Question

Poly-Poly + a[i] * power 6. (15%) Consider the nested loops shown below, where N is assumed to be a power of 2. i.e., N-2 for some positive integer k. i=N; while (i>-1){ while (j =N){ j-2 *j; i=i/2. a) Determine the number of outer iterations (associated with the outer while loop) to be executed? Show your work. b) For each outer iteration (for each value of i), determine the number of iterations of the inner while loop to be executed? Show your work. c) Determine the total number of times the statement ) - 2 "); will be executed. Show your work

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

a)

Outer loop iterations will get over when

N/2^k=1 because at every iteration i=i/2 where k is number of iterations-1

So,

k=log2(N)

So, iterations of outer loop will be log2(N)+1

b)

Outer loop iterations will get over when

i*2^k=N because at every iteration j=j*2 where k is number of iterations-1

So,

k=log2(N/i)

So, iterations of outer loop will be log2(N/i)+1

c)

For i=1, inner loop will run log2(N)+1 times

For i=2, inner loop will run log2(N/2)+1 times

For i=2^2, inner loop will run log2(N/2^2)+1 times

..

..

So, Total=log2(N)+log2(N/2)+......log2(N/2^(k-1))+N=log2(N^k/2^(1+2+3....k-1))+N

=log2(N^(log2(N)+1)/2^(log2(n)*(log2(n)+1)/2))+N

Kindly revert for any queries

Thanks.