Question

a) Suppose that computer A executes 1 billion instructions per second, and computer B executes 10 million instructions per second, i.e, Computer A is 100 times faster than computer B in raw computing power. Suppose an expert programmer implements insertion sort in machine language for computer A, and the resulting code requires 2 * n² instructions to sort n numbers. Suppose an average programmer implements merge sort, using a high-level language on computer B, with the resulting code taking 5 * n *log₂n instruction. How long does computer A and computer B take to sort 10 million numbers respectively?

b) For each of the following functions, either f (n) is in O(g(n)), f (n) is in Ω(g(n)), or f (n) is in Θ(g(n)). For each pair shown in the following table, determine which relationship is correct:

f(n)	g(n)	Relationship f (n) = ____ g(n)
Logn2	logn + 5
nlogn + n	logn
log2n	logn
10	log10
2n	10n2
2n	3n

Table 1: Relationship of pair of functions.

Answer 1

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