Data Structure Operations Data Structure Time Complexity Average Access Search 0(1) Array Stack o(n) Singly-Linked List (n) Doubly-Linked List (n) Skip List 0(log(n)) Hash Table Binary Search Tree Cartesian Tree B-Tree Red-Black Tree Splay Tree AVL Tree o(n) B o(n) o(n) 0(log(n)) E 0(1) O(log(n)) 0(log(n)) 0(log(n)) O(log(n)) O(log(n)) Insertion O(A) 0(1) 0(1) 0(1) 0(log(n)) 0(1) Deletion o(n) 0(1) 0(1) C O(log(n)) 0(1) Worst Access A o(n) D 0(log(n)) 0(log(n)) O(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) 0(log(n)) O(log(n)) 0(log(n)) O(log(n)) F O(n) ILL o(n) O(n) O(log(n)) o(n) Search O(n) O(n) O(n) O(n) o(a) O(n) O(n) Insertion Deletion o(n) o(n) 0(1) 0(1) O(n) 0(1) 0(1) O(n) O(n) O(n) 0(1) 0(1) O(n) O(n) O(n) Space Complexity Worst O(n) O(n) o(n) O(n) O(n) 0(log(n)) 0(log(n))] 0(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n) O(log(n)) O(log(n)) O(log(n)) O(n) O(n) 0(log(n)) O(log(n)) 0(log(n)) 0(log(n)) O(n) O(n) O(n) O(A) On log(n)) O(n)

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
Problem 1PE
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### Activity: Understanding Big O Notation

**Instruction**: Fill in the missing fields for Big O notation for operations A through F.

- **A -** 
- **B -**
- **C -**
- **D -**
- **E -**
- **F -**

This activity is designed to help students practice and understand Big O notation, which is essential for analyzing the time complexity of algorithms. Consider typical algorithm complexities such as O(1), O(n), O(log n), O(n^2), etc., to complete the exercise.
Transcribed Image Text:### Activity: Understanding Big O Notation **Instruction**: Fill in the missing fields for Big O notation for operations A through F. - **A -** - **B -** - **C -** - **D -** - **E -** - **F -** This activity is designed to help students practice and understand Big O notation, which is essential for analyzing the time complexity of algorithms. Consider typical algorithm complexities such as O(1), O(n), O(log n), O(n^2), etc., to complete the exercise.
# Data Structure Operations

This table outlines the time and space complexities for various operations in different data structures. It is divided into categories such as average and worst time complexity for operations like access, search, insertion, and deletion. Space complexity in the worst-case scenario is also included.

### Table Structure:

- First column lists various data structures.
- Subsequent columns provide time complexity for each operation under average and worst conditions.
- The last column shows the worst-case space complexity.

### Data Structure and Complexity:

1. **Array**  
   - Average: Access: O(1), Search: O(n), Insertion: O(n), Deletion: O(n)
   - Worst: Access: O(1), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n)

2. **Stack**
   - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n)

3. **Singly-Linked List**
   - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n)

4. **Doubly-Linked List**
   - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n)

5. **Skip List**
   - Average: Access: O(log(n)), Search: O(log(n)), Insertion: O(log(n)), Deletion: O(log(n))
   - Worst: Access: O(n), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n log(n))

6. **Hash Table**
   - Average: Access: N/A, Search: O(1), Insertion: O(1), Deletion: O(1)
   - Worst: Access: N/A, Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n)

7. **Binary Search Tree**
   - Average: Access: O(log(n)), Search: O(log(n)), Insertion: O(log(n)), Deletion: O(log(n))
   - Worst: Access: O(n), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n)

8.
Transcribed Image Text:# Data Structure Operations This table outlines the time and space complexities for various operations in different data structures. It is divided into categories such as average and worst time complexity for operations like access, search, insertion, and deletion. Space complexity in the worst-case scenario is also included. ### Table Structure: - First column lists various data structures. - Subsequent columns provide time complexity for each operation under average and worst conditions. - The last column shows the worst-case space complexity. ### Data Structure and Complexity: 1. **Array** - Average: Access: O(1), Search: O(n), Insertion: O(n), Deletion: O(n) - Worst: Access: O(1), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n) 2. **Stack** - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n) 3. **Singly-Linked List** - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n) 4. **Doubly-Linked List** - Average & Worst: Access: O(n), Search: O(n), Insertion: O(1), Deletion: O(1), Space: O(n) 5. **Skip List** - Average: Access: O(log(n)), Search: O(log(n)), Insertion: O(log(n)), Deletion: O(log(n)) - Worst: Access: O(n), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n log(n)) 6. **Hash Table** - Average: Access: N/A, Search: O(1), Insertion: O(1), Deletion: O(1) - Worst: Access: N/A, Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n) 7. **Binary Search Tree** - Average: Access: O(log(n)), Search: O(log(n)), Insertion: O(log(n)), Deletion: O(log(n)) - Worst: Access: O(n), Search: O(n), Insertion: O(n), Deletion: O(n), Space: O(n) 8.
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