Question

2. (15 marks) Consider the abstract datatype SEQ whose objects are sequences of elements and which supports two operations . PREPEND(x, S), which inserts element r at the beginning of the sequence S and . ACCESS(S, i), which returns the ith element in the sequence Suppose that we represent S by a singly linked list. Then PREPEND(, S) takes 1 step and ACCESS(S, i) takes i steps, provided S has at least i elements Suppose that S initially has exactly one element. A sequence of n operations are performed. Each operation in the sequence is (independently) chosen to be a PREPEND with probability p and an ACCESS with probability 1-p. For each ACCESS operation the value of the parameter i is chosen uniformly from [1.. S (a) (3 marks) Consider when n 2. List the set of all possible sequences of length two and the corresponding probability that each one occurs. For example, for n-2 the probability space consists of 5 sequences probability sequence ACCESS (1) ACCESS (1) (1- p) ACCESS (1) PREPEND (1-p)p PREPEND: ACCESS(1) p(1- p)/2 PREPEND:ACCESS(2) | p(1-p)/2 PREPEND:PREPEND p (b) (4 marks) Derive the expected length of the linked list just before the k'th operation is performed. HINT: You may find it useful to use indicator random variables

do (b) please

Answer 1

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