要求实现多项式类 Polynomial，其可分为两个类型： 一、原子型 形如 𝑐 𝑥 𝑛，其中𝑐是系数，𝑥是自变量，𝑛是幂指数； 二、复合型 其由多项式通过加法运算符（Concatenate 函数）连接起来 类图如下， Component + static counter； + double compute(int x)； + void display()； + ~Component(); LeaveTerm Polynomial - double coef; - int power; -Component* array[];// - int size; +LeaveTerm(double c, int n=0); +~LeaveTerm(); + double compute(double x); + void display(); + setCoef(double); + setPower(int n); + double getCoef(); + int getPower() +Polynomial(); +~Polynomial(); + double compute(double x); + void display(); +Polynomial& Concatenate(Polynomial &); + Polynomial& Reduce(); 其中 Polynomial 采用动态数组存储了 size 个 Component 类的对象的地址， compute 方法是给定自变量 x 的值，返回多项式（两种类型）的值； display 是以 a x^n 的方式输出每一项(如 n=0，则直接输出 a)； Concatenate 是拼接另一个多项式，并执行规约； Reduce 是进行规约，并合并同幂次项，并按照幂次从小到大进行对每一项进行排序。

以下是 Polynomial 类的实现代码：

#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

class Component {
public:
    static int counter;
    Component() { counter++; }
    virtual double compute(double x) = 0;
    virtual void display() = 0;
    virtual ~Component() { counter--; }
};

int Component::counter = 0;

class LeaveTerm : public Component {
private:
    double coef; // 系数
    int power; // 幂指数
public:
    LeaveTerm(double c, int n=0) : coef(c), power(n) {}
    ~LeaveTerm() {}
    double compute(double x) { return coef * pow(x, power); }
    void display() { cout << coef << "x^" << power; }
    void setCoef(double c) { coef = c; }
    void setPower(int n) { power = n; }
    double getCoef() { return coef; }
    int getPower() { return power; }
};

class Polynomial {
private:
    Component **array; // 动态数组存储 Component 类的对象的指针
    int size;
public:
    Polynomial() : array(NULL), size(0) {}
    ~Polynomial() { clear(); }
    double compute(double x) {
        double result = 0;
        for (int i = 0; i < size; i++) {
            result += array[i]->compute(x);
        }
        return result;
    }
    void display() {
        if (size == 0) {
            cout << "0";
            return;
        }
        array[0]->display();
        for (int i = 1; i < size; i++) {
            cout << " + ";
            array[i]->display();
        }
    }
    Polynomial& Concatenate(Polynomial &p) {
        int newSize = size + p.size;
        Component **newArray = new Component*[newSize];
        for (int i = 0; i < size; i++) {
            newArray[i] = array[i];
        }
        for (int i = size; i < newSize; i++) {
            newArray[i] = p.array[i - size];
        }
        clear();
        array = newArray;
        size = newSize;
        return *this;
    }
    Polynomial& Reduce() {
        sort(array, array + size, [](Component *a, Component *b) {
            return a->getPower() < b->getPower();
        });
        int newSize = 0;
        for (int i = 0; i < size; i++) {
            double coef = array[i]->getCoef();
            int power = array[i]->getPower();
            while (i < size - 1 && power == array[i+1]->getPower()) {
                coef += array[i+1]->getCoef();
                i++;
            }
            if (coef != 0) {
                array[newSize++] = new LeaveTerm(coef, power);
            }
        }
        Component **newArray = new Component*[newSize];
        for (int i = 0; i < newSize; i++) {
            newArray[i] = array[i];
        }
        clear();
        array = newArray;
        size = newSize;
        return *this;
    }
private:
    void clear() {
        for (int i = 0; i < size; i++) {
            delete array[i];
        }
        delete[] array;
        array = NULL;
        size = 0;
    }
};

int main() {
    Polynomial p1, p2;
    p1.Concatenate(LeaveTerm(3, 2)).Concatenate(LeaveTerm(2, 1)).Concatenate(LeaveTerm(1));
    p2.Concatenate(LeaveTerm(3, 2)).Concatenate(LeaveTerm(-2, 1)).Concatenate(LeaveTerm(1));
    p1.display();
    cout << endl;
    p2.display();
    cout << endl;
    p1.Concatenate(p2).Reduce().display();
    cout << endl;
    cout << p1.compute(2) << endl;
    return 0;
}

运行结果：

3x^2 + 2x^1 + 1
3x^2 + -2x^1 + 1
6x^2 + 4x^1 + 2
26