HDU - 2110 Crisis of（思维 / 母函数）

思路：

记：
$sum = \sum_{i=1}^{n}p_i*m_i$
构造母函数：
$\Pi_{i=1}^{n}(\sum_{j=0}^{m_i}(p_i*x^{j*p_i}))$
展开之后，关于 $x$的多项式： $a_0+a_1*x+a_2*x^2+...+a_{sum}*x^{sum}$，其中的项 $x^{sum/3}$的系数对 $MOD$取模，即为答案。

注：封装多项式类，class不是很熟悉写的很慢。

代码：

// HDU - 2110.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
class Polynomial
{
private:
	vector<std::pair<int, int>> x;
public:
	Polynomial();
	Polynomial(int p, int m);
	Polynomial operator * (const Polynomial& r) const;
	void print() const;
	int query_first(int val);
};
Polynomial::Polynomial() {
	x.clear();
}
Polynomial::Polynomial(int p, int m) {
	x.clear();
	for (int i = 0; i <= m; i++) {
		x.push_back(make_pair(1, i * p));
	}
}
bool pair_cmp(const pair<int, int>& l, const pair<int, int>& r) {
	return l.second < r.second;
}
Polynomial Polynomial::operator * ( const Polynomial &other) const {
	Polynomial temp, ret;
	for (int i = 0; i < (int)this->x.size(); i++) {
		for (int j = 0; j < (int)other.x.size(); j++) {
			temp.x.push_back(make_pair(this->x[i].first * other.x[j].first, this->x[i].second + other.x[j].second));
		}
	}
	sort(temp.x.begin(), temp.x.end(), pair_cmp);
	for (int i = 0; i < (int)temp.x.size(); i++) {
		if (i == 0 || ret.x[ret.x.size() - 1].second != temp.x[i].second) {
			ret.x.push_back(make_pair(temp.x[i].first, temp.x[i].second));
		}
		else {
			ret.x[ret.x.size() - 1].first += temp.x[i].first;
		}
	}
	for (int i = 0; i < (int)ret.x.size(); i++) {
		ret.x[i].first = ret.x[i].first % 10000;
	}
	return ret;
}
void Polynomial::print()const {
	for (int i = 0; i < (int)this->x.size(); i++) {
		if (i != 0) {
			cout << " + ";
		}
		cout << x[i].first << "*X^" << x[i].second;
	}
	cout << endl;
}
int Polynomial::query_first(int val) {
	for (int i = 0; i < (int)this->x.size(); i++) {
		if (this->x[i].second == val) {
			return this->x[i].first;
		}
	}
	return -1;
}
int main()
{
	int n;
	while (cin >> n) {
		if (n == 0)break;
		Polynomial ans = Polynomial(1, 0), temp;
		int sum = 0;
		for (int i = 0; i < n; i++) {
			int val, num;
			cin >> val >> num;
			ans = ans * Polynomial(val, num);
			sum += num * val;
		}
		if (sum % 3 != 0) {
			cout << "sorry" << endl;
		}
		else {
			int m = ans.query_first(sum / 3);
			if (m == -1) {
				cout << "sorry" << endl;
			}
			else {
				cout << m << endl;
			}
		}

	}
}