2. For the following questions select the operation that is "faster" based on its Big-O running time? Write A, B or C in your answer sheet in each case i. Deleting a value: A. Deleting a value at the head of a linked-list B. Deleting a value from a sorted array C. Both are equally fast ii. Searching for an element: A. Searching for an element in a balanced BST B. Searching for an element in a sorted array using binary search C. Both are equally fast iii. Finding the minimum element: A. Finding the minimum element in a min Heap B. Finding the minimum element in a sorted array where elements are stored in ascending order C. Both are equally fast iv. Finding the minimum element: A. Finding the minimum element in an unsorted array B. Finding the minimum element in a balanced BST C. Both are equally fast V. Searching for an element: A. Searching for an element in a sorted linked list B. Searching for an element in a balanced BST C. Both are equally fast

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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### Understanding Big-O Notation in Various Data Structures

#### For the following questions, select the operation that is “faster” based on its Big-O running time.
**Write A, B, or C in your answer sheet in each case.**

i. **Deleting a value:**

- **A.** Deleting a value at the head of a linked-list
- **B.** Deleting a value from a sorted array
- **C.** Both are equally fast

ii. **Searching for an element:**

- **A.** Searching for an element in a balanced BST
- **B.** Searching for an element in a sorted array using binary search
- **C.** Both are equally fast

iii. **Finding the minimum element:**

- **A.** Finding the minimum element in a min Heap
- **B.** Finding the minimum element in a sorted array where elements are stored in ascending order
- **C.** Both are equally fast

iv. **Finding the minimum element:**

- **A.** Finding the minimum element in an unsorted array
- **B.** Finding the minimum element in a balanced BST
- **C.** Both are equally fast

v. **Searching for an element:**

- **A.** Searching for an element in a sorted linked list
- **B.** Searching for an element in a balanced BST
- **C.** Both are equally fast

*Explanations:*

1. **Deleting a value:**
    - **Linked List:** Removing the head of a linked list is an O(1) operation, as it involves reassigning the head pointer.
    - **Sorted Array:** Deleting a value can be O(n) due to the need for shifting elements.
   
2. **Searching for an element:**
    - **Balanced BST (Binary Search Tree):** Searching is O(log n).
    - **Sorted Array with Binary Search:** Also O(log n).
  
3. **Finding the minimum element:**
    - **Min Heap:** The minimum element is always at the root, making it an O(1) operation.
    - **Sorted Array (ascending order):** The minimum element is the first element in the array, so it is O(1).
 
4. **Finding the minimum element:**
    - **Unsorted Array:** Finding the minimum requires scanning all elements, making it an
Transcribed Image Text:--- ### Understanding Big-O Notation in Various Data Structures #### For the following questions, select the operation that is “faster” based on its Big-O running time. **Write A, B, or C in your answer sheet in each case.** i. **Deleting a value:** - **A.** Deleting a value at the head of a linked-list - **B.** Deleting a value from a sorted array - **C.** Both are equally fast ii. **Searching for an element:** - **A.** Searching for an element in a balanced BST - **B.** Searching for an element in a sorted array using binary search - **C.** Both are equally fast iii. **Finding the minimum element:** - **A.** Finding the minimum element in a min Heap - **B.** Finding the minimum element in a sorted array where elements are stored in ascending order - **C.** Both are equally fast iv. **Finding the minimum element:** - **A.** Finding the minimum element in an unsorted array - **B.** Finding the minimum element in a balanced BST - **C.** Both are equally fast v. **Searching for an element:** - **A.** Searching for an element in a sorted linked list - **B.** Searching for an element in a balanced BST - **C.** Both are equally fast *Explanations:* 1. **Deleting a value:** - **Linked List:** Removing the head of a linked list is an O(1) operation, as it involves reassigning the head pointer. - **Sorted Array:** Deleting a value can be O(n) due to the need for shifting elements. 2. **Searching for an element:** - **Balanced BST (Binary Search Tree):** Searching is O(log n). - **Sorted Array with Binary Search:** Also O(log n). 3. **Finding the minimum element:** - **Min Heap:** The minimum element is always at the root, making it an O(1) operation. - **Sorted Array (ascending order):** The minimum element is the first element in the array, so it is O(1). 4. **Finding the minimum element:** - **Unsorted Array:** Finding the minimum requires scanning all elements, making it an
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