Suppose the running time of an algorithm is given by the following recurrence relation:
T(0) = 1
T(n) = 2T(n/2) + n^2
What is the Big O complexity of T(n)? Give as tight a bound as possible and show your work.

Answers

Answer 1

The Big O complexity of the given recurrence relation, T(n) = 2T(n/2) + n^2, is O(n²).Step-by-step explanation: To obtain the Big O complexity of T(n), we can solve this recurrence relation using the master theorem, which states that if the recurrence relation is of the form

T(n) = aT(n/b) + f(n),where a ≥ 1 and b > 1 are constants, and f(n) is a function, then the time complexity of T(n) is given by:1. If f(n) = O(nᵏ) for some constant k, then

T(n) = Θ(nᵏlog n).2. If f(n) = Θ(nᵏlogⁱ n), where i ≥ 0 and logⁱ n = (log n)ᵢ, then

T(n) = Θ(nᵏlogⁱ⁺¹ n).3. If f(n) = Ω(nᵏ), and if a⋅

f(n/b) ≤ cf(n) for some constant c < 1 and all sufficiently large n, then

T(n) = Θ(f(n)).Now, let's apply the master theorem to the given recurrence relation:

T(n) = 2T(n/2) + n²

Here, a = 2, b = 2, and

f(n) = n².

Hence, the Big O complexity of T(n) is O(n²).

To know more about recurrence visit:

https://brainly.com/question/6707055

#SPJ11

Related Questions

A uniform plane electromagnetic wave propagating in a lossless dielectric medium with relative permittivity & = 4 is obliquely incident at the common plane shared by the medium with permittivity =4 with another lossless dielectric medium with =2. The wave is given to be polarized in the plane of incidence. i) Does the critical angle phenomenon exist? If it does, find the critical angle 0 ii) Does the Brewster angle phenomenon exist? If it does, find the Brewster angle 0, and the power reflection and power transmission coefficients when the angle of incidence is equal to 0 iii) Does the Brewster angle phenomenon exist even when the two media are interchanged, i.e., the medium on the left has e = 2 and the medium to the right has e = 4? If it does, find the new Brewster angle 0 iv) Does the critical angle phenomenon exist if the wave polarization is changed from parallel polarized to perpendicular polarized relative to the plane of incidence? Explain your answer.

Answers

1) Critical angle is 45° .

2) Brewster angle is 35.26° .

3) The new Brewster angle is 54° .

4) Theoretically it is possible.

At critical angle the angle of refraction is 90°

sinФc = √∈r2/∈r1

sin Фc = √2/4

Фc = 45° .

The brewster angle is given as

tanФb = √∈2/∈1

tanФb = √1/2

Фb = 35.26°

If incident angle is equal to brewster angle than there is no reflection .

So power reflected is zero and power transmitted is 100% .

Reflection Coefficient (R) = 0

Transmission coefficient = 1

tanФb = √4/2

Фb = 54°

When polarisation is changed from parallel to perpendicular, there is no existence of brewster angle as

tanФb1 = √µ2/µ1

The situation is theoretically possible but rare in practice .

Know more about wave propagation,

https://brainly.com/question/31084304

#SPJ4

Design a code converter circuit that takes a 4-bits binary number as inputs and find the corresponding output as follows -If the input number is multiple of 5 then the output = (input * 4 + 2)/3 - If the input number is not multiple of 5 then output = (input * 3 - 1)/4 (Note that 0 is multiple of 5,, Note if the output = 5.7 the floor of 5.7 which = 5) Follow the steps for combinational circuit design and find the minimum POS for each output. Implement the design using Verilog, verify it by using waveform then download your circuit on the altera board, for Inputs switches will be used and for Outputs use LEDs.

Answers

The code converter circuit that takes a 4-bits binary number as inputs to find the corresponding output is in the explanation part below.

Here's an example of a code converter circuit implemented in Verilog:

module CodeConverter (

input wire [3:0] input_number,

output wire [3:0] output_number

);

reg [4:0] temp;

always (*) begin

if (input_number % 5 == 0) begin

temp = (input_number * 4 + 2) / 3;

end else begin

temp = (input_number * 3 - 1) / 4;

end

assign output_number = temp[3:0];

endmodule

You can build a testbench module and simulate it using a waveform viewer to ensure the code is functional.

module CodeConverter_TB;

reg [3:0] input_number;

wire [3:0] output_number;

CodeConverter dut (

.input_number(input_number),

.output_number(output_number)

);

initial begin

$display("Input\tOutput");

// Test case: input_number = 5 (multiple of 5)

input_number = 4'b0101;