signifificant decimal digits are exact over a similar reach? [6 marks]

7 (TURN OVER)CST.2014.1.8

Segment D

7

Calculations

(a) Consider the radix sort calculation.

(I) Explain how radix sort works, to what inputs it very well may be applied and what

its asymptotic intricacy is. [5 marks]

(ii) Explain why running radix sort doesn't continue from most to least

signifificant digit, as would at fifirst appear to be more instinctive. [4 marks]

(iii) Give a proof by acceptance of the rightness of radix sort. [4 marks]

(b) Clearly portray a calculation, stringently better than O(n2 ), that takes a positive

whole number s and a set An of n positive whole numbers and returns a Boolean response to the

question whether there exist two particular components of A whose total is actually s.

Assess its intricacy. [7 marks]

8CST.2014.1.9

8

Calculations

(a) Explain an effiffifficient technique to fifind the k-th most modest number in a bunch of n

numbers (yield: one number), without fifirst arranging the n numbers, and talk about

its intricacy with regards to n and k. [4 marks]

(b) Explain an effiffifficient technique to fifind the k littlest numbers in a bunch of n numbers

(yield: k numbers), without fifirst arranging the n numbers, and talk about its

intricacy concerning n and k. How much additional work is required analyzed

to (a)? [4 marks]

(c) Draw four unmistakable paired search trees (BSTs) for the accompanying arrangement of keys:

{1, 2, 3, 4}. [2 marks]

(d) Let a tallness adjusted BST (hBST) be a BST with the extra defifining

invariant that every hub is the parent of subtrees whose statures diffffer by at

generally 1. Give an effiffifficient system to embed into a hBST and demonstrate that the

it is saved to defifining invariant. [10 marks]

9 (TURN OVER)CST.2014.1.10

9

Calculations

(a) Explain the terms amortized examination, total investigation and possible strategy.

[6 marks]

(b) Consider an inconsistent grouping of n stack tasks PUSH(), POP() and

MULTIPOP(x) in which POP() or MULTIPOP(x) never endeavor to eliminate more

components than there are on the stack. Expecting that the stack starts with

s0 things and fifinishes with sn things, decide the most pessimistic scenario absolute expense for

executing the n activities as an element of n, s0 and sn. You might accept

PUSH() and POP() cost 1 each and MULTIPOP(x) costs x. [5 marks]

(c) Suppose we need to store various things in an exhibit, yet we don't be aware in

advance the number of things should be put away. The INSERT(x) activity annexes

a thing x to the cluster. All the more exactly, assuming that the size of the exhibit is sufficiently huge, x

is embedded straightforwardly toward the finish of the cluster. In any case, another variety of bigger size

is made that contains all past things with x being annexed toward the end.

The all out cost of INSERT(x) is 1 in the fifirst case, and the size of the new exhibit

in the subsequent case.

(I) Devise a methodology which, for any number n, plays out any arrangement of n

Embed(.) tasks at an absolute expense of O(n). [5 marks]

(ii) For the methodology portrayed in (c)(i), give a proof of the expense of the calculation

utilizing the likely strategy. [4 marks]

10CST.2014.1.11

10

Calculations

(a) Given any coordinated chart G = (V, E) with non-negative edge loads, consider

the issue of all-matches most brief way (APSP). Give the asymptotic runtimes of

the accompanying four calculations when applied (straightforwardly or iterated) to the APSP

issue as a component of |V | and |E|, and give a concise justifification to your

reply: Bellman-Ford, Dijkstra, lattice increase and Johnson. [8 marks]

(b) Consider the issue of changing over monetary standards displayed by a coordinated diagram

G = (V, E) with |V | vertices addressing monetary forms and |E| coordinated edges

(u, v) every one of which has a rigorously sure weight w(u, v) > 0 addressing

the conversion scale. For example, for any genuine number x, we have x USD =

w(dollars, pounds) x GBP. Our objective is, given a couple of monetary standards s, t ? V , to

fifind the most affordable approach to trading from s to t, conceivably by utilizing more

than one trade.

(I) How might you at some point change the chart by reweighting the edges so that the

issue could be addressed with a most limited way calculation? Demonstrate which

most brief way calculation is utilized. [8 marks]

(ii) How might you manage negative-weight cycles assuming they happened in the

changed chart? Give the point of view of the money broker as well as

that of a PC researcher.

Rowland-Shteiwi Company offers computer training seminar on a variety of topics. In the seminars each student works at a personal computer, practicing activity that the instructor is presenting. Rowland-Shteiwi is currently planning a three-day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $250 per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $4800. Rowland-Shteiwi rents computers for its seminars at a cost of $30 per computer per day. a) What is the projected profit if 100 students attend the seminar? b) Compute the breakeven point. studentsFE ELECTRICAL AND COMPUTER PRACTICE E resem The Boolean function for / shown in the truth table below is most nearly. and the he firm 1 0 0 1 0 1 1 1 0 0 0 O A. A+ B O B. BAC O C. B + AC O D. B + AC