Download DataStructuresExamSupp12 - School of Computer Science

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Fundamentals: Data Structures & Algorithms
Supplementary Examination Paper 2012
(Answer any THREE questions)
QUESTION 1
(a)
Define data type and abstract data type.
[8%]
(b)
Abstract data types may be created from combinations of sets, lists, trees
and graph data types e.g. a set of objects each of which is a set. Suggest one
or more abstract data types for each of the following (i)
(ii)
(iii)
(iv)
(v)
several shipping crates for various artifacts
the seating arrangement in a concert hall
64 tennis players competing in a club knock-out tournament
tourist guides to several regions and cities in the UK
the campus map of The University of Birmingham
[25%]
QUESTION 2
(a)
Composite data types are constructed from components of the four
fundamental data types: sets, lists, trees and graphs. e.g. set of sets. Give
one real world example for each of the following:
(i)
(ii)
(iii)
(iv)
(v)
A set with components which are sets.
A list with components which are a set.
A list with components which are a tree.
A tree with components which are lists.
A list with components which are graphs.
[25%]
(b)
A list data type may be represented and implemented in Java using an array
or using object references to create a linked structure. State one advantage
and one disadvantage for each of these mechanisms for implementing a list
data type.
[8%]
QUESTION 3
(a)
Construct a Binary Search Tree from the following strict sequence of integer
values –
16, 10, 12, 8, 6, 11, 14, 20, 31, 9, 18, 19, 46, 17, 13
(10%)
(b)
Draw the tree you constructed in part (a) after deleting node 16. Outline
your deleting procedure.
(10%)
(c)
The delete operation on a BST can be achieved by moving entire sub trees
as the following illustrates Deleting node D in the tree below
D
B
is rearranged to
B
A
C
E
A
E
C
Apply this procedure to delete node 20 in the BST you constructed in part
(a) above.
(13%)
QUESTION 4
(a)
(i)
Construct and draw a binary search tree (BST) from the following strict
sequence of integers 8, 4, 12, 16, 18, 8, 14, 4
[6%]
(ii)
State, giving reasons, whether or not the tree you have grown in
answering (i) above is a height balanced (AVL) tree.
[9%]
(b)
(i)
Describe briefly how the integer 23 might be inserted into the
following AVL tree to maintain its property as an AVL Tree:
25
21
20
29
22
Draw the resulting AVL tree.
[12%]
(ii)
State one advantage and one disadvantage of AVL trees
[6%]
Fundamentals of Computer Science 1: Data Structures/Algorithms
Questions to Learning Outcomes
Question 1 – Learning Outcomes Refs – 1, 2
Question 2– Learning Outcomes Refs – 2, 3
Question 3 – Learning Outcomes Refs – 1, 2, 3
Question 4 – Learning Outcomes Refs – 1, 4, 5
Learning Outcomes
Ref
1
2
3
4
5
N.B.
Objective, Learning Outcome
Understand the internal representation of basic data structures (linear
and non-linear lists) and associated algorithms as well as hash
tables (implementation for sets).
Judge the suitability of a particular type of data type for a given
application.
Select appropriate internal data structures to ensure efficient
searching, insertion and deletion of data types
Understand how to build binary trees, heaps, graphs together with
their internal representations and relevant algorithms.
Appreciate differences between basic complexity classes of
algorithms (constant, linear, quadratic and logarithmic).
The above Learning Outcomes were distributed to the students at the
beginning of the Module and during the revision lectures