials multiply(Polynomials &b, Polynomials &c) {
	Polynomials e;
	e.coefficient = b.coefficient*c.coefficient;
	e.exponent = b.exponent + c.exponent;
	return e;
}
int main() {
	int n, m;
	cin >> n;
	vector<Polynomials>v1, v2;
	for (int i = 0; i < n; ++i) {
		Polynomials p;
		cin >> p.exponent >> p.coefficient;
		v1.push_back(p);
	}
	cin >> m;
	for (int i = 0; i < m; ++i) {
		Polynomials p;
		cin >> p.exponent >> p.coefficient;
		v2.push_back(p);
	}
	map<int, double> _map;
	map<int, double>::iterator iter1;
	map<int, double>::reverse_iterator iter;
	for (unsigned i = 0; i < v1.size(); ++i) {
		for (unsigned j = 0; j < v2.size(); ++j) {
			if (v1[i].coefficient == 0 || v2[j].coefficient == 0)  //当参与运算的两个系数有一个是0时就直接忽略了
				continue;
			Polynomials c = multiply(v1[i], v2[j]);
			_map[c.exponent] += c.coefficient;
		}
	}
	for (iter1 = _map.begin(); iter1 != _map.end(); ++iter1) {  //运算之后还必须要再检查一遍，防止系数出现-1+1=0的情况出现
		if (!iter1->second) {
			_map.erase(iter1);
		}
	}
	cout << _map.size() << (_map.size() == 0 ? "" : " ");
	for (iter = _map.rbegin(); iter != _map.rend(); ++iter) {
		static int mm = 0;
		printf("%d %.1lf", iter->first, iter->second);
		++mm;
		if (mm != _map.size()) {
			cout << " ";
		}
	}
	return 0;
}