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6. f(n) is of the order of g(n) if there exist positive integers "a" and "b" such that
f(n) = b
f(n) <= a * g(n) for all n <= b
g(n) = a * f(n) for all n >= b
none of these
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7. The running time of an algorithm T(n) where (n) is the input size is given by T(n) = 8T (n/2) + qn, if n > 1 p, if n = 1 where p, q are constants. The order of the algorithm is
n2
nn
n3
n
8. The running time T(n), where (n) is the input size of a recursive algorithm is given as follows : T(n) = C + T(n - 1); if n > 1 = d, if n ≤ 1 The order of the algorithm is
9. Consider following two functions f(n) = n3, if 0 ≤ n < 10,000 n2, otherwise g(n) = n, if 0 ≤ n < 100 n2 + 5n, otherwise Which of the following are true?
f(n) is O(n3)
g(n) is O(n3)
O(f(n)) is same as O(g(n))
g(n) is O(n2)
10. The complexity of comparison based sorting algorithms is
8(n logn)
8(n)
θ(n2)
θ (n A n)
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