A)
true
yes if the equation is simplified it atmost n run time.
b)
False
Its complexity as to be written in O(2 Log n) as the equation is exponential
C)
False
littile o notation classifies it as o(n2)
d)
TRUE
E)
Flase
Big O notation for the log n factorial must to be
O(n)
As the big o notation says that degree of the polynomial here it repeats at n times
poin (a) 20n-O(n) (c) n=o(log n) (e) log n!= 0(n log nioo) (b) 3(2) 2: 100
(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n). (b) The multi Pop (i) method pops i items from the top of a stack. Analyse the amortized complexity of the multiPop (i) method.
O(log(log(N))) < O(log(N)) a. True b. False O(N ) < O(log(N)) a. True b. False O( N5) < O(N2 - 3N + 2) a. True b. False O(2N) < O(N2) a. True b. False
What is the order of the following growth function? t(n)= 5 nlog n + 20n +20 O(log n) Oin log n) o O(n2) 0(1)
Which of the following could be false? A. n2/(log(n)) = O(n2). B. (log n)1000 = O(n1//1000). C. 1/n = O(1/(log(n))). D. 2(log(n))^2 = O(n2). E. None of the above.
2. If x e [0, 1] and n E N, show that xn+1 log(1 + x) – 10g(1 (:- (-) + nxn +(-1)n-1 n n+1 Use this to approximate log 1.5 with an error less than 0.02.
1. Prove that log2(n) is O(n) 2. Prove that log(n!) is O(n log(n))
When sorting n records, Merge sort has worst-case running time a. O(n log n) b. O(n) c. O(log n) d. O(n^2)
2. [6 marks] Are the following functions O(n)? Justify your answer. a) n log n b) f(n) = Vn (log n)
n)2" log log(n)O(n)? I don't How does =n. VIn) T n understand how VITn) 2" log 7 -)? I know we can take out the T, because 1) Vn) T* n it's in our natural logarithm. It's a constant factor. but how does (n) show up in the denominator after it used to be in the numerator? I need to know how the expression (1) right on the left is equal to the expression (1) on the n)2" log log(n)O(n)?...
Prove this using the definition R7: log(n*) is O(log n) for any fixed x > 0