C++

好的，以下是C++的代码实现：

#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;

// 多项式结构体
struct Polynomial {
    vector<int> coefficient;  // 系数数组，从低次到高次排序
};

// 读取文件中的多项式
vector<Polynomial> readPolynomialsFromFile(const string& filename) {
    vector<Polynomial> polynomials;
    ifstream file(filename);
    if (file.is_open()) {
        string line;
        while (getline(file, line)) {
            Polynomial p;
            int coefficient;
            istringstream iss(line);
            while (iss >> coefficient) {
                p.coefficient.push_back(coefficient);
            }
            polynomials.push_back(p);
        }
        file.close();
    }
    return polynomials;
}

// 比较多项式的次数，用于排序
bool comparePolynomialDegree(const Polynomial& p1, const Polynomial& p2) {
    return p1.coefficient.size() < p2.coefficient.size();
}

// 将多项式按照次数升序排列并输出
void sortAndPrintPolynomials(const vector<Polynomial>& polynomials) {
    vector<Polynomial> sortedPolynomials = polynomials;
    sort(sortedPolynomials.begin(), sortedPolynomials.end(), comparePolynomialDegree);
    for (const auto& p : sortedPolynomials) {
        for (int i = 0; i < p.coefficient.size(); i++) {
            cout << p.coefficient[i] << "x^" << i << " + ";
        }
        cout << "0" << endl;
    }
}

// 将多项式按照次数升序排列并输出到文件
void sortAndWritePolynomialsToFile(const vector<Polynomial>& polynomials, const string& filename) {
    vector<Polynomial> sortedPolynomials = polynomials;
    sort(sortedPolynomials.begin(), sortedPolynomials.end(), comparePolynomialDegree);
    ofstream file(filename);
    if (file.is_open()) {
        for (const auto& p : sortedPolynomials) {
            for (int i = 0; i < p.coefficient.size(); i++) {
                file << p.coefficient[i] << "x^" << i << " + ";
            }
            file << "0" << endl;
        }
        file.close();
    }
}

int main() {
    string filename = "polynomials.txt";
    vector<Polynomial> polynomials = readPolynomialsFromFile(filename);
    sortAndPrintPolynomials(polynomials);
    sortAndWritePolynomialsToFile(polynomials, "sorted_polynomials.txt");
    return 0;
}

这里假设文件中每个多项式单独一行，每个多项式的项数和系数用空格隔开。程序首先读取文件中的多项式，然后按照次数升序排列并输出到屏幕和文件。在输出时，程序按照 $ax^b + cx^d + ...$ 的格式输出每个多项式。