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Asymptotic notation O satisfies the transitive property i.e. if f(n)=O(g(n)) and g(n)=O(h(n)), then f(n)=O(h(n)). Now we know that 2n =O(2n-1), 2n-1 =O(2n-2?),....... , 2i=O(2i-1?),....... So using rule of transitivity, we can write 2n =O(2i-1?).We can go extending this, so that finally 2n =O(2k?), where k is constant.So we can write 2n =O(1?). Do you agree to what has been proved?If not,where is the fallacy? 6 marks (ALGORITHM ANALYSIS AND DESIGN based problem)
Show that either g(n) = O(f(n)) or f(n) = O(g(n)) : 1. g(n) = n^2 +7n , f(n) = ^3 -2n^2 2. g(n) = 2n +4 , f(n) = 6lg(n^2)
is these true or false ?and explain why a)if f(n)=O(g(n)) then 2^(f(n)=O(2^(g(n)))... please solve without lim b)if f(n)=o(g(n)) then 2^(f(n)=o(2^(g(n)))... please solve without lim
Please answer the question and write legibly (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of G.) (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of...
Question2: 1. f(n)-O(g(n) if there exist c, no>0 such that f(n)for all n 2 no- 2. f(n)-2(g(n)) if there existc, no>0 such that f(n)for all n 2 no- 3. f(n)- (g(n)) if there exist C1, C2,no > 0 such that-for all n 2 no-
Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f(n) = O (h (n)). You may assume that low degree (i.e., low-exponent) polynomials do not dominate higher degree polynomials, while higher degree polynomials dominate lower ones. For example, n^3 notequalto O (n^2), but n^2 = O (n^3). Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily...
D Question 11 if f(n) = n and g(n) = n*8, we can say that f(n) - O(g(n)) (Big-Oh) and also f(n) - o(g(n) [little-o] True @ False
Using the Method of Repeated Substitutions, we have: f(n) = (3 * f(n - 1)) + 2 = ... = 3^(n - 1) - 1. HW: Prove that f(n)=3"-I, n21, using induction HW: Prove that f(n)=3"-I, n21, using induction
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
For each pair of functions f(n) and g(n), indicate whether f(n) = O(g(n)), f(n) = Ω(g(n)), and/or f(n) = Θ(g(n)), and provide a brief explanation of your reasoning. (Your explanation can be the same for all three; for example, “the two functions differ by only a multiplicative constant” could justify why f(n) = n, g(n) = 2n are related by big-O, big-Omega, and big-Theta.) i. f(n) = n^2 log n, g(n) = 100n^2 ii. f(n) = 100, g(n) = log(log(log...