Develop a C++ program that manages a collection of rectangle objects. Each rectangle is defined by its width and height. Implement the solution using a class hierarchy where a base class Shape provides an interface for calculating the area, and a derived class Rectangle inherits from Shape and implements the area calculation. Store multiple rectangle objects in an array, compute the area for each, and determine which rectangle has the largest area. Display the index of the rectangle with the largest area.Class Structure and Implementation:Shape Class (Base Class):Attributes: None specific, mainly used for interface purposes.Member Functions:virtual double area() const = 0; Pure virtual function to compute the area of the shape.Rectangle Class (Derived Class):Inherits from Shape.Attributes:double width, height: Dimensions of the rectangle.Constructor:Rectangle(double w, double h): Initializes a rectangle with specified width and height.Member Functions:double area() const override: Computes and returns the area of the rectangle.Sample Input/Output Cases:Input:33 45 62 8Output:1

Sure, here is the C++ code for the problem:

#include <iostream>
#include <vector>
#include <algorithm>

// Base class
class Shape {
public:
    virtual double area() const = 0; // Pure virtual function
};

// Derived class
class Rectangle : public Shape {
private:
    double width, height;
public:
    // Constructor
    Rectangle(double w, double h) : width(w), height(h) {}

    // Overriding area() function
    double area() const override {
        return width * height;
    }
};

int main() {
    // Create a vector of Rectangle pointers
    std::vector<Rectangle*> rectangles;
    rectangles.push_back(new Rectangle(33, 45));
    rectangles.push_back(new Rectangle(62, 8));

    // Find the rectangle with the largest area
    int maxIndex = 0;
    double maxArea = rectangles[0]->area();
    for (int i = 1; i < rectangles.size(); i++) {
        double currentArea = rectangles[i]->area();
        if (currentArea > maxArea) {
            maxArea = currentArea;
            maxIndex = i;
        }
    }

    // Print the index of the rectangle with the largest area
    std::cout << "The rectangle with the largest area is at index: " << maxIndex << std::endl;

    // Clean up
    for (Rectangle* rectangle : rectangles) {
        delete rectangle;
    }

    return 0;
}

This program first creates a vector of Rectangle pointers and adds two rectangles to it. It then iterates over the vector to find the rectangle with the largest area, keeping track of the maximum area and the index of the rectangle with this area. Finally, it prints the index of the rectangle with the largest area and cleans up the dynamically allocated memory.