Suppose for a directed graph G = (V, E) in which edges that leave the source vertex s may have negative weights, all other edge weights are non-negative, and there are no negative-weight cycles. We also assume that the graph has no self-loop.In this question we will argue that Dijkstra’s algorithm correctly finds shortest paths from s in this graph.
Explain for Dijkstra's algorithm, (in above situation) why does the proof holds?

Answers

Answer 1

Dijkstra's algorithm works correctly in this situation because it always chooses the vertex with the minimum distance from the source and updates the distances of its neighbors, ensuring that the shortest path is found.

Dijkstra's algorithm works by maintaining a priority queue of vertices and their tentative distances from the source vertex. It then repeatedly extracts the vertex with the minimum tentative distance and updates the distances of its neighbors. This process ensures that the shortest path to each vertex is found, as long as there are no negative-weight cycles.

In the given situation, since all edges leaving the source vertex have negative weights and all other edges have non-negative weights, the algorithm will first explore all the negative-weight edges leaving the source vertex and update the distances of the neighboring vertices.

Once all the negative-weight edges have been explored, the algorithm will continue exploring the non-negative-weight edges, always choosing the vertex with the minimum tentative distance. Since there are no negative-weight cycles, the algorithm is guaranteed to find the shortest path to each vertex.

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Related Questions

A force of 10 N acts to the left and a force of 5 N acts to the right on an object of mass 1 kg. If its initial speed is zero , what is its velocity after 1 second ?

Answers

Answer: -5 m/s

Explanation:

First find the net force by summing up the forces:

-10N + 5N = -5N

Use Newton's Second Law of motion to solve for the acceleration:

F = ma

-5N = 1kg(a)

a = -5 m/s^2

Use the first kinematic equation to solve for the final velocity:

Vf = Vi + at

Vf = 0 + (-5)(1)

Vf = -5 m/s

How are the sun and Earth's moon different?(2 points)
The sun is a ball of gases that revolves around Earth, while the moon is the center of the solar system,
The sun is a ball of rock and gas, while the moon is a ball of rock that revolves around the sun.
The sun is the center of the solar system, while the moon is a ball of rock that revolves around Earth
The moon is the center of the solar system, while the sun is the center of the Milky Way.

Answers

Answer: The Sun measures 1.4 million km across, while the Moon is a mere 3,474 km across. In other words, the Sun is roughly 400 times larger than the Moon. But the Sun also happens to be 400 times further away than the Moon, and this has created an amazing coincidence.

Explanation:

can you suggest improvement that can be made towards the design of siphon so that the transfer of liquid is much higher.​

Answers

Answer:

A siphon is a tube that makes use of the potential energy of fluid at an elevated level to transfer the fluid to a lower level, due to pressure differences between the inlet and the outlet points of the tube, such that the pressure at the outlet is higher than the pressure at the inlet

The pressure energy is converted into velocity (kinetic) energy, and therefore, in other to increase the flow rate through the tube of a siphon, with constant diameter, the level of the fluid in the container at the inlet (supply) of the siphon is raised higher than the level at the outlet receiving) container or the outlet point of the siphon tube

The larger the difference between the inlet and outlet levels, the faster the transfer of fluid by the siphon

Explanation:

This tasty snack starts as a kernel and is “popped” then
covered in salt, butter, caramel, peanuts, you name it.
Through thermal energy we've learned to heat things, you
could use conduction, convection and/or radiation. Describe
1 cooking option in detail including whether it is convection,
conduction or radiation. Must be at least 2 sentences.

Answers

Popcorn can be popped by either of the three forms of heat transfer:

Conduction in a pan with hot oil on a stove element.

Convection by an air popper and warm air rising over a heating element... no direct contact with heat source.

Radiation is what occurs in a microwave. Invisible radiant heat activates water molecules in the popcorn.

All the above heat the kernel over 100 Celsius. Water vaporizes/boils (latent heat) and erupts through the kernel.

Mmmm popcorn watch out for the lipids (fat in the oil and butter)

the organelles are giving their job description to you can you identify which organelle are they? write your answers in your answer sheet.
1. Hi! My responsibility is to add stability and protection to plant cells. What am I?
2. Hi! produce proteins inside the cell. What am I ?
3. Hello! I have a green pigment called the clorophyll. I also absorb solar energy to do the process of photosynthesis. What am I?
4. Good morning po! my work is to store food materials and excretes waste materials. I take a large space on plants. I make the leaves of plants fresh. what am i?
5. Hi! All organelles are embedded in me. I am a "jelly- like" substance. What am I?
Please real answer ​

Answers

1. cell wall?

2. ribosomes?

3. chloroplast

4. vacuoles

5. cytoplasm

Select the correct answer.
Which pair of atoms has the highest electronegativity difference?
OA.
H-S
B.
H-Cl
o c.
N-H
OD.
О – Н
O E.
C-H

Answers

Answer:O – H

Explanation:

the force required to lift a load of 800 Newton by using a Lever having a mechanical advantage of 1.6 is​

Answers

Answer:force required to lift the load = 500N

Explanation:

Mechanical advantage for a lever is given by the formulae

= force output/force input

or

Mechanical Advantage = Load / Effort

where

Force output  / Load= 800 N

mechanical advantage = 1.6

Force input / Effort =??

Force input=  Force output /Mechanical advantage

= 800N / 1.6

=500N

OR

Effort = Load/ Mechanical Advantage = 800/ 1.6 = 500N

A rocket at rest with a mass of 942 kg is acted on by an average net force of 6,731 N upwards for 21 s. What is the final velocity of the rocket?

Answers

Answer:

Final velocity, V = 150.15 m/s

Explanation:

Given the following data;

Mass = 942kg

Net force = 6,731N

Time = 21secs

To find the final velocity of the rocket;

First of all, we would determine the acceleration of the rocket with respect to time.

Force = mass * acceleration

Substituting into the equation, we have;

6,731 = 942*acceleration

Acceleration = 6731/942

Acceleration = 7.15m/s²

Now, to find the final velocity we would use the first equation of motion.

V = U + at

Since the rocket started from rest, its initial velocity (U) is zero.

V = 0 + 7.15*21

Final velocity, V = 150.15 m/s

Energy is defined as ____________.

The ability of an object to produce a change in the environment or itself

motion

the effort required to perform work

power

Answers

Answer:

The effort required to perform work

Explanation:

A plane has a take off speed of 1 point
300 km/h. What is the
acceleration in m/s2 of the
plane if the plane started from
rest and took 45 seconds to
take off? *​

Answers

Answer:

Acceleration = 1.85m/s²

Explanation:

Given the following data;

Final velocity = 300km/h to m/s = 300*1000/3600 = 83.33m/s

Time = 45 seconds

Since the plane started from rest, initial velocity is equal to 0m/s.

To find the acceleration;

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.

Mathematically, acceleration is given by the equation;

[tex]Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}[/tex]

Where,

a is acceleration measured in [tex]ms^{-2}[/tex]

v and u is final and initial velocity respectively, measured in [tex]ms^{-1}[/tex]

t is time measured in seconds.

Substituting into the equation, we have;

Acceleration = (83.33 - 0)/45

Acceleration = 83.33/45

Acceleration = 1.85m/s²

Therefore, the acceleration of the plane is 1.85m/s².

how do I write an essay on how I feel about online school​

Answers

Answer:

Some students appreciated the social aspect of Zoom classrooms, while others felt online education worked best for them when they were working on their own. ... Students said they appreciated having a well-planned work week and didn't appreciate “surprise” assignments online any more than they appreciate them in class

Explanation:

What's I know I said

What do you u write it

what are common in the pictures?​

Answers

Answer:

the flowers the left have them on there heads the middle on there chest and the right one has them on there shoulders

What is the kinetic energy of a 5kg ball that is rolling 3m/s?

Answers

Answer:

22.5

Explanation:

As the mass is 5 kg,velocity is 3m/s so the derivation use for kinetic energy is 1÷2 mv*2 . By this derivation we will find out the kinetic energy

Importance of Forest ​

Answers

Answer:

to help keep fresh air

Explanation:

To produce oxygen and protect oxygen

Which of the following have the most GPE. 1.) a car at the top of a hill 2.) a car at the bottom of the hill 3.) a car half way down the hill 4.) on the straight part of the track. (I don't know how to give Brainly)

Answers

Answer: car at the top of a hill

Explanation:

How many total molecules are present in the formula below
2H2O

Answers

There are 4 in there I believe

I'm guessing 6.

the coefficient of two turns our hydrogen into 4 and our oxygen into 2 which makes a total of 6 molecules.

A tractor pulls a 1,000 kg wagon with a force of 4,000N. What is the wagon’s acceleration in m/s2? *

Answers

Answer:

4m/s^2

Explanation:

acceleration=force/mass

therefore a=4000/1000

=4m/s^2

please please help!!!!!

Answers

All resistors are in series
Therefore R=r1+r2+r3
=1+5+2=8 ohm
V=16v

Therefore V=IR
I=V/R
=16/8=2A
Current=2A

A rock with a mass of 80grams dropped into a graduated cylinder with 30 ml of water in it the readingof water became 70 ml what is the density of the rock

Answers

Explanation:

[tex]b = m \div v \\ 80 \div 30 \times 10 { -}^{2} [/tex]

solve: A car travels 2 km North , 10 km East, then 3 km West. pythagorean theorem

Answers

________b_____ 7 km east

|

| 2km north.

|a

|

°

pythagorean theorem : ✓a² + b² = c²

c² = a² + b² = 4 + 49 = 53

c = ✓53 km

displacement = c = ✓53 km

distance = 10 + 3 + 2 = 15 km

plzz helpppp meee!!!!

A farmer cannot get his cow to move without help. The cow has a mass of 425 kg. He returns with some neighbors, and they are able to exert a net force of 900 N on the cow. What is its acceleration?​

Answers

A=f/m
A=900/425
A=2.18

To determine acceleration you divide the force by the mass.

Answer:

hhh

Explanation:

What is the direction of the current in the loop as the north pole of the magnet is pulled away (to the right) from the loop of wire. Answer as you face the loop from the magnet.

Answers

Answer:

Explanation:

Applying Fleming's right hand rule, the induced current would flow in a clockwise direction in the loop. Explanation: Current, magnetic field and motion are mutually dependent and perpendicular to one another.Aug 27, 2019

Two spheres are moving towards each other. Which of the following is the
best evidence that the spheres have transferred energy from one to the other?

A.The friction of the surface decreases

B.Gravity is always acting on the spheres

C.The motion of the sphere changes

Or

D.Both of the spheres have the same mass

Answers

Answer:

D

Explanation:

If they are both moving at the same speed then its D.

Una pieza de platino metalico con densidad 21.5 g/cm3 tiene un volumen de 4.49 cm3. Cual es su masa

Answers

Answer:

m = 96.53 grams

Explanation:

Given that,

The density of metallic platinum, d = 21.5 g/cm³

Volume, V = 4.49 cm³

We need to find the mass. Let it is m. We know that the density is equal to the mass per unit volume. So,

[tex]d=\dfrac{m}{V}\\\\m=d\times V\\\\m=21.5\times 4.49\\\\m=96.53\ g[/tex]

So, the required mass is 96.53 grams.

Complete the sentence. Friction always ____________

a. helps the motion

b. opposes the motion

c. both of these

d. none of these

Answers

Answer:

B- Opposes the motion

Explanation:

When two object touches each other. friction acts in a opposite direction to the motion of the object

B. Opposes the motion.

A marble rolling across a flat surface will not roll forever. This is due to friction. The marble rubs against the flat surface, slowing down until it finally stops.

someone please helppp

Answers

okay, so what i have learned from my experiences with doing school on e.d.g.e.n.u.i.t.y (they won't let me say the website name on here lol) is that after you write an extended response, they show you a sample response as well as these checkboxes which show things they wanted you to have included in your answer. ideally they want you to select all of them, meaning that all of those elements were included in your answer. it's not a matter or right or wrong; none of those checkboxes contain a wrong answer. you just select the ones that apply to your answer, and you won't get penalized if you don't select all of the checkboxes. you don't even have to select any of them. there's been times where my answer has been not at all what it should've been and i just click done without checking any of those boxes because i did not include any of those elements in my response. as long as the box that you wrote your answer in is outlined in green (which yours is, and that means that the computer likes your answer), you will be fine.

i hope this makes sense! it's sort of hard to explain. if you have any questions, just comment and i'll try my best to explain better lol. have a great rest of your day! <3

Electrical energy in motion is what type of energy ?

Answers

Answer:

kinetic energy

Explanation:

Electrical energy is a type of kinetic energy caused by moving electric charges. The amount of energy depends on the speed of the charges – the faster they move, the more electrical energy they carry.

It’s Kinetic energy

percent of Earth's surface is made up of Oxygen.
a) 30
b) 46
c) 62

Answers

Answer: it's made up about 21% so if you do not have this option I say go with 30

Explanation:


what is the wavelength of the wave

Answers

Explanation:

it is equal to the speed (v) of a wave train in a medium divided by its frequency (f): λ = v/f. Waves of different wavelengths.

Answer:

It is measured in the direction of the wave. Description: Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave).

give three example what are the aims of each team in playing basketball?​

Answers

Answer:

The main objective of basketball is to make a goal and score points.Each team should not only try to make a goal and prevent the opposite team from taking control of the ball, but should also try to protect the basket in their court and prevent the opponent from making a goal.

hope that helps..

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