Question

Given the following algorithm, matching each statement to the correct sequence for complexity analysis.

procedure Alg3(A): A is a list of n integers

1 for i = 1 to n-1 do

2   x=aix=ai

3 j = i − 1

4 while (j ≥≥ 0) do

5 if x≥ajx≥aj then

6 break

7 end if

8   aj+1=ajaj+1=aj

9 j = j − 1

a end while

b   aj+1=xaj+1=x

c end for

d return A

The complexity of this algorithm is O(n2)O(n2)	Respuesta 1Elegir...1572634
The inner loop is a while loop for variable jj and the number of iterations is i−1i−1 in the worst case.	Respuesta 2Elegir...1572634
The outer loop is a for loop for variable ii and the number of iterations is n−1n−1.	Respuesta 3Elegir...1572634
In each iteration in the inner loop, there are 2 operations.	Respuesta 4Elegir...1572634
We consider comparison as the operation to be analyzed	Respuesta 5Elegir...1572634
There are at most 2×(1+2+⋯+(n−1)+2(n−1)+12×(1+2+⋯+(n−1)+2(n−1)+1 operation.	Respuesta 6Elegir...1572634
The pseudocode contains a nested loop.	Respuesta 7Elegir...1572634

Answer 1

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Solution :- Clearly, text in the question in gambled, but i can understand the steps. below i've ordered the time complexity analysis according to the given code.

- The pseudocode contains a nested loop.

- The outer loop is a for loop for variable i and the number of iterations is n−1.

- The inner loop is a while loop for variable j and the number of iterations is i−1 in the worst case.

- In each iteration in the inner loop, there are 2 operations.

- We consider comparison as the operation to be analyzed

-  There are at most 2×(1+2+⋯+(n−1)+2(n−1)+1 operation.

- The complexity of this algorithm is O(n2).