For this programming project from Chapter $23$ of the Liang textbook, I implemented a heap using a generic class $`$Heap$`.$ This heap supports adding elements, removing the root, cloning, and equality checking.

Key Features of the Program:

$1.$ Heap Construction: The program constructs a heap from an array of strings. The heap is a binary heap where the root is the maximum element, as it follows a max$-$heap ordering property.

$2.$ Cloning: The $`$clone$()`$ method ensures that when a heap is cloned, the list inside the heap is deep copied, preventing shared references between the original and the cloned heap.

$3.$ Equality Check: The $`$equals$()`$ method checks if two heaps are equal by comparing the list of elements inside them.

$4.$ Heap Operations:

$-$ Add Operation: When a new object is added to the heap, it is appended to the end of the list and then "bubbled up$"$ to maintain the max$-$heap property.

$-$ Remove Operation: The root of the heap is removed, and the last element is placed at the root and "bubbled down" to maintain the heap structure.

Issues Encountered:

$1.$ Clone Implementation: Initially, I implemented a shallow copy of the heap using the default $`$clone$()`$ method. However, I quickly realized that this led to issues with shared references between the original and cloned heaps. Changing the internal list in one heap also affected the other. To fix this, I deep$-$copied the internal list of the heap to ensure that both the original and cloned heaps maintain independent states.

Solution: I modified the $`$clone$()`$ method to perform a deep copy of the internal $`$ArrayList$`.$

$2.$ Type Casting in Clone and Comparison: Since the heap is a generic class, casting from $`$Object$`$ in the $`$clone$()`$ and $`$equals$()`$ methods required careful handling of type parameters. It was important to ensure type safety while casting and comparing the lists. This was addressed by using wildcard $`?`$ in the $`$equals$()`$ method and ensuring safe casting in the $`$clone$()`$ method.

Lessons Learned:

$1.$ Deep vs$.$ Shallow Copy: This project highlighted the importance of understanding the difference between shallow and deep copies, especially when cloning objects. It is essential to deep copy any mutable fields $($like lists$)$ to avoid unintended side effects when modifying cloned objects.

$2.$ Comparator Usage in Generics: Managing generic types with comparators can be tricky, but crucial for ensuring proper ordering in a heap. I learned how to define comparators for generic types and apply them within the heap to maintain the max$-$heap property.

$3.$ Testing Equality for Complex Structures: I learned that when implementing equality checks $(`$equals$()`),$ it$$s necessary to compare not just the content, but also the structure of the objects. For the heap, I had to ensure that the underlying list is identical for the heaps to be considered equal.

do you agree with this statement and why?