Analysis of Algorithms - Midterm (Solutions)
نویسنده
چکیده
(a) The hypothesis states that f(n) ∈ Ω(g(n)), from which it follows that f(n) ≥ c1 · g(n), for some c1 > 0 and all n ≥ N1. Likewise, we have g(n) ∈ Ω(h(n)), which implies that g(n) ≥ c2 · h(n), for some c2 > 0 and all n ≥ N2. Observe that for all n ≥ N3 = max (N1, N2), we have f(n) ≥ c1 ·gn and g(n) ≥ c2 ·hn and therefore, f(n) ≥ c1 · c2 · h(n). Putting c3 = c1 · c2, we get f(n) ≥ c3 · h(n), for all n ≥ N3, where c3 > 0. In other words,
منابع مشابه
Problem Set 3 Midterm Exam
Solutions must be submitted at beginning of class on Wednesday, March 3, 2004. This is an open-book exam. Handwritten answers are fine as long as they are legible and organized. Please show all work. I've tried to leave space on this handout for your solutions. The midterm is worth 15% of your total grade.
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