7/24/2019 Am Mortised Analysis Errata

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Algorithms & Complexity Theory

Ammortised Analysis Errata

The cost of a sequenceSof size n of operations of type insert, performed

on an initially empty arraylist is given by:

cost(S) =cost copy(S) +cost ins(S)

We analyse cost copy(S). We observe that:

2k1 < n 2k

for some k N. Moreover, k represents the number of times the arraylistcapacity was doubled. It follows that: k 1 < log(n) k, and thus k =log(n). The cost of the ith doubling is 2i1, hence:

cost copy(S) =

log(n)

i=1

2i1 =

log(n)1

i=0

2i

log(n)

i=0

2i = 2log(n)+1 1 = 2n 1

It follows that:cost(S) 3n

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