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SSSSS
2 months ago
13

Let Deterministic Quicksort be the non-randomized Quicksort which takes the first element as a pivot, using the partition routin

e that we covered in class on the quicksort slides. Consider another almost-best case for quicksort, in which the pivot always splits the arrays 1/3: 2/3, i.e., one third is on the left, and two thirds are on the right, for all recursive calls of Deterministic Quicksort. (a) Give the runtime recurrence for this almost-best case. (b) Use the recursion tree to argue why the runtime recurrence solves to Theta (n log n). You do not need to do big-Oh induction. (c) Give a sequence of 4 distinct numbers and a sequence of 13 distinct numbers that cause this almost-best case behavior. (Assume that for 4 numbers the array is split into 1 element on the left side, the pivot, and two elements on the right side. Similarly, for 13 numbers it is split with 4 elements on the left, the pivot, and 8 elements on the right side.)
Engineering
1 answer:
Daniel [329]2 months ago
3 0
For Deterministic Quicksort, which operates by selecting the first element as the pivot, consider a scenario where the pivot consistently divides the array into segments of 1/3 and 2/3 for all recursive calls. (a) The runtime recurrence for this case needs to be determined. (b) Use a recursion tree to justify that this recurrence resolves to Theta(n log n). (c) Provide distinct sequences of 4 and 13 numbers that prompt this behavior.
You might be interested in
Retype the below code. Fix the indentation as necessary to make the program work. if 'New York' in temperatures: if temperatures
Daniel [329]

Answer: Below is the correctly formatted code:

if 'New York' in temperatures:

if temperatures['New York'] > 90:

   print('The city is melting!')

else:

   print('The temperature in New York is', temperatures['New York'])

else:

   print('The temperature in New York is unknown.')

Explanation:

This is the entire program:

temperatures = {

   'Seattle': 56.5,

   'New York': 105,

   'Kansas City': 81.9,

   'Los Angeles': 76.5

}

if 'New York' in temperatures:

if temperatures['New York'] > 90:

   print('The city is melting!')

else:

   print('The temperature in New York is', temperatures['New York'])

else:

   print('The temperature in New York is unknown.')

The output will be:

The city is melting!

This program mainly comprises nested if statements. The first check determines if 'New York' exists within the temperature data. When confirmed, it moves to another if statement to see if New York's temperature exceeds 90. If true, it outputs the message, "The city is melting!". If false, it presents the actual temperature of New York. If neither condition is satisfied, it defaults to showing that the temperature is unknown. Given that New York's temperature is 105, the output reflects that the city is melting!

Proper indentation is crucial in Python, as it distinguishes code blocks without needing brackets, enhancing readability. Observe how the nested if statements are structured within the outer if statement. The else statements align appropriately beneath their respective if declarations, and print statements follow the necessary indentation.

4 0
3 months ago
A 10-ft-long simply supported laminated wood beam consists of eight 1.5-in. by 6-in. planks glued together to form a section 6 i
pantera1 [306]
Point B is where Q_B = 101.25 \ in^3 shows the highest Q value at section a–a. The missing diagram that was supposed to accompany this question can be found in the attached file. Based on the given information, we must identify the point with the greatest Q value at section a–a. To achieve this, we're working with the attached image. The image reveals that there are 8 blocks stacked vertically on the right-hand side, totaling 12 inches; thus, each block measures 1.5 inches in height. Additionally, the blocks are divided into sections marked as A, B, C, and D. For point A, we use the formula Q representing the moment of Area A. For point B, we set Q as the moment of Area B, and similarly for points C and D. However, point D has no area, resulting in a moment of 0.
3 0
1 month ago
A piston–cylinder assembly contains propane, initially at 27°C, 1 bar, and a volume of 0.2 m3. The propane undergoes a process t
Viktor [391]
The work completed is -19.7 KJ, and the heat transferred amounts to 17.4 KJ. Given the temperature is 27°C and the volume is 0.2 m³, with pressure shifting from 1 bar to 4 bar, we recognize the equation pV¹°¹ is a constant. From the superheated propane table, the corresponding specific volume and internal energy values at initial conditions allow us to assess the work and heat transfer between state changes.
8 0
1 month ago
. Were you able to observe ???? = 0 in the circuit you constructed during lab? Why or why not? Hint: What value of resistance wo
Mrrafil [318]

Answer:

An attachment follows below

Explanation:

1) The formula used for the damping coefficient in a series RLC circuit.

If \xi = 0, it is possible to set c = 0 but an inductor will still possess some capacitance.

2) The behaviors of critically damped and underdamped systems are illustrated along with comments on their temporal responses.

4) While several answers might suffice, the four I’ve highlighted are the crucial parameters necessary about an unknown op-amp before utilizing it in a circuit.

Hope this addresses all your inquiries.

5 0
2 months ago
An open vat in a food processing plant contains 500 L of water at 20°C and atmospheric pressure. If the water is heated to 80°C,
Mrrafil [318]

Answer:

Volume change percentage is 2.60%

Water level increase is 4.138 mm

Explanation:

Provided data

Water volume V = 500 L

Initial temperature T1 = 20°C

Final temperature T2 = 80°C

Diameter of the vat = 2 m

Objective

We aim to determine percentage change in volume and the rise in water level.

Solution

We will apply the bulk modulus equation, which relates the change in pressure to the change in volume.

It can similarly relate to density changes.

Thus,

E = -\frac{dp}{dV/V}................1

And -\frac{dV}{V} = \frac{d\rho}{\rho}............2

Here, ρ denotes density. The density at 20°C = 998 kg/m³.

The density at 80°C = 972 kg/m³.

Plugging in these values into equation 2 gives

-\frac{dV}{V} = \frac{d\rho}{\rho}

-\frac{dV}{500*10^{-3} } = \frac{972-998}{998}

dV = 0.0130 m³

Therefore, the percentage change in volume will be

dV % = -\frac{dV}{V}  × 100

dV % = -\frac{0.0130}{500*10^{-3} }  × 100

dV % = 2.60 %

Hence, the percentage change in volume is 2.60%

Initial volume v1 = \frac{\pi }{4} *d^2*l(i)................3

Final volume v2 = \frac{\pi }{4} *d^2*l(f)................4

From equations 3 and 4, subtract v1 from v2.

v2 - v1 =  \frac{\pi }{4} *d^2*(l(f)-l(i))

dV = \frac{\pi }{4} *d^2*dl

Substituting all values yields

0.0130 = \frac{\pi }{4} *2^2*dl

Thus, dl = 0.004138 m.

Consequently, the water level rises by 4.138 mm.

8 0
2 months ago
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