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INFORMATICS 2: INTRODUCTION TO ALGORITHMS AND DATA STRUCTURES
创建日期：2024-07-04 15:03:16
标签： ALGORITHMS
INFORMATICS 2: INTRODUCTION TO ALGORITHMS AND DATA STRUCTURES
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PART A:
1. (a) Illustrate the application of MergeSort to the list [3,9,8,2,4,1,6,5], by means
of a diagram showing the recursive call structure. You should show both
the argument passed to MergeSort on each call and the result returned by
each call as the lists are recombined. [5 marks]
(b) Suppose we restrict our use of MergeSort to lists of length 2m for various
natural numbers m.Give ⇥-estimates in terms of m for the best-case, worst-
case and average-case number of comparisons performed by MergeSort on
such lists. You need not justify your answers. [3 marks]
(c) Give a ⇥-estimate, again in terms of m,fortheamountofmemoryusedby
MergeSort on lists of length 2m,assumingaversionofMergeSortthatisas
space-e”cient as possible. Briefly justify your answer. [2 marks]
2. Consider functions f1(n) = (lg(n))lg(n)
, f2(n)= nlg(n)
, f3(n)= n2
and f4(n)= n.
(a) There is exactly one i 2 {1, 2, 3, 4} such that
fi(n) 2 O(fj (n)) for all j = {1, 2, 3, 4}.
(ie, fi is “big-O” of all the other fj ).
State which function is fi,givinginformaljustificationof fi(n) 2 O(fj (n))
for each j = i.[5 marks]
(b) There is also exactly one k 2 {1, 2, 3, 4} such that
fk(n) 2 ⌦(fj (n)) for all j = {1, 2, 3, 4}.
(ie, fk is “big-⌦” of all the other fj ).
State which function is fk,andrigorouslyjustify fk = ⌦(fj )foreach j = k.[5 marks]

3. (a) Suppose you require a data structure for storing sets of up to 10,000 integers,
supporting membership testing and insertion. You are trying to decide
between two implementation schemes:
• abucket-arrayhashtableofsize2,000,usingchainingtoresolvecolli-
sions,
• ared-blacktreeimplementation,storingintegersattheinternalnodes.
Discuss the relative advantages and disadvantages of each scheme. Your
discussion should be as specific as possible, including rough numerical es-
timates of relevant quantities based on your understanding of these data
structures. [6 marks]

FOR INTERNAL SCRUTINY (date of this version: 1/4/2021)
(b) The following red-black tree is a possible representation of the set {2, 3, 4}.
The letters R and B show whether nodes are red or black. We have omitted
the trivial leaf nodes.
With the help of diagrams, explain the steps that occur when the new ele-
ment 1 is inserted into this set. [4 marks]

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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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