1. Let G be a directed acyclic graph (DAG). In the lecture, we described how to perform topological sort of the vertices of G by running DFS on G. Here, let us examine another way to do so. (a) Show that there exists some vertex v of G whose in-degree is 0. That is, there is no directed edge pointing to v. (b) Consider the following algorithm, which removes the vertices of G, successively, if the in-degree is 0. 0. Initialize an array InDeg[1..n] and an empty queue Q; 1. Compute InDeg[v] of every vertex v; 2. for each vertex v 3. if InDeg[v] = 0 then Insert v to Q; 4. while Q is not empty 5. v Q.pop(); Output v; 6. for each neighbor u of v 7. Decrease InDeg[u] by 1; 8. Insert u to Q if InDeg[u] is now 0; Show that the algorithm correctly performs topological sort on G. Show that the running time is linear. If the input graph G is a directed graph but not a DAG, what will happen? How should we modify the algorithm to detect such a case occurs?
Answers
We assume the contrary, that is, for any vertex v in G, there is some vertex u pointing to v. Since G is a DAG, starting from any vertex of G, we can perform DFS and traverse all vertices.
Consider a vertex v visited last in the DFS traversal. Then all vertices pointing to v have been visited before v. Since every vertex u pointing to v is visited before v, the DFS algorithm must have discovered the edge (u, v) in its traversal, hence v cannot be the last vertex to be visited, contradicting our assumption.
(b) To prove the correctness of the algorithm, we need to show that the output sequence is a valid topological sort. Assume to the contrary that there exist vertices u and v such that u precedes v in the output sequence, but there is a directed edge from v to u in G.
Then when we process vertex v, vertex u is not yet in Q, hence the condition "if InDeg[u] is now 0" fails and we do not insert u into Q. Therefore u cannot be output before v.
This contradicts the assumption that u precedes v in the output sequence. Thus the output sequence is a valid topological sort. The running time of the algorithm is O(m+n), where m is the number of edges and n is the number of vertices.
Computing the in-degree of each vertex takes O(m) time, and each vertex is added to and removed from Q exactly once, and each edge is scanned at most once to update the in-degree of its endpoint.
If the input graph G is a directed graph but not a DAG, the algorithm will get stuck in a loop, since there is at least one cycle and no vertex has in-degree 0.
To detect this case, we can add a counter C and initialize it to 0. Each time we remove a vertex v from Q, we increment C by 1.
If at the end C is less than n, then there is a cycle and the graph is not a DAG. We can modify the algorithm to output a message indicating that the graph is not a DAG.
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Related Questions
in the above environment and store, if we execute lettuce expression deref(y)(deref(z)) do changes occur in the memory store?
Answers
Based on the information provided, it seems that you are referring to some specific environment and store, possibly related to a programming language or framework.
However, without additional context or details about the environment and store, I cannot provide a specific answer.In general, the behavior of executing the expression deref(y)(deref(z)) depends on the semantics of the language or framework you are using, as well as the values and references stored in memory. The expression may perform operations such as dereferencing pointers or accessing values stored in variables or objects.If the expression modifies the values or references stored in memory, then changes can occur in the memory store. However, without more information about the specific environment and store, it is not possible to determine the exact impact of executing that expression.
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Who created the idea of a general purpose computing machine.
Answers
Answer:
Charles Babbage
Explanation:
1822 - Charles Babbage (1792-1871) designed his first mechanical computer, the original prototype for the Difference Engine. Babbage invented two machines, the Analytical Engine (a general purpose mathematical device) and the Difference Engine.
which symbol is used in standard sql as a wildcard to represent a series of one or more unspecified characters?
Answers
% (percent sign) is the symbol is used in standard sql as a wildcard to represent a series of one or more unspecified characters.
What is Wildcard in SQL?
A wildcard character replaces one or more characters in a string. The LIKE operator employs wildcard characters. In a WHERE clause, the LIKE operator is used to look for a specific pattern in a column.
What is SQL?
Structured query language (SQL) is a programming language used to store and process data in relational databases. A relational database is a tabular database that stores information in tabular form, with rows and columns representing different data attributes and the various relationships between the data values. SQL statements can be used to store, update, delete, search, and retrieve data from a database. SQL can also be used to maintain and improve database performance.
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How to code 2.9.5: Four colored triangles {Code HS}
Answers
Answer: penup()
backward(100)
for i in range(4):
pensize(5)
pendown()
left(60)
color("green")
forward(50)
right(120)
color("blue")
forward(50)
color("red")
right(120)
forward(50)
penup()
left(180)
forward(50)
Explanation:
L
In this exercise we have to use the knowledge of computational language in python to write the code.
This code can be found in the attached image.
To make it simpler the code is described as:
ipenup()
backward(100)
for i in range(4):
pensize(5)
pendown()
left(60)
color("green")
forward(50)
right(120)
color("blue")
forward(50)
color("red")
right(120)
forward(50)
penup()
left(180)
forward(50)
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what are the main hardware/software components used in cell phone communication? define/explain.
Answers
Processors, display screens, rechargeable batteries, memory storage, operating systems, and mobile applications.
The details of these components are explained below:Hardware components:Processors: The central processing unit (CPU) is responsible for executing instructions on a device. It is the “brain” of the phone and processes commands from the user. Most cell phone processors are built on ARM architecture. The processor speed is measured in gigahertz (GHz). The faster the processor, the more efficiently a device runs.Display screens: A screen is one of the essential hardware components in cell phones. It is responsible for the phone's visual output. Display screens are used to show text, images, and videos. The screen is made up of glass or plastic and consists of pixels that show the picture's resolution.Batteries: A rechargeable battery provides power to the phone. Lithium-ion batteries are widely used in cell phones and can be charged through a USB cable.Memory storage: Memory is the cell phone's storage capacity, allowing it to store data. Memory storage can be categorized into two types: volatile and non-volatile memory. The volatile memory is known as RAM (Random Access Memory) and the non-volatile memory is known as ROM (Read-Only Memory).Software components:Operating systems: The operating system (OS) controls all the hardware and software components on a cell phone. The most common mobile operating systems are iOS, Android, and Windows Mobile.Operating systems provide a platform for running applications. Mobile Applications: Mobile applications are software programs that run on a mobile device. Apps provide users with a variety of functions, such as gaming, messaging, navigation, and entertainment. They can be downloaded from an app store or installed on a device via a website. In conclusion, these are some of the main hardware and software components that are used in cell phone communication.
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In Python, if var1 = “Happy” and var2= “Birthday” and var3 = (var1+var2) *2, then var3 stores the string
A)“Happy BirthdayHappyBirthday”
B)“HappyHappyBirthday”
C)“HappyBirthdayHappyBirthdayHappyBirthday”
D)“HappyBirthdayBirthday”
Answers
Answer:
A
Explanation:
var3 is happy + birthday, ×2
l.e happy birthday happy birthday
Answer:
Your answer is A
which network device provides multiple ports for connecting nodes and is aware of the exact address or identity of all the nodes attached to it?
Answers
The network device that provides multiple ports for connecting nodes and is aware of the exact address or identity of all the nodes attached to it is a switch.
A switch is a network device that is typically used in Ethernet local area networks (LANs) and is designed to provide multiple ports for connecting nodes to the network. A switch is able to identify the physical address or MAC address of every device connected to it and then create a table or database of these MAC addresses so that it can quickly route data packets to their intended destinations.
A switch operates at the data link layer of the OSI model and is responsible for creating and maintaining the network topology. It also ensures that data packets are delivered to the correct device by examining the destination MAC address of the packet and then forwarding it to the appropriate port on the switch.
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What are 6 subtopics to the topic “computer programming”? Please let them be good answers that are middle school level
Answers
Answer:
1. Array programming language.
2. Aspect-oriented programming language.
3. Class-based programming language.
4. Concatenative programming language.
5. Concurrent programming language.
6. Data-structured language.
I'm not sure if this is what you want, but these are a couple types of programming languages
What potential downsides can you see to Face book’s Groups for Schools initiative
Answers
Answer:
Probably hate speech, and invasion of privacy on face book xD
Most brass instruments have a ____________________, ____________________, ____________________, and, ____________________.
Bells
Composer
Control
French horn
Highest
Hunting
Largest
Left
Lowest
Mouthpiece
Mute
Oldest
Pitch
Smallest
Tubing
Sousaphone
Trombone
Trumpet
Tuba
Valves
Answers
Which tool can most easily be used to find synonyms for words in
your document?
Answers
Answer:
The Thesaurus
Explanation:
Answer:
The dictionary
Explanation:
HELP PLS!!! In a presentation, what is layout?
Answers
Please help with this code!
Answers
import random
months = ["jan", "feb", "mar", "apr", "may", "june", "july", "aug", "sept", "oct", "nov", "dec"]
pick1 = random.choice(months)
pick2 = random.choice(months)
if months.index(pick1) < months.index(pick2):
print(pick1)
print(pick2)
else:
print(pick2)
print(pick1)
Since the months are already in chronological order in the list, we can compare their index and print the string with the smaller index first. I wrote my code in python 3.8. I hope this helps.
What is output? Select all that apply. c = 0 while (c < 5): c = c + 1 print(c) 6 5 2 4 3 0 1
Answers
Answer:
2 4 3 0 1
Explanation:
what is an example of analog device
Answers
Explanation:
Thermometer. Speedometer. Analogue Clock. Seismometer. Voltmeter. Flight Simulators.hope it helps stay safe healthy and happy...Which of the following enables you to click an item when using a touchscreen?
a.Tap the item
b.home
c.A place where you can insert an object
d.pressing the Esc key
Answers
When using a touchscreen, tapping an item allows you to click it. The term "tap" refers to a quick, light touch with one finger or a stylus, which is the equivalent of a mouse click on a conventional computer mouse.
A touchscreen is an electronic display that allows you to interact with a computer by touching the screen. By tapping, swiping, or pinching the screen, you can navigate the device, type messages, open apps, and perform other tasks. The user's finger acts as a pointer on the screen, and tapping an icon or button activates the corresponding command or function.
The touchscreen is becoming increasingly popular in mobile devices, including smartphones, tablets, and laptops. A touchscreen monitor, which is a computer display that recognizes touch input, is also available. Some touchscreens require a stylus to interact with the screen, while others use finger input. Tap is the primary input method for most touchscreens, and it has become a standard gesture for many users.
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not sure what this means.
Answers
Answer:
should be text effects............
In cell K2 enter a formula using the IF and OR functions, as well as structured references, to determine if Adam Moriarty can be a group leader. a. The IF function should first determine if the staff member’s Service Years is greater than 3 OR if the staff member’s college graduate status is "Yes". Remember to use a structured reference to the Service Years and the College Graduate columns.
Answers
Solution :
The value of the K2 cell is filled by IF and OR functions with structured references as :
\(K2=IF(OR([CBF\ \text{Staff[ Service years]} > 3, \text{CBF Staff[College graduate]}="Yes"),"Yes","No")\)
Now if the syntax of the formula is not provided, then we can use :
\($K2=IF(OR([[\text{Service Years}]]>3,[[\text{College Graduate}]]="Yes"),"Yes","No")$\)
The staff member are required to satisfy one of the two or both the conditions so as to become a group leader. The conditions are :
--- staff member should served for more than 3 years
--- staff members should be college graduate
read in an input value for variable numin. then, read numin floating-point values from input and output the lowest of the floating-point values read to one decimal place. end with a newline. note: all floating-point values are of type double. ex: if the input is 3 68.0 21.8 -64.9, then the output is: -64.9
Answers
Here's a Python code snippet that reads an input value for the variable `numin` and then reads `numin` floating-point values from the input. It outputs the lowest of the floating-point values read, formatted to one decimal place.
```python
numin = int(input("Enter the number of values: ")) # Read the input value for numin
min_value = float('inf') # Initialize min_value with positive infinity
for _ in range(numin):
value = float(input("Enter a floating-point value: ")) # Read a floating-point value
if value < min_value:
min_value = value
print(f"The lowest value is: {min_value:.1f}") # Output the lowest value to one decimal place
```
In this code, `numin` is the number of floating-point values to be read. The code then enters a loop where it reads `numin` floating-point values one by one. It keeps track of the minimum value encountered so far and updates it whenever a new lower value is read.
Finally, the code outputs the lowest value using f-string formatting with `:.1f` to format it to one decimal place.
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What is the purpose of the central processing unit (CPU) in a computer?This task contains the radio buttons and checkboxes for options. The shortcut keys to perform this task are A to H and alt+1 to alt+9.
A
It provides electricity to the rest of the system.
B
It houses the main circuit board.
C
It performs the calculations and processing.
D
It stores the software and data
Answers
C: The CPU (Central Processing Unit.) Is the main way to perform tasks or calculations on a computer.
What are the qualities of strong leaders? Check all that apply. They inspire others. 1)They are easily influenced by others. 2)They are outstanding role models. 3)They have a strong sense of purpose. 4)They lack self-confidence.
Answers
Explanation:
I would pick 2 and 3 based on process of elimination
Assignment 4: Evens and Odds
How do I fix this?
Answers
There's definitely something wrong with your for loop. Try this:
for x in range(n):
You might want to check if all your print statements are correct. You might be missing just a period and it will be counted wrong.
What icon indicated video mode?
Av
Tv
The video camera icon
Answers
The video camera icon indicated video mode.
The video camera icon is a universally recognized symbol that indicates video mode on electronic devices such as cameras, smartphones, and video recorders. This icon usually appears on the interface of the device, usually on the screen or as a button that you can press, when you are in video mode, and it allows you to record videos.
AV and TV icons are related to audio-video and television, but they are not used specifically to indicate video mode. AV icon can be used for different purposes such as indicating the audio-video input/output of a device or indicating an audio-video format. The TV icon is used to indicate the television mode, which typically refers to the display mode of a device.
¿ Porque la madera presenta mayor resistencia a ser cortada en sentido travesal que en sentido longitudinal
Answers
La madera es más fuerte en la dirección paralela al grano. Debido a esto, las propiedades de resistencia y rigidez de los paneles estructurales de madera son mayores en la dirección paralela al eje de resistencia que perpendicular a él
AD and BC are equal perpendiculars to a line segment AB (see figure). Show that CD
bisects AB.
Answers
Along with chaining together blocks of data using hashes, what two other features help blockchain remain secure?.
Answers
Along with chaining together blocks of data using hashes, the two other features that help blockchain remain secure is decentralization and consensus.
What other two characteristics aid in keeping blockchain secure?Data structures created by blockchain technology include built-in security features. It is founded on cryptographic, decentralized, and consensus concepts that guarantee the integrity of transactions.
Note that the two types of cryptographic keys are private key and public key. Both of these keys are held by each person or node, and they are used to generate digital signatures. The most significant feature of blockchain technology is this digital signature, which serves as a specific and secure reference for a digital identity.
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Do all careers or professions need computer science? Why or why not?
Answers
Answer:
Most careers or professions need computer science
Explanation:
As humanity is improving technological wise most jobs will be replaced and other jobs would come into play and in order for individuals to become employed in jobs that will be available in the future to come they will have to have a degree in computer science or know how to operate computers.
Answer:
No not all careers and professions require computer science
Explanation:
There are so many careers, many in which you may not sit in front of a computer. If you become a farmer, janitor, teacher or more you may not need computer science skills.
Write a class IN BLUEJ to overload a function num_calc() as follows:
i) void num_calc(int num, char ch) with one integer argument and one character argument, computes the square of integer argument if choice ch is ‘s’ otherwise finds its cube.
ii) void num_calc(int a, int b, char ch) with two integer arguments and one character argument. It computes the product of integer arguments if ch is ‘p’ else adds the integers.
iii) void num_calc(String s1, String s2) with two string arguments, which prints whether the strings are equal or not.
Write a main method to call the above methods and pass the values.
Answers
Answer:
.
Explanation:
if your vista computer is on a workgroup, what applet is used to manage user accounts?
Answers
The "User Accounts" applet is used to manage user accounts on a Windows Vista computer that is on a workgroup.
The "User Accounts" applet is a built-in feature of the Windows operating system that allows administrators to manage user accounts and their privileges. On a Windows Vista computer that is on a workgroup, the "User Accounts" applet can be accessed by going to the Control Panel and selecting "User Accounts and Family Safety," and then clicking on "User Accounts." From there, administrators can create and delete user accounts, change passwords, set account types and privileges, and configure other account settings. This applet is useful for managing user accounts on a workgroup, where there may be multiple users accessing the same computer, but there is no centralized server for managing accounts.
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Which data type is –7?
int
single
string
float
Answers
Answer:
Int
Explanation:
Good Luck!