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Given the following algorithm, matching each statement to the correct sequence f...

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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=aix = a_i

3 j = i − 1

4 while (j ≥≥\geq 0) do

5 if x≥ajx≥ajx \geq a_j then

6 break

7 end if

8 aj+1=ajaj+1=aja_{j+1} = a_j

9 j = j − 1

a end while

b aj+1=xa_{j+1} = x

c end for

d return A

The pseudocode contains a nested loop.

The complexity of this algorithm is O(n2)O( n^2 )

We consider comparison as the operation to be analyzed

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

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

There are at most 2×(1+2+⋯+(n−1))+2(n−1)+12\times (1+2+\cdots+(n-1)) + 2(n-1)+1 operation.

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

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