Example Of Priority Queue Use Case 1 – Hospital Waiting Room ✓ Solved

Example of Priority Queue Use case 1 – hospital waiting room

One use (application) of a priority queue (PQ) could be the waiting queue in the hospital patient waiting room. It is common sense that patients should be treated based on their illness severity instead of the order they arrive. This hurt level can be assigned as the priority key value. We can organize all the patients in the waiting room into a priority queue, and more specifically, a binary heap. The most severely hurt patient is positioned at the front of the queue, which is the root of the queue with the highest priority key value.

When a new patient arrives, a key (priority) value is assigned to them, corresponding to the patient's hurt level. The higher the number, the more urgent the treatment required. The first patient is added to the queue at the root, and as more patients arrive, they are added to the heap. Once the binary heap has been created, all nodes that are not leaves must have a higher or equal key value than their children.

Patients will be treated starting from the highest key value to the lowest key value, which represents the Remove operation. For instance, when patient-16 is treated, it is removed from the queue. Following this, the next patient with the highest key value now occupies the front position (root) of the queue through specific operations that maintain the heap structure. If a new patient arrives and the queue is not full, they will be assigned a priority (hurt level) value and placed into the correct position in the queue. This process is known as the Add operation.

The Full operation indicates that the maximum number of patients has been reached, while the Empty operation occurs when all patients have been treated and no new patients are added.

Use case 2 – Dijkstra's algorithm

Dijkstra’s algorithm is designed to identify the shortest path from a starting node to a target node, creating a tree of shortest paths from the start to all other nodes within a graph. This algorithm applies a priority queue to assign distance values or efforts between different nodes, subsequently identifying the shortest path from the starting node to adjacent nodes while marking the closest vertex as the next to process.

Dijkstra’s algorithm operates by consistently tracking the distances from the starting point to its adjacent nodes, marking them appropriately. The shortest distance to any node is documented and used to update paths accordingly. The algorithm continues this process until the destination is reached. It employs priority queues by defining the distances between nodes as key values, where smaller distances yield higher priorities. As the shortest nodes are processed first, the structure of the priority queue is maintained as nodes with the highest key values are moved out for processing.

In summary, both use cases illustrate the implementation of a priority queue through practical scenarios; a hospital waiting room prioritizing patients based on their condition severity and Dijkstra's algorithm optimizing paths within a graph. The efficiency of these operations relies heavily on the underlying data structure, ensuring that high-priority elements are addressed promptly.

Conclusion

In conclusion, priority queues serve crucial roles in real-world applications, as exemplified through the use cases of hospital patient management and graph traversal algorithms. The binary heap is an effective underlying structure for such a queue, enabling fast processing for Add and Remove operations, thereby facilitating efficient prioritization based on the defined key values. Considering the demands of such applications, priority queues remain indispensable in optimizing performance and ensuring timely processing of critical elements.

References

• Abiy, T., Pang, H., & Wilkiams, C. (NA). Dijkstra’s Shortest Path Algorithm. Retrieved from [source]
• Barngrader. (2014, Nov 14). Dijkstra’s Algorithm: Another example. Retrieved from [source]
• Cha, S. (2018, June 29). E-mail with student.
• Cha, S. (2018, June). CISC610-50 Unit 5 class presentation. Retrieved from [source]
• Gunes, M. H. (2016). Chapter 17. Heaps. CS 302 – Data Structures Lecture Slide, University of Nevada, Reno.
• Iyappan. (2017, July 6). Dijkstra’s Rules – Graph: Dijkstra’s Algorithm with Animation (Shortest Path Search). Retrieved from [source]
• Laakso, M., Korhonen, A., & Karavirta, V. (2011, May 30). Priority Queues and Binary Heap - Delete Max. Department of Computer Science, Aalto University. Retrieved from [source]
• Lam, (2016). [details needed].
• Additional source 1: [details needed].
• Additional source 2: [details needed].