1009. Product of Polynomials

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本文介绍了一种使用C++实现多项式乘法的方法。通过定义结构体表示多项式的项，并利用map来检查和累加相同指数的项，实现了两个多项式的相乘运算。此外，还提供了输入和输出多项式系数的函数。

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<vector>
#include<map>
#include<algorithm>
#include<functional>
using namespace std;
struct item {
	int index;
	double number;
	item(int _index = 0, double _number = 0) :index(_index), number(_number) {}
};
bool cmp(const item &a, const item &b) {
	return a.index < b.index;
}
vector<item> multiply(vector<item> &a, vector<item> &b);
void Scan(vector<item> &a);
void Print(const vector<item> &c);
int main() {
	freopen("D://input.txt", "r", stdin);
	vector<item> a, b, c;
	Scan(a);
	Scan(b);

	c = multiply(a, b);

	Print(c);
	return 0;
}
void Scan(vector<item> &a) {
	int sumTerm, i;
	cin >> sumTerm;
	a.resize(sumTerm);
	for (i = 0; i < sumTerm; i++)
		cin >> a[i].index >> a[i].number;
	return;
}
vector<item> multiply(vector<item> &a, vector<item> &b) {
	map<int, double, greater<int> > check;
	auto ait = a.begin();
	auto bit = b.begin();
	vector<item> ret;
	int _index;
	double _number;
	for (; ait != a.end(); ait++) {
		bit = b.begin();
		for (; bit != b.end(); bit++) {
			_index = ait->index + bit->index;
			_number = ait->number * bit->number;
			check[_index] += _number;
		}
	}
	auto checkit = check.begin();
	while (checkit != check.end()) {
		if (checkit->second != 0) {
			ret.push_back(item(checkit->first, checkit->second));
		}
		checkit++;
	}
	return ret;
}
void Print(const vector<item> &a) {
	int i;
	cout << a.size();
	for (i = 0; i < a.size(); i++)
		printf(" %d %.1lf", a[i].index, a[i].number);
	cout << endl;
	return;
}