8/17/2019 CSCI2100B

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Course

Code: CSCI 2100B Final

Examination

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The Chinese University of Hong Kong

Course

Code & Title

Course Examinations

First

Term, 2013-2014

noLt

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Course Code: CSCI 21 B Final Examination

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o

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(c) (4) What are the advantages and disadvantages

of

the various collision strategies in the first two

questions? Justify your answer.

(d) (4) Which hash function is a bette r hash function for the above sequence: 1) hI x) = x mod 11

or (2)

h2 x) x

mod 12? Justify your answer. Note that the size of hash table will change

according to hash function.

4. Graph (28)

(a) (3) Draw the corresponding adjacency matrix for the graph.

(b) (2) one node is removed, the graph will no longer be strongly connected.

Which

node is it?

(c) (3) Please list the breath-first search sequence started from vertex

D.

(d) (8) Find the shortest weighed path from vertex

E

to all other vertices for the graph above.

Illustrate intermediate steps with a table or figures.

(e) (8) Use Prim algorithm to find the minimum cost spanning tree of the graph. Show the interme

diate steps

of

the algorithm and the final result

of

the minimum cost spanning tree that you have

obtained.

(f) (4) Find the maximum flow in the network above assuming that the source is node D and the

sink is node G .

No

intermediate steps are required.

5. Sorting (21)

(a) (3) Show all the inversion pairs in the list (4,

1,2,5,

3)? List them out in an organized manner,

i.e., sort them in an ascending order by the first element and then by the second element.

(b) (5) Given the sequence

(4,6, 1,8,3,7,2,5), sort the sequence using the Bubble Sort algorithm.

Illustrate the result after each pass. How many comparisons and swap have you performed?

Justify your answer by using a table with a column for comparison and swap performed in each

pass.

(c) (5) Given the sequence

(5,2,8,1,4,7,6,3),

sort the sequence using Mergesort. Illustrate the

result after each pass. How many comparisons have you performed?

(d) (4) Using the median

of

the first, middle, and last element

of

the array as pivot, demonstrate

ONLY the process

of

partition the sequence, (5,

7,8,4,

1, 2, 3, 6), into two parts of the Quicksort

(do not show the whole Quicksort algorithm!). Illustrate intermediate steps clearly.

(e) (4) while doing partition in the Quicksort, the loop invariant (a property that holds before each

iteration) can be illustrated as follows,

where ?,

represents unsorted elements.

Now you have an array which consists only

R

G and

B

to be sorted in alphabetical order from

left to right. You can use an algorithm similar with the partition process to solve t by using

only one pass (i.e., one for-loop). What is the loop invariant

of

this algorithm?

You

can either

describe it

or

draw

it

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CourseCode:

  S I

2100B

Final

Examination

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6. Short Answers(18)(Pleasegiveonlyconciseandshortanswers!)

(a)

6)

Thefollowings arethepartialresultsof abinarytreestraversals

in

pre-order, in-orderand

post-order(X representsUNKNOWN).Pleasedraw thecorrespondingtree. Note thatthetree

has   nodesintotal,whicharefromAtoK

Pre-order:XFXBXIHECXG In-order:DXKBIAXEJHX Post-order:XKXBFCJXGXA

(b) (12)Whatis theAverage- andWorst-caseruntimesof asingleFindMax operationonthefol

lowingtypesof data structures? Theanswers shouldbe expressedin thebig-Oh notation in

termsof,n thenumberof elementsstoredinthedatastructure.

IAverage-CaseIWorst-CaseI

Ascending-SortedSingleLinkedList

UnsortedArray

I

DecendingSortedArray

BinarySearchTree

AVL Tree

Max-Heap

-End