Question

Derive the runtime of dynamic Fibonacci algorithm shown below

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def fib( iN ):

iP = iQ = 1

for i in range( iN - 1 ):

      iP, iQ = iP + iQ, iP

return iP

Answer 1

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def fib( iN ):

iP = iQ = 1 ----------> Line 1

for i in range( iN - 1 ): ----------> Line 2

      iP, iQ = iP + iQ, iP ----------> Line 3

return iP ----------> Line 4

The complexity of Line 1: O(1) as it takes constant time.

The complexity of Line 2: O(iN) as the for loop is run iN-1 times from i = 0 to iN-2

The complexity of Line 3: O(1) as it takes constant time.

The complexity of Line 4: O(1) as it takes constant time.

Hence, the overall complexity of this code is:

O(iN) + O(1) = O(iN) (Answer)