Please use C++ for this program.

Please read the problem and follow the instruction in main.cpp for this program.

Problem:
 - Design an abstract class called Shape:
   - Private variables double x and y, this is x and y position in postscript file
   - Constructor shape (x, y) that assign x and y values
   - function area take no parameters return double const equal zero, pure virtual function
   - function draw take ostream file return void and equal zero, pure virtual function
   - make deconstruct ~Shape
   - Hint: you need to use virtualthe question is okay plz
 - Design class Circle that inherit class shape functions
   - private variable x, y, radius
   - Make the following functions:
     - Circle constructor that take x, y, radius, Note that x and y are assigned to Shape(x,y)
       - for example constructor_name(double x, double y) : Shape(x,y)
     - draw that take ostream file to write postscript instruction the function return void
     - area take no parameters and return double area of the circle
     - ~Circle deconstruction
 - Design class Rect that inherit class shape with same functions as class Circle
   - private variables are x, y, weight, height
 - Design class FilledRect that inherit class shape with same functions as class Circle
   - private variables are x, y, weight, height
 - Hint for Circle, Rect, and FilledRect: you will need to use override keyword
   - e.g.: data_return_type function_name(inputs) override {}
 - Design class Drawing that take all shapes created and save it in vectors. Then use draw function for each Shape to write test.ps file with postscripts instructions
   - it has private variables of type: ofstream and vector
   - Drawing constructor that take location to open and create new "test.ps" file and write postscript line in it
   - void add function that push_back new shapes to vector. It takes "Polymorphism" shape
   - void draw function take no parameter that loop through all shapes and write postscript instruction for each shape
   - void showArea take no parameters and loop inside vector to run area function for each shape class
   - void setrgb function take three double for red, green, and blue. It writes postscript to change the color for all shapes
   - All postscript line to draw shapes are given in main.cpp comments
 
## Postscript language
 Check Wiki. for some background about Postscript (https://en.wikipedia.org/wiki/PostScript) \
 You can use online website to view .ps file (https://products.aspose.app/page/viewer/ps) \
 Postscript line you need to use to draw shapes are given in the code.

 

main.cpp:

#include     #include     #include         using namespace std;            // -------------- Design Shape class here ---------------    // -----------------------------------------------------------    // Shape abstract class with private double variable x and y that indicate shape position    // make the following functions    //  1. Constructor shape (x, y)    //  2. function area take no parameters return double const equal zero - pure virtual function    //  3. function draw take ostream file return void  equal zero - pure virtual function    //  4. make deconstruct ~Shape            // -------------- Design your Circle class here ---------------    // -----------------------------------------------------------    // Class Circle inherit Class Shape    // private variable x, y, radius    // Make the following functions:    // Circle constructor that take x, y, radius, Note that x and y are assigned to Shape(x,y)    //  for example constructor_name(double x, double y) : Shape(x,y)    // draw that take ostream file to write postscript instruction the function return void    //   postscript:    //    x y radius  0  360  arc \n    // stroke \n    // area take no parameters and return double    // ~Circle deconstruction            // -------------- Design your Rect class here ---------------    // -----------------------------------------------------------    // Class Rect inherit Class Shape    // private variable x, y, width, and height    // Make the following functions:    // Rect constructor that take x, y,  width,  height    // draw that take ostream file to write postscript instruction the function return void    // draw that take ostream file to write postscript instruction the function return void    //   postscript:    //    x y moveto \n    //    x+w y lineto \n    //    x+w y+h lineto \n    //    x y+h lineto \n    //    closepath \n    //    stroke \n    // area take no parameters and return double    // ~Rect deconstruction            // -------------- Design your FilledRect class here ---------------    // -----------------------------------------------------------    // Class FilledRect inherit Class Shape    // private variable x, y, width, and height    // Make the following functions:    // FilledRect constructor that take x, y,  width,  height    // draw that take ostream file to write postscript instruction the function return void    //   postscript:    //    x y moveto \n    //    x+w y lineto \n    //    x+w y+h lineto \n    //    x y+h lineto \n    //    closepath \n    //    fill \n    // area take no parameters and return double    // ~FilledRect deconstruction            // -------------- Design your Drawing class here ---------------    // -----------------------------------------------------------    // private variables ofstream and vector    // Make the following functions:    // Drawing constructor as following (is given):    //  Drawing(string filename) : f(filename.c_str()), shapes() {} // where f is ofstream    // void add that take shape and push_back to vector    // void draw take no parameters and loop inside vector to rum draw function for each shape class    // void showArea take no parameters and loop inside vector to run area function for each shape class    // void setrgb take three double for red, green, and blue and write postscript line to change color    //   postscript:    //    r_value g_value b_value setrgbcolor \n            int main() {        cout << "########" << endl;        cout << "Main Problem" << endl;        cout << "########" << endl;            // set path to create .ps file to write postscript instructions        Drawing d("Write_full_path/test.ps");        // set color        d.setrgb(1,0,0); // set drawing color to be bright red:  1 0 0 setrgbcolor        // add FilledRect        d.add(new FilledRect(100.0, 550.0, 200.0, 50)); // x y moveto x y lineto ... fill        // add Rect        d.add(new Rect(200.0, 650.0, 200.0, 50));       // x y moveto x y lineto ... stroke        // add Circle        d.add(new Circle(300,300, 100)); // centered in 300 , 300 pixel with radius        // draw all shapes added to d        d.draw();        // print out all shapes area        d.showArea();            cout << "====[ end ]====" << endl;        cout << "               " << endl;            return 0;    }    State the conditions for a relation to be a partial order. 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Explain how each oddity    you identify is either something that would prevent the program from compiling,    something that would cause it to stop abruptly reporting failure at runtime, a    reason why the program might not do anything sensible or just a stylistic oddity.    //* A comment to start with: Exam:2000 */    public Class mycode.java    {    void static public fun main(String [junk])    begin    Leaf tr = null;    for (i=1; i>10; ++i) tr = new Node(i, tr)    tr.print();    end;    }    class Leaf    {    integer value;    Leaf(int value)    { this = value; }    public void print()    { System.out.println(value); }    }    class Node extends Leaf    {    Leaf left, right;    Node(leaf l, Leaf r)    { left = l, right = r;    }    void print()    { left.print();    System.out.println("val=" @ value);    right.print();    }    }    [10 marks]    3 [TURN OVER    CST.2000.1.4    SECTION B    5 Foundations of Computer Science    State the time complexity of the lookup and update operations for each of the    following:    (a) association lists    (b) binary search trees    (c) functional arrays (implemented as binary trees)    Use O-notation and include both the average-case and worst-case complexity.    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I need help implementing the following public methods in the header file, language is c++:        (Hashtable.h)        #ifndef ORDEREDLINKEDLIST_H    #define ORDEREDLINKEDLIST_H    #include         class Hashtable    {      private:         int hash(int v) const;    public:    Hashtable(); //Constructs and empty hash table with a default capacity of 17 and a default load factor threshold of .65    Hashtable(int size); //Constructs and empty hash table with the given capacity and a default load factor threshold of .65    Hashtable(int, double); //Constructs and empty hash table with the given capacity and load factor threshold values    Hashtable(const Hashtable& other); //creates a deep-copy of the given hashtable    Hashtable& operator=(const Hashtable& other); //replaces the current hashtable with a deep-copy of the given hash table    ~Hashtable(); //cleans up all allocated memory of the hashtable               int size() const; //returns the number of items currently in the hashtable           int capacity() const; //returns the capacity of the hashtable (i.e. the size of the array)           double getLoadFactorThreshold() const; //returns the load factor threshold used to determine when to resize the hashtable.           bool empty() const; //returns true if the table is empty or false otherwise    void insert(const int); //Inserts the given value into the hashtable. Automatically resizes the table as necessary.           void remove(int); //Removes the given value from the hashtable. If the value is not present it takes no action and throws no errors.           bool contains(int) const; //Returns true if the given value is contained in the hashtable or false if the value is not in the hashtable.           int indexOf(int) const; //Returns the index of the given value.           // If the value is not in the hashtable, returns -1. This is not a normal mehtod for a hashtable and is here solely to test that your hashtable does quadratic probing.           void clear(); //Removes all values from the hashtable, resetting it to an empty state           static bool isPrime(int n); //Returns true if the value is a prime number.            //One way to implement this method is to check if the number is divisible by 2-sqrt(n).           // If it is then it is not prime. If it is not then it is prime. 2 and 3 must be tested separately.           static int nextPrime(int n); //Returns the next prime number greater than or equal to n           //One way to implement this method is to test if n is prime and then repeatedly increment n and test again if it is prime.    };    #endif    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////                 (Hashtable.cpp)        #include "Hashtable.h"        int Hashtable::hash(int v) const{      return v % capacity();    }        Hashtable::Hashtable()    {    }        Hashtable::Hashtable(int capacity)    {    }        Hashtable::Hashtable(int capacity, double threshold)    {    }        Hashtable::Hashtable(const Hashtable& other)    {    }        Hashtable& Hashtable::operator=(const Hashtable& other)    {    return *this;    }        Hashtable::~Hashtable()    {    }        int Hashtable::size() const    {    return -1;    }        int Hashtable::capacity() const    {    return -1;    }    double Hashtable::getLoadFactorThreshold() const    {      return 0;    }        bool Hashtable::empty() const    {    return -1;    }        void Hashtable::insert(int value)    {    }        void Hashtable::remove(int value)    {    }        bool Hashtable::contains(int value) const{    return false;    }        int Hashtable::indexOf(int) const    {      return -2;    }        void Hashtable::clear()