Consider the following algorithm assume N to be a positive i

Consider the following algorithm; assume N to be a positive integer. 1. X 0 2. Y 1 3. WHILE (X < N) a. X X + 1 b. Y Y + 2 X 4. Y Y / N Calculate what value of Y the algorithm will compute for the following values of N. Explain your solution. a) N = 3 b) N = 5

Solution

1. X 0

2. Y 1

3. WHILE (X < N)

a. X X + 1

b. Y Y + 2 X

4. Y Y / N

Solution:   for N =3

initially x₀ = 0 and y₀ = 1
in while loop steps the values changes as shown below

step1 : X₁ = 1 and Y₁ = Y₀ + 2*X₁ = 1+2*1 = 3

step2 : X₂= 2 and Y₂ = Y₁+ 2*X₂= 3+2*2 = 7

step3 : X₃= 3 and Y₃ = Y₂+ 2*X₃= 7+2*3 = 13
when the loop ends Y₄ = Y₃ /3 = 13/3 = 4.3
finall value of Y becomes 4.3

similarlly for N = 5 we can see that finall value of Y will be Y₆ = 31/5 = 6.2