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CPS_616_Midterm_with 100% correct answers

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Question 1: [6,marks] Prove or disprove the following: L -’—‘_—:_1 FEn 2 g | fn) =T +n g(n) = 4n® f(n) € O(g(n)) Use the Big-Oh definition and set appropriate parameters (do not use limits for this question). | — Question 2: [6 marks] Find the cost function of the following algorithm and express the upper bound of the time complexity in asymptotic notation. func (n) { | Yoln hi=1 ~———— . for (i=0;i myi++4) { ~— 7 | hi=hi*2} X = while (hi 0){ — & X hi=hi—2} = ¥ SIS i 5 (LI] Question 3: [6 marks] Using a greedy algorithm, schedule the following tasks in order to minimize the penalty accumulated for missing deadlines. Explain your algorithm and calculate the overall penalty. Each task takes 1 unit of time to complete. State your selection function, and wr

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Question 1: [6,marks]

Prove or disprove the following: L > -’—‘_—:_1
FEn 2 g |
fn) =T +n

g(n) = 4n®
f(n) € O(g(n))

Use the Big-Oh definition and set appropriate parameters (do not use limits for this question).

, | —
Question 2: [6 marks]

Find the cost function of the following algorithm and express the upper bound of the time
complexity in asymptotic notation.


func (n) { | Yoln
hi=1 ~————> .
for (i=0;i <myi++4) { ~— 7 |
hi=hi*2} X =
while (hi
> 0) { —> & X
hi=hi—2} =
¥
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