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C++ Programming: From Problem Analysis to Program Design

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter17: Linked Lists

Section: Chapter Questions

Problem 9PE

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Question

In classes we define the set of linked lists on the natural ones LN as the smallest set
that meets the following rules:
1. Ø E LN.
2. Yes LE LN and kEN, then L→ k E LN.
The operator of concatenation of lists, denoted by , receives two lists and returns the list that
results from adding all the numbers from the second list to the end of the first. For instance:
(→3 →4 → 10) °(→2 →6) =→3 →4 →10 →2 →6
We then define the operator •: Ln × LN → Ln inductively like:
1. L•Ø = L, with LE LN.
2. L•(L-→ k) = (L • L} → k, with L, L'E Ln.
Notice that the concatenation operator is associative: (L1 • L2) • L3 = L1 •(L2 • L3).
On the other hand, the operator back ()r: Ln → Ln receives a list and returns the list that results
from reversing the order of its elements. For instance:
(→3 →4 → 10 →7),=→7 →10 →4 →3
a) Inductively define the reverse operator.
b) Show by structural induction that given two lists L1 and L2 It is true that
(L1 • L2)r= Lr 2 ° Lr1

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