gen-define-a-priority-queue-and-give-one-short-worked-example-e191

Define a priority queue and give one short worked example.

# Priority Queue ## Definition A **priority queue** is an abstract data type where each element has an associated priority value. Elements are served based on their priority rather than their insertion order. The element with the highest (or lowest) priority is always removed first. **Key operations:** - **Insert/Enqueue**: Add an element with a priority - **Remove/Dequeue**: Remove and return the highest priority element - **Peek**: View the highest priority element without removing it ## Worked Example **Scenario:** Hospital Emergency Room (lower number = higher priority) ``` Operations: 1. Insert("Sprained ankle", priority=3) 2. Insert("Broken arm", priority=2) 3. Insert("Heart attack", priority=1) 4. Insert("Minor cut", priority=4) 5. Dequeue() → Returns "Heart attack" (priority 1) 6. Dequeue() → Returns "Broken arm" (priority 2) ``` **Visual representation after insertions:** ``` Priority Queue (min-heap): [Heart attack:1] ← front (highest priority) [Broken arm:2] [Sprained ankle:3] [Minor cut:4] ``` **After two dequeues:** ``` Priority Queue: [Sprained ankle:3] ← front [Minor cut:4] ``` Despite "Sprained ankle" being inserted first, "Heart attack" is treated first because it has the highest priority (lowest number).