CSE 310 Exam 1 questions with answers

CSE 310 Exam 1 questions with answers
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Big O notation - CORRECT ANSWERS ✔✔O(g(n) = f(n) if f(n) <=
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a*g(n) while n >= b |\ |\ |\ |\




Big Ω notation - CORRECT ANSWERS ✔✔Ω(g(n)) = f(n) if f(n) >=
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a*g(n) while n >= b |\ |\ |\ |\




Big Θ notation - CORRECT ANSWERS ✔✔Θ(g(n)) = f(n) if f(n) <=
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a*g(n) and f(n) >= b*g(n) for all n >= c
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To prove correctness of algorithm, show ______, _____ and _____
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hold - CORRECT ANSWERS ✔✔initialization, maintenance, and
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termination


Index of left child of node - CORRECT ANSWERS ✔✔i = index of
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node
2*i = index of node's left child
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parent index in heap - CORRECT ANSWERS ✔✔i = index of node
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floor(i/2) = index of node's parent|\ |\ |\ |\ |\




What does heap-extract max do? - CORRECT ANSWERS ✔✔1)
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takes out the head of heap and replaces it with last node
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2) performs max-heapify on head
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, Find the expression associated with the runtime of this
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pseudocode (i.e. C1 x n + C2 x n ... etc) and find the big O |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\


approximation


k=1 // C1 |\ |\




do // C2 |\ |\




{
|\ j = 1 // C3
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|\ do // C4 |\ |\




|\ {
|\ j = j*2 // C5
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|\ }while(j < n) // C6 |\ |\ |\ |\




|\ k++ // C7 |\ |\




}while (k < n) // C8 - CORRECT ANSWERS ✔✔C1 x 1 + C2 x n +
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C3 x n + C4 x n(log_2(n)) + C5 x n(log_2(n)) + C6 x n(log_2(n))
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+ C7 x n + C8 x n = O(nlogn)
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Time of max-heapify - CORRECT ANSWERS ✔✔O(logn)
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O approximation of T(n) = T(n/2)+cn+b - CORRECT ANSWERS
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✔✔O(nlogn)


What is the height of a heap? - CORRECT ANSWERS ✔✔The
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number of edges from head to lowest node |\ |\ |\ |\ |\ |\ |\