分别为正方形、 矩形、三角形构建类Square、Rectangle、Triangle，分别包含各自的边长，用doulble 型数据表示。每个类都至少包含4个西数成员，函数init用于设置图形的边长，函数perimeter用来计算图形的周长，函数area用来计算图形的面积，函数show用于显示图形的类别（方形、矩形或三角形）、周长和面积。编程分别显示一个方形、一个短形、一个三角形的周长和面积。思考并回答，能否将3个类合并成一个类，如果能，怎么做？如果不能，为什么？

以下是实现三个类的代码：

#include <iostream>
#include <cmath>

using namespace std;

class Square {
private:
    double side;
public:
    void init(double s) {
        side = s;
    }

    double perimeter() {
        return 4 * side;
    }

    double area() {
        return side * side;
    }

    void show() {
        cout << "Shape: Square" << endl;
        cout << "Perimeter: " << perimeter() << endl;
        cout << "Area: " << area() << endl;
    }
};

class Rectangle {
private:
    double length;
    double width;
public:
    void init(double l, double w) {
        length = l;
        width = w;
    }

    double perimeter() {
        return 2 * (length + width);
    }

    double area() {
        return length * width;
    }

    void show() {
        cout << "Shape: Rectangle" << endl;
        cout << "Perimeter: " << perimeter() << endl;
        cout << "Area: " << area() << endl;
    }
};

class Triangle {
private:
    double a;
    double b;
    double c;
public:
    void init(double x, double y, double z) {
        a = x;
        b = y;
        c = z;
    }

    double perimeter() {
        return a + b + c;
    }

    double area() {
        double p = perimeter() / 2;
        return sqrt(p * (p - a) * (p - b) * (p - c));
    }

    void show() {
        cout << "Shape: Triangle" << endl;
        cout << "Perimeter: " << perimeter() << endl;
        cout << "Area: " << area() << endl;
    }
};

int main() {
    Square s;
    s.init(5);
    s.show();

    Rectangle r;
    r.init(3, 4);
    r.show();

    Triangle t;
    t.init(3, 4, 5);
    t.show();

    return 0;
}

输出结果：

Shape: Square
Perimeter: 20
Area: 25
Shape: Rectangle
Perimeter: 14
Area: 12
Shape: Triangle
Perimeter: 12
Area: 6

可以将三个类合并成一个类，因为它们都具有计算周长和面积的方法，并且都是二维图形。我们可以将图形的类型作为类的一个成员变量，通过不同的初始化方法来设置不同的图形类型和边长。以下是合并后的代码：

#include <iostream>
#include <cmath>

using namespace std;

class Shape {
private:
    int type; // 0: Square, 1: Rectangle, 2: Triangle
    double a, b, c;
public:
    void initSquare(double s) {
        type = 0;
        a = b = c = s;
    }

    void initRectangle(double l, double w) {
        type = 1;
        a = b = l;
        c = w;
    }

    void initTriangle(double x, double y, double z) {
        type = 2;
        a = x;
        b = y;
        c = z;
    }

    double perimeter() {
        switch(type) {
            case 0:
                return 4 * a;
            case 1:
                return 2 * (a + c);
            case 2:
                return a + b + c;
        }
    }

    double area() {
        switch(type) {
            case 0:
                return a * a;
            case 1:
                return a * c;
            case 2: {
                double p = perimeter() / 2;
                return sqrt(p * (p - a) * (p - b) * (p - c));
            }
        }
    }

    void show() {
        switch(type) {
            case 0:
                cout << "Shape: Square" << endl;
                break;
            case 1:
                cout << "Shape: Rectangle" << endl;
                break;
            case 2:
                cout << "Shape: Triangle" << endl;
                break;
        }
        cout << "Perimeter: " << perimeter() << endl;
        cout << "Area: " << area() << endl;
    }
};

int main() {
    Shape s, r, t;
    s.initSquare(5);
    s.show();

    r.initRectangle(3, 4);
    r.show();

    t.initTriangle(3, 4, 5);
    t.show();

    return 0;
}

输出结果和之前相同，但代码更简洁。