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Dynamically Allocating 2D Arrays in C++ using `new`

Dynamically allocating 2D arrays in C++ using the `new` operator involves a bit more complexity than allocating 1D arrays. This is because a 2D array is essentially an array of arrays. We need to manage memory for both the "outer" array (pointers to the "inner" arrays) and the "inner" arrays themselves (the actual data storage). There are several approaches, each with its own trade-offs regarding memory contiguity and access patterns.

This tutorial will cover the most common and recommended method, which involves allocating a contiguous block of memory for the entire 2D array, followed by creating an array of pointers to "fake" the 2D array structure. This offers good performance and is relatively easy to understand. We'll also touch upon alternative methods and discuss their pros and cons.

*Understanding the Problem*

Before diving into the code, let's understand the underlying concepts:

*Contiguous Memory:* Allocating memory in a contiguous block means that the elements are stored sequentially in memory. This is generally the most efficient way to store data, as it allows for faster access due to spatial locality.
*Pointers to Pointers:* In C++, a 2D array can be represented as an array of pointers, where each pointer points to a row of the array. `int** arr` declares a pointer to a pointer to an integer, which can be used to represent a 2D array.
*`new` operator:* The `new` operator is used to dynamically allocate memory from the heap. It returns a pointer to the allocated memory.
*`delete` operator:* The `delete` operator is used to free dynamically allocated memory. It's crucial to `delete` the memory allocated with `new` to prevent memory leaks.

*The Recommended Approach: Contiguous Memory Allocation with Pointer Array*

This approach allocates a single contiguous block of memory for the entire 2D array and then creates an array of pointers that point to the start of each row ...

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