Heaps and Priority Queues

Learning Objectives Define a Priority Queue as an abstract data type. Explain the two core properties of a binary heap: the shape property and the heap property. Differentiate between a Min-Heap and a Max-Heap. Manually perform an insertion operation on a Max-Heap, demonstrating the 'bubble-up' process. Manually perform an 'extract-max' operation on a Max-Heap, demonstrating the 'bubble-down' process. Identify real-world scenarios where a Priority Queue is the ideal data structure. Ever wonder how an emergency room decides which patient to see first, or how your computer's operating system picks the next task to run? 🏥 It's not always first-come, first-served! In this lesson, we'll explore the Priority Queue, a data structure th...

TermDefinitionExample Priority QueueAn abstract data type where each element has an associated 'priority'. Elements with higher priority are served before elements with lower priority, regardless of when they were added.A to-do list app where tasks can be marked as 'Urgent', 'High', 'Medium', or 'Low' priority. The 'Urgent' tasks are always shown at the top. HeapA specialized tree-based data structure that satisfies the 'heap property'. It's a common way to implement a Priority Queue.A family tree where every parent is older than their children would be a simple analogy for a Max-Heap. Binary HeapA heap where each node has at most two children. It must also be a 'complete' binary tree, meaning all levels...

Heap Insertion Algorithm (Bubble-Up) 1. Add the new element to the first available spot at the bottom of the tree. 2. Compare the new element with its parent. 3. If it's larger (in a Max-Heap) than its parent, swap them. 4. Repeat until the element is in the correct spot or it becomes the root. Use this algorithm to add a new item to a heap while maintaining the heap property. Heap Deletion Algorithm (Extract-Max & Bubble-Down) 1. Remove the root element (the max value). 2. Move the last element of the heap to the root position. 3. Compare the new root with its children. 4. Swap it with its larger child. 5. Repeat this 'bubble-down' process until the heap property is restored. Use this algorithm to get and remove the highest-priority item from a Max-Heap....