Part 2: Heap vs. Stack Allocation Trade-offs 1. Provide two modes for the Vector: 。 Heap Mode: Default mode where the data array is allocated on the heap. Stack Mode: If the Vector size is small (e.g., fewer than 10 elements), use a fixed-size array allocated on the stack instead of the heap. Use conditional compilation or a template-based design for this. Compare the performance of both modes in terms of memory access speed and overhead. Part 3: Testing and Benchmarks 1. Write a test suite that: 。 Initializes vectors with various sizes. 。 Demonstrates the use of copy and move constructors in operations like Vector v = anotherVector;. о Times operations like push_back and resize for both heap and stack modes. 。 Tests edge cases, e.g., exceeding stack allocation limits or repeatedly resizing. 2. Benchmark and analyze: 。 Heap vs. stack performance: Measure how each mode affects allocation and deallocation times. 。The cost of unnecessary copying if move semantics are not used. Bonus Challenges: 1. Short String Optimization (SSO): Implement a small buffer optimization similar to how std::string works, storing a small number of elements directly within the Vector object to reduce heap allocations. 2. Iterator Support: Add support for iterators so the custom Vector can be used in range-based for loops. 3. Exception Safety: Ensure strong exception safety during reallocation (use the copy- and-swap idiom for the copy assignment operator). Deliverables: Source Code: Well-documented Vector class with all requested features. Test Cases: Demonstrations of the Big Five in action and performance comparisons. Report: A short analysis of the heap vs. stack trade-offs observed during the benchmarks. Objective: 1. Implement a custom Vector class in C++ that manages dynamic memory efficiently. 2. Demonstrate an understanding of the Big Five by managing deep copies, move semantics, and resource cleanup. 3. Explore the performance trade-offs between heap and stack allocation. Task Description: Part 1: Custom Vector Implementation 1. Create a Vector class that manages a dynamically allocated array. 。 Member Variables: ° T✶ data; // Dynamically allocated array for storage. std::size_t size; // Number of elements currently in the vector. std::size_t capacity; // Maximum number of elements before reallocation is required. 2. Implement the following core member functions: Default Constructor: Initialize an empty vector with no allocated storage. 。 Destructor: Free any dynamically allocated memory. 。 Copy Constructor: Perform a deep copy of the data array. 。 Copy Assignment Operator: Free existing resources and perform a deep copy. Move Constructor: Transfer ownership of the data array without copying. 。 Move Assignment Operator: Release existing resources and take ownership. A push_back method to add elements dynamically, resizing the array if needed. 。 operator[]: Provide access to elements by index with bounds checking for safety. 。size Method: Return the current number of elements in the vector. Method signatures: // Default Constructor Vector(); // Destructor ~Vector (); // Copy Constructor Vector (const Vector& other); // Copy Assignment Operator Vector & operator (const Vectors other); // Move Constructor Vector (Vector&& other) noexcept; // Move Assignment Operator Vector & operator= (Vector&& other) noexcept; // Push an element to the vector void push_back(const T& value); // Access elements by index (non-const) T& operator [] (std::size_t index); // Access elements by index (const) const T& operator[] (std::size_t index) const; // Get the current size of the vector std::size_t size() const; // Optional: Get the capacity of the vector std::size_t capacity() const; 3. Efficiency Requirements: Use exponential growth for capacity (e.g., double the capacity when resizing). Use a strategy that minimizes the number of heap allocations.

(For thought) a. What’s an advantage of namespaces? b. What’s a possible disadvantage of namespaces?

(General math) a. Construct a class named Cartesian containing two double-precision data members named x and y, which will be used to store the x and y values of a point in rectangular coordinates. The member functions should include a constructor that initializes an object’s x and y values to 0 and functions to input and display an object’s x and y values. Additionally, include an assignment function that performs a memberwise assignment between two Cartesian objects. b. Include the class written for Exercise 2a in a working C++ program that creates and displays the values of two Cartesian objects; the second object is assigned the values of the first object.