#include <iostream>
#include <string>
using std::cout, std::string, std::endl;

class Integrate
{
protected:
    double a, b;
    int n;

public:
    virtual double fun(double x) = 0;
    Integrate(double _a, double _b, int _n = 10000) : a{_a}, b{_b}, n{_n} {}
    double integrate()
    {
        double result{(fun(a) + fun(b)) / 2};
        double h{(b - a) / n};
        for (int i{1}; i < n; i++)
            result += fun(a + i * h);
        result *= h;
        return result;
    }
};

class F1 : public Integrate
{
public:
    using Integrate::Integrate;
    double fun(double x) override
    {
        return x;
    }
};

class F2 : public Integrate
{
public:
    using Integrate::Integrate;
    double fun(double x) override
    {
        return x * x;
    }
};

class F3 : public Integrate
{
public:
    using Integrate::Integrate;
    double fun(double x) override
    {
        return x * x * x;
    }
};

int compare(Integrate &a, Integrate &b)
{
    // 比较两个积分对象值的结果，a大返回1，b大返回-1，相同返回0
    if (a.integrate() > b.integrate())
        return 1;
    if (a.integrate() < b.integrate())
        return -1;
    return 0;
}

int main()
{
    F1 f1{0, 1};
    F2 f2{0, 1};
    F3 f3{0, 1};
    cout << f1.integrate() << ' ' << f2.integrate() << ' ' << f3.integrate() << '\n';
    // 设计通用接口compare，积分类的任意派生对象可进行比较
    cout << compare(f1, f2) << '\n';
    cout << compare(f1, f3) << '\n';
    cout << compare(f2, f3) << '\n';
}