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1. Show that (n+1)5 is O(n5).2. Show that 2n+1 is O(2n).3. Show that n is O(nlogn).4. Show that n2 is Ω(nlogn).

1. Show that nlogn is Ω(n).2. Show that ⌈ f(n)⌉ is O(f(n)), if f(n) is a positive nondecreasing function that is always greater than 1.3. For each function f(n) and time t in the following table,...

1. Algorithm A executes an O(logn)-time computation for each entry of an array storing n elements. What is its worst-case running time?2. Given an n-element array X, Algorithm B chooses logn...

1. Given an n-element array X of integers, Algorithm C executes an O(n)-time computation for each even number in X, and an O(logn)-time computation for each odd number in X. What are the best-case...

There is a well-known city (which will go nameless here) whose inhabitants have the reputation of enjoying a meal only if that meal is the best they have ever experienced in their life. Otherwise,...

Consider the following “justification” that the Fibonacci function, F(n) is O(n): Base case (n ≤ 2): F(1) = 1 and F(2) = 2. Induction step (n > 2): Assume claim true for n′ What is wrong with this...