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The graph below shows different function growth complexities (Big-O orders). Label each line with the appropriate Big-O growth function from the table on the chart.

The graph below shows different function growth complexities (Big-O orders). Label each line with the appropriate Big-O growth function from the table on the chart.

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
Problem 1PE
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The graph below shows different function growth complexities (Big-O
orders). Label each line with the appropriate Big-O growth function from the
table on the chart.

The image is a graph illustrating the growth of different computational complexities based on input size, \( N \). The graph plots various Big O notations, demonstrating their relative running times as \( N \) increases. Each line represents a different complexity class: 1. **O(1):** A constant time complexity, shown as a horizontal line near the x-axis, indicating it does not change regardless of input size. 2. **O(log N):** This curve grows slowly and represents algorithms whose time complexity grows logarithmically. It's depicted with a very gradual increase. 3. **O(N):** A linear time complexity, shown as a diagonal line. The running time increases linearly with the size of the input. 4. **O(N log N):** Typically associated with more efficient sorting algorithms, this line rises more steeply than O(N) but less than quadratic time complexities. 5. **O(N^2):** A quadratic time complexity, depicted as a steep curve, showing how the running time increases exponentially with the size of the input. 6. **O(N!):** Representing factorial time complexity, this line shoots up sharply, indicating an extremely rapid increase in running time, typical for algorithms with very poor scalability. The graph provides a visual representation of how different algorithmic complexities affect the running time relative to the input size, helping learners understand the impact of algorithm efficiency on performance.
Transcribed Image Text:The image is a graph illustrating the growth of different computational complexities based on input size, \( N \). The graph plots various Big O notations, demonstrating their relative running times as \( N \) increases. Each line represents a different complexity class: 1. **O(1):** A constant time complexity, shown as a horizontal line near the x-axis, indicating it does not change regardless of input size. 2. **O(log N):** This curve grows slowly and represents algorithms whose time complexity grows logarithmically. It's depicted with a very gradual increase. 3. **O(N):** A linear time complexity, shown as a diagonal line. The running time increases linearly with the size of the input. 4. **O(N log N):** Typically associated with more efficient sorting algorithms, this line rises more steeply than O(N) but less than quadratic time complexities. 5. **O(N^2):** A quadratic time complexity, depicted as a steep curve, showing how the running time increases exponentially with the size of the input. 6. **O(N!):** Representing factorial time complexity, this line shoots up sharply, indicating an extremely rapid increase in running time, typical for algorithms with very poor scalability. The graph provides a visual representation of how different algorithmic complexities affect the running time relative to the input size, helping learners understand the impact of algorithm efficiency on performance.
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