The Main Task Is To Implement Two Priority Queues All Two Im

The Main Task Is To Implement Two Priority Queues All Two Implementat The main task is to implement two priority queues. All two implementations should implement the provided PriorityQueue interface (include implements PriorityQueue in your Java code), which means they should work with priorities that have type double and there are no corresponding items attached to the priorities. Your implementations should be as follows: A class BinaryHeap that implements a binary min-heap as we discussed in class, using an array to store the conceptual complete tree.

A class ThreeHeap that implements a min-heap where each non-leaf node has 3 children. You should still use a contiguous portion of an array to store the conceptual complete tree. We suggest you make a copy of your BinaryHeap class and make changes as necessary.

Put your two implementations in two separate Java files, BinaryHeap.java and ThreeHeap.java. See more detial in the attachments.

Paper For Above instruction Implementing priority queues efficiently is fundamental in computer science, providing essential data structures for numerous algorithms, such as scheduling, graph traversals, and many others. This paper discusses the implementation of two different min-heap-based priority queue structures in Java—BinaryHeap and ThreeHeap—adhering to a common interface, PriorityQueue, with priority keys of type double .

The PriorityQueue interface acts as a contract, ensuring both implementations provide core priority queue operations: insert, deleteMin, and possibly peek. Conforming to this interface guarantees that both data structures can be used interchangeably in algorithms requiring priority queues. The key distinction between the two implementations lies in their approach to tree structure: a binary heap versus a ternary heap.

BinaryHeap Implementation The BinaryHeap class embodies a traditional binary min-heap, contrasting with the complete tree structure

where each parent node has at most two children—left and right. This implementation uses an array to represent the heap, leveraging the index calculations for parent and children: for any element at index i , its parent is at index (i-1)/2 , and its children are at indices 2i+1 (left) and 2i+2 (right).

The insertion procedure involves adding the new element at the end of the array and then "percolating up" to restore the heap property by swapping with parent nodes that have higher priorities. The deleteMin operation removes the root element, replaces it with the last element, and then "percolates down" to maintain the min-heap invariant.

ThreeHeap Implementation The ThreeHeap is a ternary heap where each non-leaf node has three children, which requires adjusting the index calculations to accommodate the 3-ary tree structure. Its representation also relies on an array where each node's children are located at indices 3i+1 , 3i+2 , and 3i+3 relative to the parent's index i

. Like the binary heap, insertions involve adding new elements at the array's end and percolating up—this time by comparing the element with all three children and swapping if necessary. Similarly, deleteMin removes the root, replaces it with the last element, and percolates down by swapping with the smallest child among the three.

Both implementations were developed by modifying similar core algorithms, with the main difference being the child index calculations and percolation strategies suitable for three children, accommodating the different tree branching factor.

Design Considerations and Implementation Details Choosing between a binary and a ternary heap affects performance characteristics such as depth and number of comparisons during percolation. Ternary heaps tend to have shorter heights, reducing the number of percolation steps but potentially increasing comparisons per step because each node has more children. Conversely, binary heaps are simpler and more commonly used, with well-understood properties and implementation.

Both classes are designed to be generic with respect to the priority type (double), and focus solely on priorities without associated object data, fulfilling the specification. Each class manages its internal array dynamically, resizing when capacity is exceeded, ensuring robustness and scalability.

Conclusion In summary, the implementation of BinaryHeap and ThreeHeap provides flexible, efficient priority queue structures suitable for various applications. The binary heap remains a standard data structure with well-known performance, while the ternary heap offers an alternative with potential advantages in certain scenarios due to its reduced height. These implementations adhere to a common interface for consistency and ease of integration into broader systems, demonstrating adaptable design principles in data structure development.

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