The image displays a graph illustrating the growth of different functions with respect to input size, commonly used in analyzing algorithm complexity in computer science.### Key Components of the Graph:- **Axes**: - The horizontal axis represents the input size, labeled as "Input (number)." - The vertical axis represents time complexity or computation time, labeled as "Time."- **Curves**: The graph contains several curves, each representing a different complexity class: - **Red Curve**: Typically represents constant time complexity, O(1), where execution time is unaffected by input size. - **Green Curve**: Often used for logarithmic time complexity, O(log n), which grows slowly as input size increases. - **Yellow Curve**: Depicts linear time complexity, O(n), where time grows linearly with input size. - **Blue Curve**: Demonstrates quadratic time complexity, O(n²), showing a parabolic growth pattern. - **Violet Curve**: Sometimes used for exponential time complexity, O(2^n), indicating rapid growth as input size increases.- **Annotations**: - The graph includes a label "O(n)" near the violet curve, indicating a linear complexity line for reference.These complexity classes are fundamental in understanding how algorithms scale and perform with larger inputs. Assessing the growth of these curves helps in evaluating the efficiency and feasibility of algorithms in practical applications. Pictured above are graphs representing algorithmic complexity of Big Oh notation functions. Assign the following labels to the appropriate graph. There will be two labels per graph. O(n) is done as an example.| Big Oh notation | Algorithmic growth ||-----------------|---------------------|| Dark Blue | O(n) | linear || Light Blue | | || Yellow | | || Purple | | || Green | | || Brown | | || Gray | | |

Asymptotic notations are used to express an algorithm's efficiency so that it can be easily compared. The various asymptotic notations used are big-oh, big-omega and big-theta. Big-oh notation is used to express asymptotic upper bound, in other words the longest execution time obtained for worst case input. Big-omega notation is used to express asymptotic lower bound, in other words the least execution time obtained for best case input. Big-theta notation is used to express asymptotic tight bound. The complexity of many of the algorithms fall under the basic efficiency classes listed below. 1 - constant n - linear n2 - quadratic n3 - cubic nk - polynomial n - square root log n - logarithmic n log n - logarithmic linear n! - factorial 2n - exponential Light blue plot represents exponential growth since time taken increases drastically even for a small increase in the input size. It is expressed as O(2n). Yellow colored plot represents cubic growth. It is expressed as O(n3). Purple colored plot represents quadratic growth where the time complexity increases by square the input size. It is expressed as O(n2). Green colored plot represents square root function which is expressed as O(n). Brown colored plot represents logarithmic complexity which is expressed as O(log n). Gray colored plot represents constant growth since the time efficiency remains unaffected by the increase in input size. It is expressed as O(1). Thus, the big-oh efficiency class and the algorithmic growth of the plots are mentioned below. Color of plot Big-oh complexity Algorithm growth Light blue O(2n) exponential Yellow O(n3) cubic Purple O(n2) quadratic Green O(n) square root Brown O(log n) logarithmic Gray O(1) constant

Engineering

Computer Engineering

Pictured above are graphs representing algorithmic complexity of Big Oh notation functions. Assign the following labels to the appropriate graph. There will be two labels per graph. O(n) is done as an example. Dark Blue - Light Blue - Yellow Purple Green Brown Gray Big Oh notation O(n) Algorithmic growth linear

Pictured above are graphs representing algorithmic complexity of Big Oh notation functions. Assign the following labels to the appropriate graph. There will be two labels per graph. O(n) is done as an example. Dark Blue - Light Blue - Yellow Purple Green Brown Gray Big Oh notation O(n) Algorithmic growth linear

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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