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16. When s be a sorted array of n integers, and t(n) denote the time taken for the most efficient algorithm to determine if there are two elements with sum less than 1000 in s, then which of the following statements is true?
t(n) is O(1)
n ≤ t(n) ≤ n log1n
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17. Consider the following functions f(n) = 3n√n g(n) = 2n√nlog2n h(n) = ∠n Which of the following is true?
h(n) is O(F(n))
h(n) is O(g(n))
g(n) is not O(F(n))
F(n) is O(g(n))
18. Let f, g, h, k : N → N. Iff = O(h) and g = O(k), then
f + g = O(h + k)
fg = O(hk)
both (a) and (b)
none of these
19. Let f is a total function from N to N and that f' = O(p) for some polynomial function p. When C and D are constants, then for every n
f(n) < Cp(n) + D
f(n) ≥ Cp(n) + D
f(n) ≥ Dp(n) + C
f(n) ≤ Dp(n) + C
20. For any total computable function f : N + N, there is a step-counting functioning so that for every n
g(n) < f(n)
g(n) > f(n)
g(n) = f(n)
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