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Given the array: 61 58 96 49 30 60 11 Heapify into a max-heap. Ex: 86, 75, 30

Given the array: 61 58 96 49 30 60 11 Heapify into a max-heap. Ex: 86, 75, 30

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Given the array: 61 58 96 49 30 60 11 Heapify into a max-heap. Ex: 86, 75, 30
Transcribed Image Text:Given the array: 61 58 96 49 30 60 11 Heapify into a max-heap. Ex: 86, 75, 30
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--- **Queue Operations Exercise** **Introduction:** This exercise involves operations on a priority queue named `numPQueue` with initial values: 20, 33, 78. **Task 1: Peek Operation** - **Question:** What does `Peek(numPQueue)` return? - **Input Box:** Ex: 100 **Task 2: Sequence of Operations** Perform the following operations on `numPQueue`: 1. `Enqueue(numPQueue, 34)` 2. `Dequeue(numPQueue)` 3. `Peek(numPQueue)` 4. `Enqueue(numPQueue, 22)` - **Question:** What is the current state of `numPQueue`? - **Input Box:** Ex: 1, 2, 3 - **Question:** What does `GetLength(numPQueue)` return? - **Input Box:** Ex: 1 **Navigation:** - **Buttons:** `Check`, `Next` - **Progress Bar:** Displays 5 steps, currently on step 3. **Note:** This exercise provides an understanding of queue operations through an interactive interface. Make use of the input fields to submit your answers, and navigate using the buttons provided. ---
Transcribed Image Text:--- **Queue Operations Exercise** **Introduction:** This exercise involves operations on a priority queue named `numPQueue` with initial values: 20, 33, 78. **Task 1: Peek Operation** - **Question:** What does `Peek(numPQueue)` return? - **Input Box:** Ex: 100 **Task 2: Sequence of Operations** Perform the following operations on `numPQueue`: 1. `Enqueue(numPQueue, 34)` 2. `Dequeue(numPQueue)` 3. `Peek(numPQueue)` 4. `Enqueue(numPQueue, 22)` - **Question:** What is the current state of `numPQueue`? - **Input Box:** Ex: 1, 2, 3 - **Question:** What does `GetLength(numPQueue)` return? - **Input Box:** Ex: 1 **Navigation:** - **Buttons:** `Check`, `Next` - **Progress Bar:** Displays 5 steps, currently on step 3. **Note:** This exercise provides an understanding of queue operations through an interactive interface. Make use of the input fields to submit your answers, and navigate using the buttons provided. ---
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Follow-up Question
The task is to transform the given array into a max-heap. **Given the array:** \[63, 53, 86, 35, 99, 34, 75\] **Objective:** Heapify this array into a max-heap. **Example:** \[86, 75, 30\] ### Explanation of Process: - A max-heap is a binary tree where the parent node is always greater than or equal to its child nodes. - Rearrange the elements of the array to ensure the largest value is at the top of the heap (the first position of the array) and maintain the property throughout the structure. ### Steps to Heapify: 1. Start with the last non-leaf node and work upwards to the root node. 2. For each node, ensure it satisfies the max-heap property: - If a node is smaller than its children, swap it with the largest child. - Continue this process recursively for the swapped child. This transformation helps in efficiently organizing the data for operations such as sorting or priority queue management.
Transcribed Image Text:The task is to transform the given array into a max-heap. **Given the array:** \[63, 53, 86, 35, 99, 34, 75\] **Objective:** Heapify this array into a max-heap. **Example:** \[86, 75, 30\] ### Explanation of Process: - A max-heap is a binary tree where the parent node is always greater than or equal to its child nodes. - Rearrange the elements of the array to ensure the largest value is at the top of the heap (the first position of the array) and maintain the property throughout the structure. ### Steps to Heapify: 1. Start with the last non-leaf node and work upwards to the root node. 2. For each node, ensure it satisfies the max-heap property: - If a node is smaller than its children, swap it with the largest child. - Continue this process recursively for the swapped child. This transformation helps in efficiently organizing the data for operations such as sorting or priority queue management.
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