Question

*********I need question 6 answered which is from question 5 which is *********

Question 5 : Program Correctness I (1 point)

Use the loop invariant (I) to show that the code below correctly computes

n P−1 k=0 2k

(this sum represents the sum of the first n even integers where n ≥ 1).

Algorithm 1 evenSum(int n)

1: p = 2(n − 1)

2: i = n − 1

3: while i > 0 do

4: //(I) p = nP−1 k=i 2k

5: i − −

6: p = p + 2i

7: end while

8: return p

Prove the Base case of the loop invariant (I):

Question 6 : Program Correctness II (4 point )

(a) Inductive step:

i. (1 point) What is your inductive hypothesis?

ii. (1 point) What are you trying to prove?

iii. (1 point) Complete the proof:

(b) Termination step:

i. (1/2 point) What is the value of i when the loop terminates? i =____________

ii. (1/2 point) Plug your answer from the previous question into (I) to show the loop is correct:

Answer 1

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